数据结构与算法学习之路：迷宫问题——回溯思想找出所有路径

今天小伙伴和我说之前写的那个迷宫问题有些问题，我就改了改，感觉之前写的东西思路也不清晰，也比较乱，就重新写了一篇……别在意哈～

一、迷宫问题描述：

给定一个迷宫，以及起点和终点，通过设计算法，找到一条可以到达终点的路径。解决以后，想办法找到最短路径和所有路径。

二、解决方法：

1、找到一条可达的路径并不难，只要设定方向，然后每个点都去找一个可以走的方向一直向可行方向走就是了。

2、找到最短路径。要找到最短路径，可以尝试广度优先算法——BFS。BFS找图中一点到另一点的最短路径还是很方便的（没有权值），主要思想是，把每一个点可到的状态都算出来，最先到达终点的状态就是最短的路径长度。就这样说可能很抽象，不妨看看下面这张图：

3、找所有路径。找所有路径比较简单的方法是先找出一条路径，然后回溯到上一个点，看看有没有别的地方可以走，再从这个方向往下走。从而不断回溯找到所有路径

三、代码：

找到所有路径的实现方式：

#include <stdio.h>#include <stdlib.h>#define WALL 1#define ROAD 0#define END -1#define TRUE 1#define FALSE 0#define VISITED 1#define UNVISITED 0#define BARRIER -1 //四周都是墙的死路#define MAXSIZE 11 //迷宫每行或每列中点的的最大数量#define DIR_SIZE 4 //方向#define STACK_SIZE 128typedef int Status;//迷宫中的点typedef struct Point{int x;int y;Status status;Status visited;}Point;typedef struct Stack{Point point[STACK_SIZE];int top;}Stack, *StackPtr;void Stack_Init(StackPtr s);void Stack_Push(StackPtr s, Point point);void Stack_Pop(StackPtr s);//搜索所有路径。//多入口多出口加个起点终点数组，将起点通过循环作为栈底，遍历到达不同终点的路径即可void Maze_Search(StackPtr s, Point maze[MAXSIZE][MAXSIZE],Point *dir);int main(){StackPtr stack;Point dir[DIR_SIZE];Point up, down, right, left;Point maze[MAXSIZE][MAXSIZE];int i, j;//初始化迷宫for (i = 0; i < MAXSIZE; i++){for (j = 0; j < MAXSIZE; j++)maze[i][j].status = ROAD;}for (i = 0; i < MAXSIZE; i++)for (j = 0; j < MAXSIZE; j++){maze[i][j].x = i;maze[i][j].y = j;maze[i][j].visited = UNVISITED;}for (i = 0; i < MAXSIZE; i++){maze[0][i].status = WALL;maze[10][i].status = WALL;maze[0][i].visited = VISITED;maze[10][i].visited = VISITED;}for (i = 0; i < MAXSIZE; i++){maze[i][0].status = WALL;maze[i][10].status = WALL;maze[i][0].visited = VISITED;maze[i][10].visited = VISITED;}maze[1][2].status = WALL;maze[1][3].status = WALL;maze[1][5].status = WALL;maze[1][6].status = WALL;maze[1][9].status = WALL;maze[2][3].status = WALL;maze[2][4].status = WALL;maze[2][7].status = WALL;maze[2][8].status = WALL;maze[2][9].status = WALL;maze[3][3].status = WALL;maze[3][5].status = WALL;maze[3][6].status = WALL;maze[3][8].status = WALL;maze[4][2].status = WALL;maze[4][4].status = WALL;maze[4][7].status = WALL;maze[4][9].status = WALL;maze[5][6].status = WALL;maze[5][3].status = WALL;maze[5][5].status = WALL;maze[5][8].status = WALL;maze[6][1].status = WALL;maze[6][4].status = WALL;maze[6][6].status = WALL;maze[6][7].status = WALL;maze[6][9].status = WALL;maze[7][4].status = WALL;maze[7][8].status = WALL;maze[7][9].status = WALL;maze[8][2].status = WALL;maze[8][6].status = WALL;maze[9][1].status = WALL;maze[9][2].status = WALL;maze[1][1].visited = VISITED;maze[1][2].visited = VISITED;maze[1][3].visited = VISITED;maze[1][5].visited = VISITED;maze[1][6].visited = VISITED;maze[1][9].visited = VISITED;maze[2][3].visited = VISITED;maze[2][4].visited = VISITED;maze[2][7].visited = VISITED;maze[2][8].visited = VISITED;maze[2][9].visited = VISITED;maze[3][3].visited = VISITED;maze[3][5].visited = VISITED;maze[3][6].visited = VISITED;maze[3][8].visited = VISITED;maze[4][2].visited = VISITED;maze[4][4].visited = VISITED;maze[4][7].visited = VISITED;maze[4][9].visited = VISITED;maze[5][6].visited = VISITED;maze[5][3].visited = VISITED;maze[5][5].visited = VISITED;maze[5][8].visited = VISITED;maze[6][1].visited = VISITED;maze[6][4].visited = VISITED;maze[6][6].visited = VISITED;maze[6][7].visited = VISITED;maze[6][9].visited = VISITED;maze[7][4].visited = VISITED;maze[7][8].visited = VISITED;maze[7][9].visited = VISITED;maze[8][2].visited = VISITED;maze[8][6].visited = VISITED;maze[9][1].visited = VISITED;maze[9][2].visited = VISITED;maze[9][9].status = END;up.x = -1;up.y = 0;up.status = ROAD;left.x = 0;left.y = -1;left.status = ROAD;right.x = 0;right.y = 1;right.status = ROAD;down.x = 1;down.y = 0;down.status = ROAD;dir[0] = left;dir[1] = down;dir[2] = right;dir[3] = up;//输出迷宫for (i = 0; i < MAXSIZE; i++){for (j = 0; j < MAXSIZE; j++){if (maze[i][j].status == WALL)printf("▇");elseprintf("  ");}printf("\n");}printf("\n");//初始化保存路径的栈stack = (StackPtr)malloc(sizeof(Stack));Stack_Init(stack);Maze_Search(stack, maze, dir);return 0;}void Stack_Init(StackPtr s){Point temp;if (s == NULL)return;temp.x = 1;temp.y = 1;temp.status = ROAD;temp.visited = VISITED;s->top = 0;s->point[s->top] = temp;return;}void Stack_Push(StackPtr s, Point point){if (s->top == (STACK_SIZE - 1)){printf("栈已满！");return;}s->top += 1;s->point[s->top] = point;}void Stack_Pop(StackPtr s){Point temp;if (s->top == -1){printf("栈为空！");return;}temp.x = 0;temp.y = 0;temp.status = ROAD;s->point[s->top] = temp;s->top -= 1;}void Maze_Search(StackPtr s, Point maze[MAXSIZE][MAXSIZE],Point *dir){int i,j;if (s->point[s->top].status == END){for (i = 0; i < MAXSIZE; i++){for (j = 0; j < MAXSIZE; j++){if (maze[i][j].status == WALL)printf("▇");else if ((maze[i][j].status == ROAD || maze[i][j].status == END) && maze[i][j].visited == VISITED && maze[i][j].visited != BARRIER)printf("※");elseprintf("  ");}printf("\n");}maze[9][9].visited = UNVISITED;Stack_Pop(s);printf("\n\n");return;}for (i = 0; i < DIR_SIZE; i++){if (maze[s->point[s->top].x + dir[i].x][s->point[s->top].y + dir[i].y].status != WALL&& maze[s->point[s->top].x + dir[i].x][s->point[s->top].y + dir[i].y].visited != VISITED){maze[s->point[s->top].x + dir[i].x][s->point[s->top].y + dir[i].y].visited = VISITED;Stack_Push(s, maze[s->point[s->top].x + dir[i].x][s->point[s->top].y + dir[i].y]);Maze_Search(s, maze, dir);}}for (i = 0; i < DIR_SIZE; i++){if (maze[s->point[s->top].x + dir[i].x][s->point[s->top].y + dir[i].y].status != WALL&& maze[s->point[s->top].x + dir[i].x][s->point[s->top].y + dir[i].y].visited != VISITED){maze[s->point[s->top].x][s->point[s->top].y].visited = UNVISITED;Stack_Pop(s);return;}}if (maze[s->point[s->top].x][s->point[s->top].y - 1].status == ROAD && maze[s->point[s->top].x][s->point[s->top].y - 1].visited == UNVISITED)maze[s->point[s->top].x][s->point[s->top].y].visited = UNVISITED;maze[s->point[s->top].x][s->point[s->top].y].visited = BARRIER;Stack_Pop(s);return;}