用栈实现迷宫多条路径求解问题

#include "pch.h"
#include <iostream>
using namespace std;
#define M 8 //行数
#define N 8 //列数
//迷宫
int a[M+2][N+2] = 
{
	{1,1,1,1,1,1,1,1,1,1},
	{1,0,0,1,0,0,0,0,1,1},
	{1,0,1,0,0,1,1,1,1,1},
	{1,0,0,0,0,0,0,0,1,1},
	{1,1,0,0,0,1,1,0,0,1},
	{1,1,1,1,0,0,0,0,1,1},
	{1,0,0,0,1,0,1,1,0,1},
	{1,0,1,0,1,0,1,1,1,1},
	{1,0,0,0,1,0,0,0,0,1},
    {1,1,1,1,1,1,1,1,1,1}
};
struct
{
	int i; // 横坐标
	int j; // 纵坐标
	int direction;//方向
}Stack[100],Path[100][200];// 定义栈和存放路径的数组

int top = -1; //栈顶指针
int roadnumber = 1; //路径数
int minlength = 100; //最短路径长度
int minroadnumber=1;//记录进行比较的最小路径数

//输出一条路径并保存最短路径
static void one_path()
{
	
	int k;
	cout <<"第"<< roadnumber++<<"条路："<< endl;// 输出第roadnumber条路径
	for (k = 0; k <= top; k++)
	{
		cout << "(" << Stack[k].i << "," << Stack[k].j << ")";
		if (k != top) cout << "->";
	}
	cout << endl;
	if (top + 1 <=minlength) //找最短路径
	{
		Path[minroadnumber][0].i= top + 1;//将路径长度存放在第一列的i中
		for (k = 1; k <= top+1; k++) //更新最短路径
		{
			Path[minroadnumber][k].i = Stack[k-1].i;
			Path[minroadnumber][k].j = Stack[k-1].j;
			Path[minroadnumber][k].direction = Stack[k-1].direction;
		}
		minroadnumber++;
		minlength = top + 1; // 更新最短长度
	}
}

//输出最短路径
static void min_path()
{
	cout << "最短路径长度为：" << minlength << endl;
	cout << "路径为："<< endl;
	for (int k = 1; k <=minroadnumber; k++)
	{
		if (Path[k][0].i == minlength)
		{
			for (int l = 1; l <=minlength; l++)
			{
				cout << "(" << Path[k][l].i << "," << Path[k][l].j << ")";
				if (l != minlength) cout << "->";
			}
			cout << endl;
		}
	}
	cout << endl;
}

static void all_path(int xi, int yi, int xe, int ye)//入口与出口
{
	int i, j, di,X, Y;
	int flag = 0;
	top++; // 进栈
	Stack[top].i = xi;
	Stack[top].j = yi;
	Stack[top].direction = 0;// 入口进栈
	a[xi][yi] = -1; //标记为访问过
	int f=0;//用来标志是否有路可走
	while (top > -1) // 栈不空时循环
	{
		i = Stack[top].i;
		j = Stack[top].j; 
		di = Stack[top].direction;// 取栈顶
		if (i == xe && j == ye) // 找到终点
		{
			one_path(); // 输出一条路径
			f = 1;//代表有路
			a[i][j] = 0; // 让出口变为其他路径可走方块
			top--; // 出口退栈
			i = Stack[top].i; 
			j = Stack[top].j;
			di = Stack[top].direction; // 更换栈顶
		}
		flag = 0;
		while (di < 4 && flag==0)
		{
			di++;
			switch (di)//四个方向寻找
			{
			case 1:X = i - 1;Y = j;break;
			case 2:X = i;Y = j + 1;break;
			case 3:X = i + 1;Y = j;break;
			case 4:X = i;Y = j - 1;break;
			}
			if (a[X][Y] == 0)//如果为通路证明找到
				flag=1;
		}
		if (flag) // 找到就修改原来栈顶的方向并且进栈新步骤
		{
			Stack[top].direction = di; // 修改原栈顶元素的di值
			top++;//入栈
			Stack[top].i = X; Stack[top].j = Y; Stack[top].direction = 0; // 下一个可走方块(i1,j1)进栈
			a[X][Y] = -1; //标志为访问过
		}
		else // 否则将该点置为通路，退栈
		{
			a[i][j] = 0;
			top--;
		}
	}
	if (f == 0) cout << "无路可走！" << endl;
	else
	{
		cout << "一共有" << roadnumber - 1 << "条路！" << endl;
		min_path(); // 输出最短路径
	}
}

int main(int argc, char *argv[])
{
	cout << "迷宫如下图所示：(1表示墙0表示通路)" << endl;
	for (int i = 0; i < M + 2; i++)
	{
		for (int j = 0; j < N + 2; j++)
			cout << a[i][j] << '\t';
		cout << endl;
	}
	cout << "所有路径如下：" << endl;
	all_path(1, 1, M, N);
	return 0;
}