Bài toán tám câu đố là một câu đố trượt bao gồm một khung các ô vuông được đánh số theo thứ tự ngẫu nhiên với một ô bị thiếu. Nó được phát minh và phổ biến bởi Noyes Palmer Chapman vào những năm 1870. Đây là một phiên bản nhỏ hơn của bài toán n câu đố, đây là một bài toán cổ điển để mô hình hóa các thuật toán liên quan đến heuristic. Nếu kích thước khung hình vuông là các ô 3×3, câu đố được gọi là câu đố 8 ô
N-Puzzle hoặc câu đố trượt là một câu đố phổ biến bao gồm N ô trong đó N có thể là 8, 15, 24, v.v. Trong ví dụ của chúng tôi N = 8. Câu đố được chia thành các hàng sqrt[N+1] và cột sqrt[N+1]. Ví dụ. 15-Puzzle sẽ có 4 hàng và 4 cột và 8-Puzzle sẽ có 3 hàng và 3 cột. Câu đố bao gồm N ô vuông và một khoảng trống nơi các ô có thể được di chuyển. Cấu hình Bắt đầu và Mục tiêu [còn gọi là trạng thái] của câu đố được cung cấp. Câu đố có thể được giải bằng cách di chuyển từng ô một trong không gian trống duy nhất và do đó đạt được cấu hình Mục tiêu
C++14
// Program to print path from root node to destination node
// for N*N -1 puzzle algorithm using Branch and Bound
// The solution assumes that instance of puzzle is solvable
#include
using
namespace
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state0
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state1
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state2
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state3
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state4
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state5
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state7
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state9
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }1
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }3
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }8
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 41
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 43
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 46
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 48
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
// Program to print path from root node to destination node
1// Program to print path from root node to destination node
2
// Program to print path from root node to destination node
3
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
// Program to print path from root node to destination node
5/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
// Program to print path from root node to destination node
7c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state5
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
// for N*N -1 puzzle algorithm using Branch and Bound
0 // for N*N -1 puzzle algorithm using Branch and Bound
1/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
// for N*N -1 puzzle algorithm using Branch and Bound
3c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state5
// for N*N -1 puzzle algorithm using Branch and Bound
6_______788_______0 // for N*N -1 puzzle algorithm using Branch and Bound
1
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
// The solution assumes that instance of puzzle is solvable
0// The solution assumes that instance of puzzle is solvable
1// The solution assumes that instance of puzzle is solvable
2// for N*N -1 puzzle algorithm using Branch and Bound
1// The solution assumes that instance of puzzle is solvable
4// The solution assumes that instance of puzzle is solvable
5
// for N*N -1 puzzle algorithm using Branch and Bound
6_______789_______2// for N*N -1 puzzle algorithm using Branch and Bound
1// The solution assumes that instance of puzzle is solvable
9#include
0
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
#include
2#include
2
#include
4
#include
5
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
#include
7/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
#include
9/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
using
1/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
using
3using
4
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
using
6/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
using
8c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state5
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
namespace
1namespace
2 namespace
3
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
namespace
5c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
namespace
7
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
namespace
9c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state01
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state02
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state03
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state04
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state06
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state08
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state10
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state12
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state14
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state16
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state18
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state20
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state22
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state24
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state25
#include
2
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state27
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state29
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state31
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state32
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state33
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state35_______2_______5
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state37
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state39
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state5
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state43
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
// for N*N -1 puzzle algorithm using Branch and Bound
0 // for N*N -1 puzzle algorithm using Branch and Bound
1/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
// for N*N -1 puzzle algorithm using Branch and Bound
3c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state49_______788_______0
// for N*N -1 puzzle algorithm using Branch and Bound
1/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
// The solution assumes that instance of puzzle is solvable
0// for N*N -1 puzzle algorithm using Branch and Bound
6______1_______55
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state56
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state57
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state58
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state24
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state61
#include
2
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state63
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state65_______2_______5
#include
9_______2_______5 c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state69
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state5
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state24
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state73
#include
2
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state75
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state76
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state77
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state5
