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#include <stdio.h>
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#include <stdlib.h>
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#include <stdbool.h>
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#include <string.h>
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#define N 3 // 拼图的维度，这是一个3x3的拼图
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typedef struct Node {
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int puzzle[N][N]; // 存储拼图状态的数组
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struct Node *parent; // 指向父节点的指针，用于追踪路径
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int f, g, h; // A*算法中的 f, g, h 值
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} Node;
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// 创建新的拼图节点
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Node *createNode(int puzzle[N][N])
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{
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Node *newnode = (Node *)malloc(sizeof(Node));
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// 复制拼图到新节点
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memcpy(newnode->puzzle, puzzle, sizeof(int) * N * N);
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newnode->parent = NULL;
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newnode->f = newnode->g = newnode->h = 0;
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return newnode;
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}
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// 检查两个拼图状态是否相同
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bool isSamePuzzle(int a[N][N], int b[N][N])
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{
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for (int i = 0; i < N; i++)
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{
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for (int j = 0; j < N; j++)
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{
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if (a[i][j] != b[i][j])
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return false;
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}
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}
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return true;
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}
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// 打印拼图状态
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void printPuzzle(int puzzle[N][N])
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{
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for (int i = 0; i < N; i++)
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{
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for (int j = 0; j < N; j++)
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{
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printf("%-2d", puzzle[i][j]);
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}
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printf("\n");
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}
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printf("\n");
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}
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// 启发函数，计算当前状态到目标状态的估计代价
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int heuristic(Node *current, Node *goal)
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{
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int h = 0;
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// 计算不匹配的拼图块数量
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for (int i = 0; i < N; i++)
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{
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for (int j = 0; j < N; j++)
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{
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if (current->puzzle[i][j] != goal->puzzle[i][j])
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h++;
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}
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}
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return h;
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}
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// 移动操作，生成新的拼图状态
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Node *move(Node *current, int dir)
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{
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int key_x, key_y; // 记录空白块的位置
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// 找到空白块的位置
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for (int i = 0; i < N; i++)
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{
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for (int j = 0; j < N; j++)
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{
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if (current->puzzle[i][j] == 0)
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{
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key_x = i;
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key_y = j;
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break;
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}
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}
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}
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int new_x = key_x, new_y = key_y;
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// 根据移动方向更新新块的位置，上下左右移动
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switch (dir)
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{
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case 0:
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new_x--;
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break;
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case 1:
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new_x++;
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break;
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case 2:
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new_y--;
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break;
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case 3:
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new_y++;
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break;
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default:
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break;
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}
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// 检查新位置是否在边界内
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if (new_x < 0 || new_x >= N || new_y < 0 || new_y >= N)
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return NULL;
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// 创建新节点，复制当前拼图状态，并交换块的位置
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Node *new_node = createNode(current->puzzle);
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new_node->puzzle[key_x][key_y] = current->puzzle[new_x][new_y];
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new_node->puzzle[new_x][new_y] = 0;
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return new_node;
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}
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// A*算法，寻找最短路径
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Node *AStar(Node *start, Node *goal)
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{
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Node *OPEN[1000]; // 开放列表，用于存储待探索的节点
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Node *CLOSED[1000]; // 关闭列表，用于存储已探索的节点
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int OPEN_SIZE = 0; // 开放列表的大小
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int CLOSED_SIZE = 0;// 关闭列表的大小
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OPEN[0] = start; // 将起始节点添加到开放列表
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OPEN_SIZE = 1; // 开放列表的大小设置为1
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CLOSED_SIZE = 0; // 关闭列表的大小设置为0
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while (OPEN_SIZE > 0)
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{
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int min_f = OPEN[0]->f;
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int min_index = 0;
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// 查找开放列表中具有最小f值的节点
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for (int i = 1; i < OPEN_SIZE; i++)
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{
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if (OPEN[i]->f < min_f)
