程序代码：

A*算法解八数码
程序代码：

八数码问题是指一个3X3的9格棋盘上放置1到8这8个数字，多余一个空格，空格周围的数字可以移动到空格中
例如输入0，2，3，1，8，4，7，6，5这九个数（0表示空格位置），按输入顺序排列为setp 0，通过若干步移动就可以到达最终状态setp 2：
setp 0
0       2       3
1       8       4
7       6       5
setp 1
1       2       3
0       8       4
7       6       5
setp 2
1       2       3
8       0       4
7       6       5
程序代码：

1 Create search tree Tr consisting only of the start node (root) n0. Put n0 on an ordered list called OPEN.
2 Create empty list called CLOSED.
3 If OPEN is empty, exit with failure.
4 Move the first node on OPEN, called n, to CLOSED.
5 If n is a goal node, exit with success; the solution is the path from n to n0 along the edges in Tr.
6 Expand node n by generating a set M of successors and connect them to n. Also put the members of M on OPEN.
7 Reorder the list OPEN according to a specific rule.
8 Go to step 3.


#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#define NUM 5
typedef struct bgMatrix
{
    int v, w;
    char matrix[NUM][NUM];
    int pre;
    int f;
    int g;
    bool isVisited;
}Matrix;
typedef struct bgQueue
{
    Matrix* data;
    int length;
    int maxLength;
    int head;
    int tail;
}BGQueue;
typedef BGQueue* Queue;
typedef struct bgStack
{
    Matrix* data;
    int top;
}BGStack;
typedef BGStack* Stack;
char srcMatrix[NUM][NUM] =
{
    {'*', '*', '*', '*', '*'},
    {'*', '2', '8', '3', '*'},
    {'*', '1', '6', '4', '*'},
    {'*', '7', '0', '5', '*'},
    {'*', '*', '*', '*', '*'}
};
char dstMatrix[NUM][NUM] =
{
    {'*', '*', '*', '*', '*'},
    {'*', '1', '2', '3', '*'},
    {'*', '8', '0', '4', '*'},
    {'*', '7', '6', '5', '*'},
    {'*', '*', '*', '*', '*'}
};
int dx[4] = {0, 0, -1, 1};
int dy[4] = {1, -1, 0, 0};
int cnt = -1;
Queue queue;
Stack stack;
bool astar(Matrix matrix);
int getG(Matrix matrix);
void initQueue(int length);
void putQueue(Matrix matrix);
Matrix getQueue(void);
int isQueueEmpty(void);
int isQueueFull(void);
void initStack(int length);
void pushStack(Matrix matrix);
Matrix popStack(void);
int isStackEmpty(void);
int matrixCmp(char src[][NUM], char dst[][NUM]);
void matrixCpy(char dst[][NUM], char src[][NUM]);
void matrixPrint(char matrix[][NUM]);
int main(int argc, char *argv[]) {
  

    Matrix src;
  

    initQueue(3628800+1);
    initStack(3628800+1);
  

    src.v = 3;
    src.w = 2;
    matrixCpy(src.matrix, srcMatrix);
    src.pre = cnt;
    src.f = 0;
    src.g = getG(src);
    astar(src);
    return 0;
}
bool astar(Matrix matrix)
{
    Matrix t, s;
  

    int v, w;
  

    int direction;
  

    putQueue(matrix);
  

    while (!isQueueEmpty())
    {
        s = getQueue();
     

        cnt++;
     

        for (direction = 0; direction < 4; direction++)
        {
            t = s;
            v = t.v + dx[direction]; w = t.w + dy[direction];
          

            if (srcMatrix[v][w] != '*')
            {
                char c = t.matrix[t.v][t.w];
                t.matrix[t.v][t.w] = t.matrix[v][w];
                t.matrix[v][w] = c;
              

                t.v = v;
                t.w = w;
                t.pre = cnt;
                t.f = s.f + 1;
                t.g = getG(t);
                t.isVisited = false;
              

                int h = 0;
                for (; h < queue->tail; h++)
                {
                    if (matrixCmp(queue->data[h].matrix, t.matrix))
                    {
                        break;
                    }
                }
              

                if (h == queue->tail)
                {
                    putQueue(t);
                 

                    if (matrixCmp(t.matrix, dstMatrix))
                    {
                        pushStack(t);
                      