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state55
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state81
// for N*N -1 puzzle algorithm using Branch and Bound
6_______1_______24
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state84
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state86
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state88
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
// The solution assumes that instance of puzzle is solvable
2// for N*N -1 puzzle algorithm using Branch and Bound
1// The solution assumes that instance of puzzle is solvable
9#include
0#include
2
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state95
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state3
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state97
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state5
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }00
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }01_______2_______02
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }03
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }02
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }05
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }02
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state5
// for N*N -1 puzzle algorithm using Branch and Bound
6______1_______24
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }11
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
#include
2// Program to print path from root node to destination node
2
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }15
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }16
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }17
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state76
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }19_______2_______5
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state37_______2_______5
#include
9/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
using
1c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state57
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state39
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state5
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }31
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }33
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }35
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }37
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }39
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }41
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }43
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }45
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }47
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }49
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }51
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }53
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }54
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state5
// for N*N -1 puzzle algorithm using Branch and Bound
6______2_______58
// for N*N -1 puzzle algorithm using Branch and Bound
6______2_______60
// for N*N -1 puzzle algorithm using Branch and Bound
6______2_______62
// for N*N -1 puzzle algorithm using Branch and Bound
6______2_______64
// for N*N -1 puzzle algorithm using Branch and Bound
6______2_______66
// for N*N -1 puzzle algorithm using Branch and Bound
6______2_______68
// for N*N -1 puzzle algorithm using Branch and Bound
6______1_______55
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }71
// for N*N -1 puzzle algorithm using Branch and Bound
6______1_______5
// The solution assumes that instance of puzzle is solvable
1_______2_______75
// The solution assumes that instance of puzzle is solvable
1_______2_______77
// The solution assumes that instance of puzzle is solvable
1_______1_______24
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state84
// for N*N -1 puzzle algorithm using Branch and Bound
6______790_______2
// for N*N -1 puzzle algorithm using Branch and Bound
6______2_______84
// for N*N -1 puzzle algorithm using Branch and Bound
6______2_______86
// for N*N -1 puzzle algorithm using Branch and Bound
6_______788_______0 // for N*N -1 puzzle algorithm using Branch and Bound
1
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }91
// for N*N -1 puzzle algorithm using Branch and Bound
6______1_______5
// The solution assumes that instance of puzzle is solvable
1____1_______55
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }96
// The solution assumes that instance of puzzle is solvable
1
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state5
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }99
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 400
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }99
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 402
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }99
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 404
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 405
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 406
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 405
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 408
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 405
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 410
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }99
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 412
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }99
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 414
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }99
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 416
// The solution assumes that instance of puzzle is solvable
1#include
2
// for N*N -1 puzzle algorithm using Branch and Bound
6______790_______2
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
#include
2#include
2
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 424
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 426
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state5
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 429
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 431
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 434
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state5
// for N*N -1 puzzle algorithm using Branch and Bound
6______24_______38
// for N*N -1 puzzle algorithm using Branch and Bound
6______24_______40
// for N*N -1 puzzle algorithm using Branch and Bound
6______24_______42
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
// Program to print path from root node to destination node
2
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 446
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 431
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 451
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state5
// for N*N -1 puzzle algorithm using Branch and Bound
6______24_______38
// for N*N -1 puzzle algorithm using Branch and Bound
6______24_______57
// for N*N -1 puzzle algorithm using Branch and Bound
6______24_______59
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
// Program to print path from root node to destination node
2
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 463
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 465
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 468
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 470
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state24
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 473
#include
2
Java