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{
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min_f = OPEN[i]->f;
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min_index = i;
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}
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}
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Node *current = OPEN[min_index]; // 获取具有最小f值的节点
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// 如果当前节点与目标状态匹配，表示找到解
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if (isSamePuzzle(current->puzzle, goal->puzzle))
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{
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return current;
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}
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// 开放列表的大小减1，表示从开放列表中移除了一个节点
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OPEN_SIZE--;
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// 将最小f值的节点移到开放列表的末尾，以便稍后将其添加到关闭列表中。
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// 这是为了优化开放列表的结构。
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Node *temp = OPEN[min_index];
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OPEN[min_index] = OPEN[OPEN_SIZE];
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OPEN[OPEN_SIZE] = temp;
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// 将当前节点添加到关闭列表，关闭列表大小加1
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CLOSED[CLOSED_SIZE++] = current;
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int key = 0;
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// 查找当前节点中空白块的位置
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for (int i = 0; i < N; i++)
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{
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for (int j = 0; j < N; j++)
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{
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if (current->puzzle[i][j] == 0)
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{
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key = i * N + j;
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break;
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}
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}
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}
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// 尝试四个方向的移动操作
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for (int dir = 0; dir < 4; dir++)
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{
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Node *new_node = move(current, dir);
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if (new_node != NULL && !isSamePuzzle(new_node->puzzle, current->puzzle))
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{
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int gNew = current->g + 1;
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int hNew = heuristic(new_node, goal);
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int fNew = gNew + hNew;
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bool in_OPEN = false;
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int open_index = -1;
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// 检查新节点是否在开放列表中
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for (int i = 0; i < OPEN_SIZE; i++)
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{
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if (isSamePuzzle(new_node->puzzle, OPEN[i]->puzzle))
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{
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in_OPEN = true;
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open_index = i;
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break;
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}
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}
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bool in_CLOSED = false;
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// 检查新节点是否在关闭列表中
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for (int i = 0; i < CLOSED_SIZE; i++)
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{
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if (isSamePuzzle(new_node->puzzle, CLOSED[i]->puzzle))
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{
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in_CLOSED = true;
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break;
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}
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}
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// 如果新节点既不在开放列表也不在关闭列表中，将其添加到开放列表
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if (!in_OPEN && !in_CLOSED)
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{
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new_node->g = gNew;
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new_node->h = hNew;
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new_node->f = fNew;
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new_node->parent = current;
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OPEN[OPEN_SIZE++] = new_node;
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}
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// 如果新节点已经在开放列表中，但新的 f 值更小，更新开放列表中已存在节点的信息
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else if (in_OPEN && fNew < OPEN[open_index]->f)
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{
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OPEN[open_index]->g = gNew;
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OPEN[open_index]->h = hNew;
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OPEN[open_index]->f = fNew;
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OPEN[open_index]->parent = current;
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}
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}
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}
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}
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return NULL; // 无解
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}
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// 打印解路径
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void printPath(Node *final)
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{
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if (final == NULL)
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{
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return;
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}
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printPath(final->parent); // 递归打印路径
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for (int i = 0; i < N; i++)
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{
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for (int j = 0;j<N;j++)
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{
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printf("%-2d", final->puzzle[i][j]);
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}
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printf("\n");
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}printf("------");
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printf("\n");
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}
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int main()
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{
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int start_puzzle[N][N] = {{2, 8, 3}, {1, 6, 4}, {7, 0, 5}}; // 起始拼图状态
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int goal_puzzle[N][N] = {{1, 2, 3}, {8, 0, 4}, {7, 6, 5}}; // 目标拼图状态
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Node *start = createNode(start_puzzle); // 创建起始节点
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Node *goal = createNode(goal_puzzle); // 创建目标节点
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Node *final = AStar(start, goal); // 运行A*算法，寻找最短路径
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if (final != NULL)
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{
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printf("Solution path:\n");
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printPath(final); // 打印解路径
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}
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else
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{
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printf("No solution found.\n");
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}
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return 0;
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} |