                        for (int father = t.pre; !matrixCmp(queue->data[father].matrix, srcMatrix); father = queue->data[father].pre)
                        {
                            pushStack(queue->data[father]);
                        }
                      

                        puts("PathFind = ");
                      

                        matrixCpy(t.matrix, srcMatrix);
                        pushStack(t);
                      

                        while (!isStackEmpty())
                        {
                            s = popStack();
                            matrixPrint(s.matrix);
                        }
                      

                        return true;
                    }
                }
            }
        }
    }
  

    return false;
}
int getG(Matrix matrix)
{
    int g = 0;
  

    for (int i = 0; i < NUM; i++)
    {
        for (int j = 0; j < NUM; j++)
        {
            if (matrix.matrix[i][j] != '*' && matrix.matrix[i][j] != dstMatrix[i][j])
            {
                g++;
            }
        }
    }
  

    return g;
}
void initQueue(int length)
{
    queue = malloc(sizeof(BGQueue));
  

    queue->data = malloc(sizeof(Matrix) * length);
    queue->length = 0;
    queue->maxLength = length;
    queue->head = 0;
    queue->tail = 0;
}
void putQueue(Matrix matrix)
{
    queue->data[queue->tail++] = matrix;
    queue->tail = queue->tail % queue->maxLength;
    queue->length++;
  

    Matrix* a = malloc(sizeof(Matrix) * queue->maxLength);
    Matrix* b = malloc(sizeof(Matrix) * queue->maxLength);
  

    int an = 0;
    int bn = 0;
  

    for (int i = 0; i < queue->length; i++)
    {
        if (queue->data[i].isVisited)
        {
            a[an++] = queue->data[i];
        }
        else
        {
            b[bn++] = queue->data[i];
        }
    }
    for (int i = 0; i < bn-1; i++)
    {
        for (int j = bn-1; j > i; j--)
        {
            int h1 = b[j-1].f + b[j-1].g;
            int h2 = b[j].f + b[j].g;
          

            if (h1 > h2)
            {
                Matrix t = b[j-1];
                b[j-1] = b[j];
                b[j] = t;
            }
        }
    }
  

    for (int i = 0; i < an; i++)
    {
        queue->data[i] = a[i];
    }
  

    for (int i = 0; i < bn; i++)
    {
        queue->data[an+i] = b[i];
    }
    free(a);
    free(b);
}
Matrix getQueue(void)
{
    queue->data[queue->head].isVisited = true;
  

    Matrix ret;
    ret = queue->data[queue->head++];
    queue->head = queue->head % queue->maxLength;
  

    return ret;
}
int isQueueEmpty(void)
{
    return queue->head == queue->tail;
}
int isQueueFull(void)
{
    return ((queue->tail+1) % queue->maxLength) == queue->head;
}
void initStack(int length)
{
    stack = malloc(sizeof(BGStack));
  

    stack->data = malloc(sizeof(Matrix) * length);
    stack->top = 0;
  

}
void pushStack(Matrix matrix)
{
    stack->data[stack->top++] = matrix;
}
Matrix popStack(void)
{
    Matrix ret;
    ret = stack->data[--stack->top];
  

    return ret;
}
int isStackEmpty(void)
{
    return (stack->top == 0);
}
int matrixCmp(char src[][NUM], char dst[][NUM])
{
    int i, j, s, t, ret;
  

    char srcString[30] = {0};
    char dstString[30] = {0};
  

    s = 0;
    t = 0;
  

    for (i = 0; i < NUM; i++)
    {
        for (j = 0; j < NUM; j++)
        {
            srcString[s++] = src[i][j];
            dstString[t++] = dst[i][j];
        }
    }
 
    ret = !strcmp(srcString, dstString);

    return ret;
}

void matrixCpy(char dst[][NUM], char src[][NUM])
{
    int i, j;
  

    for (i = 0; i < NUM; i++)
    {
        for (j = 0; j < NUM; j++)
        {
            dst[i][j] = src[i][j];
        }
    }
}
void matrixPrint(char matrix[][NUM])
{
    char s[60] = {0};
    int i, j, k;
    k = 0;

    for (i = 0; i < NUM; i++)
    {
        for (j = 0; j < NUM; j++)
        {
            s[k++] = matrix[i][j];
        }
    
        s[k++] = '\r';
        s[k++] = '\n';
    }
 
    s[k++] = '\r';
    s[k++] = '\n';

    puts(s);
}