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 475
// for N*N -1 puzzle algorithm using Branch and Bound
// The solution assumes that instance of puzzle is solvable
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 478
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 479
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 478
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 481
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 482
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 483
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 484
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 486
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 487
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 489
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 490
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state84
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 486
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 487
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 482
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state4
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state5
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state49
// for N*N -1 puzzle algorithm using Branch and Bound
6______1_______7
// for N*N -1 puzzle algorithm using Branch and Bound
6______1_______9
// for N*N -1 puzzle algorithm using Branch and Bound
6______787_______05
// for N*N -1 puzzle algorithm using Branch and Bound
6_______2_______5 // Program to print path from root node to destination node
08namespace
2
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
// Program to print path from root node to destination node
11_______2_______3// for N*N -1 puzzle algorithm using Branch and Bound
6______2_______5
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 41
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }8
// for N*N -1 puzzle algorithm using Branch and Bound
6______2_______5
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 46
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 43
// for N*N -1 puzzle algorithm using Branch and Bound
6______2_______5 // Program to print path from root node to destination node
1
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 48
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
#include
2c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
// Program to print path from root node to destination node
3c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 486
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 487
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state76
// Program to print path from root node to destination node
5/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
// Program to print path from root node to destination node
36// for N*N -1 puzzle algorithm using Branch and Bound
6_______788_______0// for N*N -1 puzzle algorithm using Branch and Bound
1
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
// Program to print path from root node to destination node
41// Program to print path from root node to destination node
42// Program to print path from root node to destination node
43// The solution assumes that instance of puzzle is solvable
1// for N*N -1 puzzle algorithm using Branch and Bound
0// for N*N -1 puzzle algorithm using Branch and Bound
1
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
// Program to print path from root node to destination node
48// Program to print path from root node to destination node
42// Program to print path from root node to destination node
50/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }99
// Program to print path from root node to destination node
52// Program to print path from root node to destination node
53#include
0// The solution assumes that instance of puzzle is solvable
1#include
2
// The solution assumes that instance of puzzle is solvable
1// Program to print path from root node to destination node
58// Program to print path from root node to destination node
59#include
0
// for N*N -1 puzzle algorithm using Branch and Bound
6______790_______2
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
#include
2c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
#include
4c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 486
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 487
// Program to print path from root node to destination node
71/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
// Program to print path from root node to destination node
73/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
#include
9/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
using
1// Program to print path from root node to destination node
78
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
using
3/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
using
6/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
// Program to print path from root node to destination node
84// Program to print path from root node to destination node
78// Program to print path from root node to destination node
86
// for N*N -1 puzzle algorithm using Branch and Bound
6______787_______88namespace
2 // Program to print path from root node to destination node
90
// for N*N -1 puzzle algorithm using Branch and Bound
6______787_______92namespace
5
// for N*N -1 puzzle algorithm using Branch and Bound
6
// for N*N -1 puzzle algorithm using Branch and Bound
6______792_______9
// for N*N -1 puzzle algorithm using Branch and Bound
6_______787_______98namespace
2
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
// Program to print path from root node to destination node
11// for N*N -1 puzzle algorithm using Branch and Bound
6_______788_______0// for N*N -1 puzzle algorithm using Branch and Bound
1
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
// Program to print path from root node to destination node
41// Program to print path from root node to destination node
42// Program to print path from root node to destination node
43// The solution assumes that instance of puzzle is solvable
1// for N*N -1 puzzle algorithm using Branch and Bound
0// for N*N -1 puzzle algorithm using Branch and Bound
1
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
// Program to print path from root node to destination node
48// Program to print path from root node to destination node
42// Program to print path from root node to destination node
50/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }99
// for N*N -1 puzzle algorithm using Branch and Bound
17// The solution assumes that instance of puzzle is solvable
1#include
2
// for N*N -1 puzzle algorithm using Branch and Bound
6______790_______2
// for N*N -1 puzzle algorithm using Branch and Bound
6
// for N*N -1 puzzle algorithm using Branch and Bound
6______1_______06
// for N*N -1 puzzle algorithm using Branch and Bound
6______2_______5 // for N*N -1 puzzle algorithm using Branch and Bound
27
// for N*N -1 puzzle algorithm using Branch and Bound
6______788_______29
// for N*N -1 puzzle algorithm using Branch and Bound
6______788_______31
// for N*N -1 puzzle algorithm using Branch and Bound
6
// for N*N -1 puzzle algorithm using Branch and Bound
6______788_______34
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state10
// for N*N -1 puzzle algorithm using Branch and Bound
6______788_______37
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state14
// for N*N -1 puzzle algorithm using Branch and Bound
6
// for N*N -1 puzzle algorithm using Branch and Bound
6______1_______18
// for N*N -1 puzzle algorithm using Branch and Bound
