数据结构与算法学习之路：迷宫问题

迷宫问题在游戏里非常常见，例如仙剑系列就有各种虐人的迷宫…………刚好有个老师布置了迷宫问题给舍友，出于兴趣我就自己查阅一些知识把他简单的实现了。废话不多说，下面进入正文：

一、阅读需要的预备知识：

栈以及栈的操作（入栈、出栈）、C语言基础、BFS（广度优先搜索算法）和DFS（深度优先搜索算法）以及邻接矩阵的概念

二、实现思路：

1、既然要解决迷宫问题，那么我们肯定需要用一种方式把迷宫给存储起来。在这里采用的是邻接矩阵maze[][]。在设计邻接矩阵的时候，为了操作方便，不使用maze[0][]和maze[][0]。但是这些空间白白浪费了很不值得呀，这时不妨考虑一下迷宫本身的特点，迷宫除了一些障碍肯定还有迷宫的“墙壁”，于是我们就可以把这些空间设置成墙壁了。

2、迷宫中的点首先会有一个坐标，所以我们需要x和y来存储坐标。此外，迷宫问题中，我们的点有三种“状态”，也就是：起点，终点，障碍（所有可行方向都是墙壁，俗称——死胡同）、通路、墙壁。所以要通过宏定义来设置一些常量

3、走迷宫当然需要确定哪些方向能走了，所以用一个dir[]数组来存储可以走的方向。

 4、最后就是设计一个搜索迷宫的算法了。最短路径用BFS算法就可以实现，所有路径这里我是用深搜，先搜到一条可达的路径，然后通过回溯找其他的路径。（关于BFS、DFS算法网上有个图非常好，可以去搜搜）

三、代码：

#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#define MAXSIZE 11 //迷宫每行或每列中点的的最大数量#define STACK_SIZE 24typedef 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_Enter(StackPtr s, Point point);void Stack_Pop(StackPtr s);//搜索所有路径，第一条路径为最短。//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[3]);void Maze_AutoCreate();int main(){StackPtr stack;Point dir[3];Point up, down, right;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;down.x = 1;down.y = 0;down.status = ROAD;right.x = 0;right.y = 1;right.status = ROAD;up.x = -1;up.y = 0;up.status = ROAD;dir[0] = down;dir[1] = right;dir[2] = 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[3]){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 < 3; 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 < 3; 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;}