八数码问题a*算法c语言
时间: 2023-07-28 11:11:56 浏览: 222
八数码问题是一种经典的搜索问题,可以使用A*算法进行求解。A*算法是一种启发式搜索算法,能够在搜索过程中有针对性地搜索最优解,减小搜索空间,提高搜索效率。
以下是使用C语言实现八数码问题A*算法的示例代码:
```c
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#define N 3
// 定义状态结构体
typedef struct state {
int board[N][N]; // 棋盘状态
int f; // f = g + h,g为从起始状态到当前状态的代价,h为从当前状态到目标状态的估价函数值
int g; // g为从起始状态到当前状态的代价
int h; // h为从当前状态到目标状态的估价函数值
int x; // 空格所在行
int y; // 空格所在列
struct state *parent; // 父状态指针
} state_t;
// 定义状态队列节点结构体
typedef struct node {
state_t *data; // 队列节点数据为状态指针
int priority; // 节点优先级,即状态f值
struct node *next; // 指向下一个节点的指针
} node_t;
// 定义状态队列结构体
typedef struct queue {
node_t *front; // 队列头指针
node_t *rear; // 队列尾指针
} queue_t;
// 初始化状态队列
void init_queue(queue_t *q) {
q->front = q->rear = NULL;
}
// 判断状态队列是否为空
int is_empty(queue_t *q) {
return q->front == NULL;
}
// 向状态队列添加状态
void enqueue(queue_t *q, state_t *s) {
node_t *new_node = (node_t *)malloc(sizeof(node_t));
new_node->data = s;
new_node->priority = s->f;
new_node->next = NULL;
if (q->rear == NULL) {
q->front = q->rear = new_node;
} else {
node_t *p = q->front;
node_t *prev = NULL;
while (p != NULL && p->priority <= new_node->priority) {
prev = p;
p = p->next;
}
if (prev == NULL) {
new_node->next = q->front;
q->front = new_node;
} else if (p == NULL) {
q->rear->next = new_node;
q->rear = new_node;
} else {
new_node->next = prev->next;
prev->next = new_node;
}
}
}
// 从状态队列中取出状态
state_t *dequeue(queue_t *q) {
if (q->front == NULL) {
return NULL;
} else {
node_t *p = q->front;
state_t *s = p->data;
q->front = q->front->next;
if (q->front == NULL) {
q->rear = NULL;
}
free(p);
return s;
}
}
// 判断状态是否为目标状态
int is_goal(state_t *s) {
int i, j, num = 1;
for (i = 0; i < N; i++) {
for (j = 0; j < N; j++) {
if (s->board[i][j] != num && !(i == N - 1 && j == N - 1 && s->board[i][j] == 0)) {
return 0;
}
num++;
}
}
return 1;
}
// 计算状态的估价函数值
int heuristic(state_t *s) {
int i, j, k, l, num, dist = 0;
for (i = 0; i < N; i++) {
for (j = 0; j < N; j++) {
num = s->board[i][j];
if (num == 0) {
continue;
}
k = (num - 1) / N;
l = (num - 1) % N;
dist += abs(i - k) + abs(j - l);
}
}
return dist;
}
// 复制状态
state_t *copy_state(state_t *s) {
state_t *new_state = (state_t *)malloc(sizeof(state_t));
memcpy(new_state->board, s->board, sizeof(s->board));
new_state->f = s->f;
new_state->g = s->g;
new_state->h = s->h;
new_state->x = s->x;
new_state->y = s->y;
new_state->parent = s->parent;
return new_state;
}
// 生成子状态
void generate_successors(state_t *s, queue_t *q) {
int i, j, tx, ty;
state_t *new_state;
for (i = -1; i <= 1; i++) {
for (j = -1; j <= 1; j++) {
if (i == 0 && j == 0) {
continue;
}
tx = s->x + i;
ty = s->y + j;
if (tx < 0 || tx >= N || ty < 0 || ty >= N) {
continue;
}
new_state = copy_state(s);
new_state->board[s->x][s->y] = s->board[tx][ty];
new_state->board[tx][ty] = 0;
new_state->x = tx;
new_state->y = ty;
new_state->g++;
new_state->h = heuristic(new_state);
new_state->f = new_state->g + new_state->h;
new_state->parent = s;
enqueue(q, new_state);
}
}
}
// 输出状态
void print_state(state_t *s) {
int i, j;
printf("f=%d, g=%d, h=%d\n", s->f, s->g, s->h);
for (i = 0; i < N; i++) {
for (j = 0; j < N; j++) {
printf("%d ", s->board[i][j]);
}
printf("\n");
}
}
// 输出解路径
void print_solution(state_t *s) {
if (s->parent != NULL) {
print_solution(s->parent);
}
print_state(s);
}
// 释放状态队列节点内存
void free_queue_node(node_t *p) {
if (p != NULL) {
free_queue_node(p->next);
free(p->data);
free(p);
}
}
// 释放状态队列内存
void free_queue(queue_t *q) {
free_queue_node(q->front);
}
// A*算法求解八数码问题
void solve(state_t *start) {
queue_t open;
state_t *s, *goal = NULL;
init_queue(&open);
start->g = 0;
start->h = heuristic(start);
start->f = start->g + start->h;
start->parent = NULL;
enqueue(&open, start);
while (!is_empty(&open)) {
s = dequeue(&open);
if (is_goal(s)) {
goal = s;
break;
}
generate_successors(s, &open);
}
if (goal != NULL) {
printf("Solution found:\n");
print_solution(goal);
} else {
printf("No solution.\n");
}
free_queue(&open);
}
int main() {
state_t start = {
{{1, 2, 3}, {4, 0, 5}, {6, 7, 8}},
0, 0, 0, 1, 1, NULL
};
solve(&start);
return 0;
}
```
以上代码实现了八数码问题A*算法的求解,代码中使用了状态队列优化搜索效率。在代码中,我们需要定义状态结构体,其中包含了当前棋盘状态、从起始状态到当前状态的代价g、从当前状态到目标状态的估价函数值h、状态f值、空格所在位置以及父状态指针。我们还需要定义状态队列节点结构体和状态队列结构体,以实现状态队列的操作。代码中使用了启发式函数h(n) = 曼哈顿距离来计算状态的估价函数值。
在main函数中,我们定义了起始状态,并调用solve函数求解八数码问题。在solve函数中,我们首先初始化状态队列,并将起始状态加入队列。然后循环取出队列头部的状态,如果该状态为目标状态,则搜索结束;否则,生成该状态的所有子状态,并将其加入状态队列中。最后,输出解路径或提示无解,并释放状态队列内存。
注意,上述代码仅为示例代码,可能存在不足之处,请以实际应用为准。
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