6______788_______43
// for N*N -1 puzzle algorithm using Branch and Bound
6______788_______45
// for N*N -1 puzzle algorithm using Branch and Bound
6
// for N*N -1 puzzle algorithm using Branch and Bound
6______1_______24
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state25
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
#include
2c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state27
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 486
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 487
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
// for N*N -1 puzzle algorithm using Branch and Bound
59// for N*N -1 puzzle algorithm using Branch and Bound
60// for N*N -1 puzzle algorithm using Branch and Bound
61// Program to print path from root node to destination node
42// for N*N -1 puzzle algorithm using Branch and Bound
63// for N*N -1 puzzle algorithm using Branch and Bound
60// for N*N -1 puzzle algorithm using Branch and Bound
61// Program to print path from root node to destination node
42 // Program to print path from root node to destination node
2c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 486
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 487
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
// for N*N -1 puzzle algorithm using Branch and Bound
72// Program to print path from root node to destination node
42// for N*N -1 puzzle algorithm using Branch and Bound
63// for N*N -1 puzzle algorithm using Branch and Bound
60// for N*N -1 puzzle algorithm using Branch and Bound
61// Program to print path from root node to destination node
42// for N*N -1 puzzle algorithm using Branch and Bound
61// for N*N -1 puzzle algorithm using Branch and Bound
60 // Program to print path from root node to destination node
2c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state32
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state33
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 486
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 487
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state35
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
// for N*N -1 puzzle algorithm using Branch and Bound
92/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
// for N*N -1 puzzle algorithm using Branch and Bound
94c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state5
// for N*N -1 puzzle algorithm using Branch and Bound
6_______2_______5 // for N*N -1 puzzle algorithm using Branch and Bound
99// Program to print path from root node to destination node
42
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state84
// for N*N -1 puzzle algorithm using Branch and Bound
6_______788_______0 // for N*N -1 puzzle algorithm using Branch and Bound
1
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
// Program to print path from root node to destination node
41// Program to print path from root node to destination node
42// The solution assumes that instance of puzzle is solvable
08// The solution assumes that instance of puzzle is solvable
09// for N*N -1 puzzle algorithm using Branch and Bound
0 // for N*N -1 puzzle algorithm using Branch and Bound
1
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
// Program to print path from root node to destination node
48// Program to print path from root node to destination node
42// The solution assumes that instance of puzzle is solvable
15// The solution assumes that instance of puzzle is solvable
1
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state55
// The solution assumes that instance of puzzle is solvable
18// Program to print path from root node to destination node
42 // The solution assumes that instance of puzzle is solvable
20// The solution assumes that instance of puzzle is solvable
21
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state58
// for N*N -1 puzzle algorithm using Branch and Bound
6______1_______24
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state61
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
#include
2// The solution assumes that instance of puzzle is solvable
28
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state63
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 486
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 487
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state65
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
#include
9/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state69
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state5
// for N*N -1 puzzle algorithm using Branch and Bound
6_______1_______24 // The solution assumes that instance of puzzle is solvable
44// Program to print path from root node to destination node
42 // The solution assumes that instance of puzzle is solvable
46// Program to print path from root node to destination node
42 // The solution assumes that instance of puzzle is solvable
48// for N*N -1 puzzle algorithm using Branch and Bound
60// The solution assumes that instance of puzzle is solvable
50// Program to print path from root node to destination node
42
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state84
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
#include
2c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state75
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 486
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 487
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state76
// The solution assumes that instance of puzzle is solvable
62// for N*N -1 puzzle algorithm using Branch and Bound
6_______1_______55// The solution assumes that instance of puzzle is solvable
65// The solution assumes that instance of puzzle is solvable
66// The solution assumes that instance of puzzle is solvable
67
// The solution assumes that instance of puzzle is solvable
1_______1_______24
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state84
// for N*N -1 puzzle algorithm using Branch and Bound
6______790_______2
// for N*N -1 puzzle algorithm using Branch and Bound
6______789_______74
// for N*N -1 puzzle algorithm using Branch and Bound
6______789_______76
// for N*N -1 puzzle algorithm using Branch and Bound
6______787_______58// Program to print path from root node to destination node
59#include
0
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
#include
2c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state95
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 486
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 487
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 482
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state97
// The solution assumes that instance of puzzle is solvable
91 // The solution assumes that instance of puzzle is solvable
92// for N*N -1 puzzle algorithm using Branch and Bound
6______789_______94
// for N*N -1 puzzle algorithm using Branch and Bound
6_______24_______86
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
// The solution assumes that instance of puzzle is solvable
98// The solution assumes that instance of puzzle is solvable
1
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state24
#include
01// for N*N -1 puzzle algorithm using Branch and Bound
60#include
03// for N*N -1 puzzle algorithm using Branch and Bound
60c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state84
// for N*N -1 puzzle algorithm using Branch and Bound
6______790_______2
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
#include
2c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }15
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }16
