3006: 迷宫问题（栈与队列）

时间限制: 1 Sec  
内存限制: 128 MB

提交: 3  
解决: 1

题目描述

编写一个求解迷宫问题的程序，要求输出迷宫的所有路径，并求最短路径长度及最短路径。

规定：

S：迷宫的入口

D：迷宫的出口

X：障碍物，无法从这里通过

*：空地

搜索顺序优先度：↑、→、↓、←

输入

输入的第一行包含一个数字n，接下来的n行输入一个n*n的迷宫地图。

输出

输出迷宫的所有路径,每一种路径占一行。最后输出所有路径中最长路径和最短路径的长度。

样例输入

6
XXXXXX
XS**XX
X*X**X
X***XX
XX**DX
XXXXXX

样例输出

→→↓↓↓→
→→↓↓←↓→→
↓↓→→↓→
↓↓→↓→→
8 6

提示

1、使用栈求解

2、搜索顺序优先度：↑、→、↓、←

3、若没有路径可以走出迷宫，则输出0 0

迷失在幽谷中的鸟儿，独自飞翔在这偌大的天地间，却不知自己该飞往何方……

#include<stdio.h>
#include<iostream>
#include<algorithm>
#include<string.h>
#define SizeMax 105
using namespace std;
int n,maxx=0,minn=0xffff;
char a[10][10];
typedef struct
{
    char data[SizeMax][5];
    int top;
} SqStack;
SqStack *s=(SqStack*)malloc(sizeof(SqStack));
void push(SqStack *&s,string k)                 //入栈
{
    char *e=(char*)k.data();                    //将string类型转换成char*
    if(s->top==SizeMax-1)return;
    s->top++;
    strcpy(s->data[s->top],e);                  //入栈
}
void print(SqStack *s)                          //输出
{
    for(int i=0; i<=s->top; i++)
        cout<<s->data[i];
    cout<<endl;
}
void dfs(int x,int y,int k)                     //深度优先扫描
{
    if(a[x][y]=='D')
    {
        maxx=maxx<k?k:maxx;                     //最大值
        minn=minn>k?k:minn;                     //最小值
        print(s);
        return;
    }a[x][y]='X';                               //走过的路用‘X’填充，防止出现重复路线
    for(int i=0; i<4; i++)
    {
        if(i==0){if(a[x-1][y]!='X'&&x-1>=0)push(s,"↑"),dfs(x-1,y,k+1),s->top--;}        //向上
        else if(i==1){if(a[x][y+1]!='X'&&y+1<n)push(s,"→"),dfs(x,y+1,k+1),s->top--;}    //向右
        else if(i==2){if(a[x+1][y]!='X'&&x+1<n)push(s,"↓"),dfs(x+1,y,k+1),s->top--;}    //向下
        else if(i==3){if(a[x][y-1]!='X'&&y-1>=0)push(s,"←"),dfs(x,y-1,k+1),s->top--;}   //向左
    }a[x][y]='*';                               //回溯结束后解开被填充的路口
}
int main()
{
    cin>>n;
    for(int i=0; i<n; i++)
        scanf("%s%*c",a[i]);
    s->top=-1;
    int x,y;
    for(int i=0; i<n; i++)
        for(int j=0; j<n; j++)
            if(a[i][j]=='S')                    //确定‘S’的位置
            {
                x=i,y=j;
                goto end1;
            }
end1:
    dfs(x,y,0);
    if(maxx==0)minn=0;
    printf("%d %d\n",maxx,minn);
    return 0;
}

附上后台一组测试数据

/*
10
XX*S***XXX
X***X*****
XX****XX**
***X****X*
*X***X***X
***X***XX*
*****X**X*
X*X*X**X**
X***D*XX*X
X*X*X****X

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