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }17
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 486
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 487
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state76
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }19
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
// for N*N -1 puzzle algorithm using Branch and Bound
92/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
#include
9#include
26_______2_______5 using
1
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
// for N*N -1 puzzle algorithm using Branch and Bound
94c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state5
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state49
// for N*N -1 puzzle algorithm using Branch and Bound
6______790_______35
// for N*N -1 puzzle algorithm using Branch and Bound
6_______790_______37namespace
2 #include
39namespace
2 #include
41
// for N*N -1 puzzle algorithm using Branch and Bound
6
// for N*N -1 puzzle algorithm using Branch and Bound
6______2_______37
// for N*N -1 puzzle algorithm using Branch and Bound
6_______790_______46// Program to print path from root node to destination node
42_______788_______61// The solution assumes that instance of puzzle is solvable
66#include
0
// for N*N -1 puzzle algorithm using Branch and Bound
6______790_______52
// for N*N -1 puzzle algorithm using Branch and Bound
6
// for N*N -1 puzzle algorithm using Branch and Bound
6______2_______43
// for N*N -1 puzzle algorithm using Branch and Bound
6______790_______57
// for N*N -1 puzzle algorithm using Branch and Bound
6
// for N*N -1 puzzle algorithm using Branch and Bound
6______2_______47
// for N*N -1 puzzle algorithm using Branch and Bound
6______2_______49
// for N*N -1 puzzle algorithm using Branch and Bound
6______2_______51
// for N*N -1 puzzle algorithm using Branch and Bound
6_______2_______53#include
67
// for N*N -1 puzzle algorithm using Branch and Bound
6______1_______5
// The solution assumes that instance of puzzle is solvable
1____790_______71
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }58
// The solution assumes that instance of puzzle is solvable
1____790_______74#include
75
// The solution assumes that instance of puzzle is solvable
1
// The solution assumes that instance of puzzle is solvable
1_______2_______68
// The solution assumes that instance of puzzle is solvable
1
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state55
#include
81// Program to print path from root node to destination node
42// The solution assumes that instance of puzzle is solvable
67/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }99
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }77
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }75
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }99
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state24
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state84
// The solution assumes that instance of puzzle is solvable
1#include
2
// The solution assumes that instance of puzzle is solvable
1_______2_______84
// The solution assumes that instance of puzzle is solvable
1_______2_______86
// The solution assumes that instance of puzzle is solvable
1// for N*N -1 puzzle algorithm using Branch and Bound
0 // for N*N -1 puzzle algorithm using Branch and Bound
1
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
// Program to print path from root node to destination node
41// Program to print path from root node to destination node
42using
02using
03using
04// The solution assumes that instance of puzzle is solvable
1
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state5
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }99
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state55
using
09// Program to print path from root node to destination node
42using
11/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }99
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state5
using
14
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 400
using
14
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 402
using
14using
19// for N*N -1 puzzle algorithm using Branch and Bound
60using
21
using
14using
23
// The solution assumes that instance of puzzle is solvable
28
using
14
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 414
using
14using
28
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }99
#include
2// The solution assumes that instance of puzzle is solvable
1#include
2
// for N*N -1 puzzle algorithm using Branch and Bound
6______790_______2
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
#include
2c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
using
39c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 486
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 487
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state76
using
44c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state5
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state49
// for N*N -1 puzzle algorithm using Branch and Bound
6______24_______29
// for N*N -1 puzzle algorithm using Branch and Bound
6______24_______31
// for N*N -1 puzzle algorithm using Branch and Bound
6______2_______5 using
54
// for N*N -1 puzzle algorithm using Branch and Bound
6______1_______5
// The solution assumes that instance of puzzle is solvable
1
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state5
// for N*N -1 puzzle algorithm using Branch and Bound
60// for N*N -1 puzzle algorithm using Branch and Bound
61using
61// for N*N -1 puzzle algorithm using Branch and Bound
611 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 490
using
64// The solution assumes that instance of puzzle is solvable
1
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state5
using
67_______788_______61using
69// for N*N -1 puzzle algorithm using Branch and Bound
61// Program to print path from root node to destination node
42using
64// The solution assumes that instance of puzzle is solvable
1
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state5
using
75// for N*N -1 puzzle algorithm using Branch and Bound
61using
77// for N*N -1 puzzle algorithm using Branch and Bound
61_______791_______03#include
2// for N*N -1 puzzle algorithm using Branch and Bound
6______787_______2
// The solution assumes that instance of puzzle is solvable
28
// for N*N -1 puzzle algorithm using Branch and Bound
6_______24_______46
// for N*N -1 puzzle algorithm using Branch and Bound
6______24_______31
// for N*N -1 puzzle algorithm using Branch and Bound
6______2_______5 using
90
// for N*N -1 puzzle algorithm using Branch and Bound
6______1_______5
// The solution assumes that instance of puzzle is solvable
1
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state5
// for N*N -1 puzzle algorithm using Branch and Bound
60// for N*N -1 puzzle algorithm using Branch and Bound
61using
61// for N*N -1 puzzle algorithm using Branch and Bound
611 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 490
using
64// The solution assumes that instance of puzzle is solvable
1
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state5
using
67// for N*N -1 puzzle algorithm using Branch and Bound
61using
77// for N*N -1 puzzle algorithm using Branch and Bound
61_______791_______69using
64// The solution assumes that instance of puzzle is solvable
1
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state5
// Program to print path from root node to destination node
42// for N*N -1 puzzle algorithm using Branch and Bound
61using
75// for N*N -1 puzzle algorithm using Branch and Bound
61_______791_______03#include
2// for N*N -1 puzzle algorithm using Branch and Bound
6______787_______2
// The solution assumes that instance of puzzle is solvable
28
// for N*N -1 puzzle algorithm using Branch and Bound
6_______24_______63
// for N*N -1 puzzle algorithm using Branch and Bound
6_______24_______65
// for N*N -1 puzzle algorithm using Branch and Bound
6_______2_______5 namespace
26// for N*N -1 puzzle algorithm using Branch and Bound
60namespace
28using
61
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state84
// The solution assumes that instance of puzzle is solvable
28
// for N*N -1 puzzle algorithm using Branch and Bound
6______792_______33
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
#include
2#include
2
namespace
37
Python3
namespace
38
namespace
39
namespace
40
namespace
41
namespace
42
namespace
43
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 478
namespace
45
namespace
46
namespace
47
namespace
48 namespace
49
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 478
namespace
51
namespace
52
namespace
53
namespace
54
namespace
55namespace
56
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 490
namespace
58
namespace
59namespace
56 namespace
61// for N*N -1 puzzle algorithm using Branch and Bound
60// for N*N -1 puzzle algorithm using Branch and Bound
61// Program to print path from root node to destination node
42// for N*N -1 puzzle algorithm using Branch and Bound
61namespace
66// for N*N -1 puzzle algorithm using Branch and Bound
60// for N*N -1 puzzle algorithm using Branch and Bound
61// Program to print path from root node to destination node
42 namespace
70
namespace
71_______792_______56 namespace
61// Program to print path from root node to destination node
42// for N*N -1 puzzle algorithm using Branch and Bound
61namespace
66// for N*N -1 puzzle algorithm using Branch and Bound
60// for N*N -1 puzzle algorithm using Branch and Bound
61// Program to print path from root node to destination node
42// for N*N -1 puzzle algorithm using Branch and Bound
61// for N*N -1 puzzle algorithm using Branch and Bound
60 namespace
70
namespace
83
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 482
namespace
85c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
namespace
88c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
namespace
90c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
namespace
92 namespace
93namespace
94namespace
95// for N*N -1 puzzle algorithm using Branch and Bound
6_______792_______94____792_______98namespace
56
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state000
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state002
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
namespace
92 c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state005
namespace
94c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state007
// for N*N -1 puzzle algorithm using Branch and Bound
6_______1_______009namespace
94
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state011
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state013
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state015
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
namespace
92 c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state018
namespace
94namespace
95// for N*N -1 puzzle algorithm using Branch and Bound
6_______1_______24
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state023
namespace
94c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state025
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state027
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
namespace
92 c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state030
namespace
94namespace
95// for N*N -1 puzzle algorithm using Branch and Bound
6_______1_______55
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state035
namespace
94c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state037
// The solution assumes that instance of puzzle is solvable
1____1_______24
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state040
// for N*N -1 puzzle algorithm using Branch and Bound
6_______1_______042// The solution assumes that instance of puzzle is solvable
50
// The solution assumes that instance of puzzle is solvable
1____1_______24
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state046
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state047
1 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 482
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state049
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
namespace
92 namespace
93namespace
94c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state055
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state056
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state057
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state058
// for N*N -1 puzzle algorithm using Branch and Bound
6______1_______060
// for N*N -1 puzzle algorithm using Branch and Bound
6______1_______062
// for N*N -1 puzzle algorithm using Branch and Bound
6______1_______064
// for N*N -1 puzzle algorithm using Branch and Bound
6______792_______94
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state067
namespace
56 c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state069
// for N*N -1 puzzle algorithm using Branch and Bound
6______1_______071
// for N*N -1 puzzle algorithm using Branch and Bound
6______792_______94
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state074
namespace
56 c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state076
// for N*N -1 puzzle algorithm using Branch and Bound
6______1_______078
// for N*N -1 puzzle algorithm using Branch and Bound
6______1_______080
// for N*N -1 puzzle algorithm using Branch and Bound
6______792_______94
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state083
namespace
56 c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state085
// for N*N -1 puzzle algorithm using Branch and Bound
6______1_______087
// for N*N -1 puzzle algorithm using Branch and Bound
6______792_______94
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state090
namespace
56 c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state092
// for N*N -1 puzzle algorithm using Branch and Bound
6______1_______094
// for N*N -1 puzzle algorithm using Branch and Bound
6_______792_______94
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state097
namespace
56 c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state099
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state101
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state103
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state105
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
namespace
92 c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state108
namespace
94c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state110
// for N*N -1 puzzle algorithm using Branch and Bound
6_______1_______24 namespace
94
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state114
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state115
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state116
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state117
namespace
92
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state119
namespace
66c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state121
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }5
// The solution assumes that instance of puzzle is solvable
50c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state126
namespace
56 // Program to print path from root node to destination node
42c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
// for N*N -1 puzzle algorithm using Branch and Bound
0 c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state131
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state132
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state133
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state134
// for N*N -1 puzzle algorithm using Branch and Bound
6_______788_______0
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state137
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state132
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state133
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state134
// The solution assumes that instance of puzzle is solvable
1____1_______55
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state143
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state144
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }99
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state146
namespace
56 c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state148
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }99
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state126
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state151
namespace
56 // for N*N -1 puzzle algorithm using Branch and Bound
60/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }99
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state24
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state126
namespace
92
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state159
// The solution assumes that instance of puzzle is solvable
1____1_______161______792_______66
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state163
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }99
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state166
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state168
namespace
56 c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state170
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state172
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state174_______792_______56
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state176
// Program to print path from root node to destination node
42namespace
70c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state180_______792_______56
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state176
// for N*N -1 puzzle algorithm using Branch and Bound
60namespace
70c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state186_______792_______56
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state188
// Program to print path from root node to destination node
42namespace
70c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state192
namespace
56 c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state188
// for N*N -1 puzzle algorithm using Branch and Bound
60namespace
70c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state198
namespace
56 c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state200
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state202
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state092
namespace
56 c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state206
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state208
namespace
56 c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state210
using
14
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state212
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state24
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state208
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state216
namespace
92
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state218
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
// for N*N -1 puzzle algorithm using Branch and Bound
0 c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state131
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state132
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state133
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state134
// for N*N -1 puzzle algorithm using Branch and Bound
6_______788_______0
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state137
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state132
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state133
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state134
// The solution assumes that instance of puzzle is solvable
1
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state233
// for N*N -1 puzzle algorithm using Branch and Bound
1// The solution assumes that instance of puzzle is solvable
4 c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state236
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state237
namespace
56 // Program to print path from root node to destination node
53using
11// The solution assumes that instance of puzzle is solvable
1
// for N*N -1 puzzle algorithm using Branch and Bound
6______1_______233
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state244
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state245
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state246
namespace
92
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state248
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state24
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state252
namespace
56 // Program to print path from root node to destination node
42 c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state144
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state256
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state144
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state258
namespace
56 // Program to print path from root node to destination node
42 c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state144
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state262
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state263
namespace
92
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state265
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state55
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state269
namespace
56namespace
56 c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state272
// The solution assumes that instance of puzzle is solvable
50// for N*N -1 puzzle algorithm using Branch and Bound
6______1_______24
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state278
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state280
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state233
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state244
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state284
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state285
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state286
namespace
92
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state288
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state291
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state293
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state295
namespace
56 c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state297
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state299
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state092
namespace
56 c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state303
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state269
namespace
56 c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state307
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state272
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state309
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }99
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state311_______787_______42
using
11
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state315
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state317
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state319
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state321
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state323
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state325
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state6
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }53
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state035
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state329
// for N*N -1 puzzle algorithm using Branch and Bound
6______1_______331
// for N*N -1 puzzle algorithm using Branch and Bound
6______1_______333
// for N*N -1 puzzle algorithm using Branch and Bound
6______1_______335
// for N*N -1 puzzle algorithm using Branch and Bound
6_______1_______337namespace
56
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state339
// for N*N -1 puzzle algorithm using Branch and Bound
6______1_______341
// for N*N -1 puzzle algorithm using Branch and Bound
6_______1_______55
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state344
namespace
56namespace
56 // Program to print path from root node to destination node
42// The solution assumes that instance of puzzle is solvable
50// The solution assumes that instance of puzzle is solvable
1
// The solution assumes that instance of puzzle is solvable
1_______1_______351
// The solution assumes that instance of puzzle is solvable
1_______1_______353
// The solution assumes that instance of puzzle is solvable
1_______1_______355
// The solution assumes that instance of puzzle is solvable
1
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state24
// for N*N -1 puzzle algorithm using Branch and Bound
6______1_______359
// for N*N -1 puzzle algorithm using Branch and Bound
6_______788_______0
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state131_______1_______132
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state133
// for N*N -1 puzzle algorithm using Branch and Bound
1using
03namespace
95// The solution assumes that instance of puzzle is solvable
1
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state369
namespace
56 namespace
61/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }99
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state373_______787_______42
namespace
70c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state151
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state377
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }99
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state373_______788_______60
namespace
70c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state151
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state383
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }99
// The solution assumes that instance of puzzle is solvable
1
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state55
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state387
// Program to print path from root node to destination node
42c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state389
// for N*N -1 puzzle algorithm using Branch and Bound
60c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state391
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }99
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }99
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state394
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }99
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state396
namespace
56 c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state398
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state399_______1_______400
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state399____1_______402
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state399_______1_______404
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state151
// for N*N -1 puzzle algorithm using Branch and Bound
60// for N*N -1 puzzle algorithm using Branch and Bound
61c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state399______1_______409
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }99
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state411
/* Algorithm LCSearch uses c[x] to find an answer node * LCSearch uses Least[] and Add[] to maintain the list of live nodes * Least[] finds a live node with least c[x], deletes it from the list and returns it * Add[x] adds x to the list of live nodes * Implement list of live nodes as a min-heap */ struct list_node { list_node *next; // Helps in tracing path when answer is found list_node *parent; float cost; } algorithm LCSearch[list_node *t] { // Search t for an answer node // Input: Root node of tree t // Output: Path from answer node to root if [*t is an answer node] { print[*t]; return; } E = t; // E-node Initialize the list of live nodes to be empty; while [true] { for each child x of E { if x is an answer node { print the path from x to t; return; } Add [x]; // Add x to list of live nodes; x->parent = E; // Pointer for path to root } if there are no more live nodes { print ["No answer node"]; return; } // Find a live node with least estimated cost E = Least[]; // The found node is deleted from the list of // live nodes } }99
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state413
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state414
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state415
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state416
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state417
namespace
56 c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state419
// for N*N -1 puzzle algorithm using Branch and Bound
60// for N*N -1 puzzle algorithm using Branch and Bound
61using
61// for N*N -1 puzzle algorithm using Branch and Bound
611 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 490
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state425
// The solution assumes that instance of puzzle is solvable
1namespace
61using
67// for N*N -1 puzzle algorithm using Branch and Bound
61using
69// for N*N -1 puzzle algorithm using Branch and Bound
61// Program to print path from root node to destination node
42
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state425
// The solution assumes that instance of puzzle is solvable
1namespace
61using
75// for N*N -1 puzzle algorithm using Branch and Bound
61using
77// for N*N -1 puzzle algorithm using Branch and Bound
61using
03
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state441
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state442
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state416
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state444
namespace
56 c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state419
// for N*N -1 puzzle algorithm using Branch and Bound
60// for N*N -1 puzzle algorithm using Branch and Bound
61using
61// for N*N -1 puzzle algorithm using Branch and Bound
611 2 3 5 6 0 7 8 4 1 2 3 5 0 6 7 8 4 1 2 3 5 8 6 7 0 4 1 2 3 5 8 6 0 7 490
c[x] = f[x] + h[x] where f[x] is the length of the path from root to x [the number of moves so far] and h[x] is the number of non-blank tiles not in their goal position [the number of mis- -placed tiles]. There are at least h[x] moves to transform state x to a goal state425