迷宫问题(DFS)
声明:图片及内容基于https://www.bilibili.com/video/BV1oE41177wk?t=3245
问题及分析
8*8的迷宫,最外周是墙,0表示可以走,1表示不可以走
设置迷宫
const int M = 8; //迷宫长(不包含墙)
const int N = 8; //迷宫宽(不包含墙)
设置方位坐标
class Box{ //栈中元素
public:
int x, y;
int di; //方向及Direction数组的下标
Box(int x, int y, int di):x(x),y(y),di(di) {}
Box() {}
};
设置方位偏移量
class Direction{ //x,y方向增量
public:
int incX, incY;
Direction(int x, int y) :incX(x), incY(y) {}
};
寻找路径
bool findPath(int maze[M + 2][N + 2], Direction direct[], stack<Box> &s) {
Box temp(1,1,-1); //temp用来记录当前所在位置
int x, y, di; //迷宫格子当前处理单元的纵横坐标和方向
int line, col; //迷宫数组下一个单元的行坐标和列坐标
maze[1][1] = -1; //走过的格子设为-1
s.push(temp);
while (!s.empty()) {
temp = s.top(); //每次获取栈的头元素
s.pop(); //弹出头元素
x = temp.x; y = temp.y; di = temp.di+1; //上次循环到没法走要换个方向,更新当前位置,下,x,y不变,di+1,换个方向
while (di < 4) {
line = x + direct[di].incX;
col = y + direct[di].incY;
if (maze[line][col] == 0) { //格子为0说明这个格子可以走
Box temp2(x, y, di);
temp = temp2;
s.push(temp); //成功走到下一个格子就压入栈
x = line; y = col; maze[line][col] = -1; //更新当前所在位置
if (x == M && y == N) return true;
else di = 0; //从最新的位置开始尝试四个方向
}
else di++; //maze[line][col]== -1 没法走,换一个方向
}
}
return false; //没有路
}
完整代码
#include<iostream>
#include<stack>
using namespace std;
const int M = 8; //迷宫长(不包含墙)
const int N = 8; //迷宫宽(不包含墙)
class Direction{ //x,y方向增量
public:
int incX, incY;
Direction(int x, int y) :incX(x), incY(y) {}
};
class Box{ //栈中元素
public:
int x, y;
int di; //方向及Direction数组的下标
Box(int x, int y, int di):x(x),y(y),di(di) {}
Box() {}
};
bool findPath(int maze[M + 2][N + 2], Direction direct[], stack<Box> &s) {
Box temp(1,1,-1); //temp用来记录当前所在位置
int x, y, di; //迷宫格子当前处理单元的纵横坐标和方向
int line, col; //迷宫数组下一个单元的行坐标和列坐标
maze[1][1] = -1; //走过的格子设为-1
s.push(temp);
while (!s.empty()) {
temp = s.top(); //每次获取栈的头元素
s.pop(); //弹出头元素
x = temp.x; y = temp.y; di = temp.di+1;
while (di < 4) {
line = x + direct[di].incX;
col = y + direct[di].incY;
if (maze[line][col] == 0) { //格子为0说明这个格子可以走
Box temp2(x, y, di);
temp = temp2;
s.push(temp); //成功走到下一个格子就压入栈
x = line; y = col; maze[line][col] = -1;
if (x == M && y == N) return true;
else di = 0; //从最新的位置开始尝试四个方向
}
else di++; //换一个方向
}
}
return false; //没有路
}
int main() {
stack<Box> s;
Direction direct[4] = { {0,1},{1,0},{0,-1},{-1,0} };
int maze[M + 2][N + 2];
for (int i = 0; i < M + 2; i++) {
for (int j = 0; j < N + 2; j++) {
cin >> maze[i][j];
}
}
int maze2[M+2][N+2]; //用maze2拷贝maze用于最后打印
for (int i = 0; i < M + 2; i++) {
for (int j = 0; j < N + 2; j++) {
maze2[i][j]= maze[i][j];
}
}
if (findPath(maze, direct, s)) {
while (!s.empty()) {
cout << "(" << s.top().x << "," << s.top().y << ")" << endl;
maze2[s.top().x][s.top().y] = s.top().di + 2; //类似哈希散列,做特殊标记。墙是0~1,箭头是2~5
s.pop(); //为了实现可视化
}
for (int i = 0; i < M + 2; i++) { //路径可视化
for (int j = 0; j < N + 2; j++) {
switch (maze2[i][j]) {
case 0:cout << "0 "; break;
case 1:cout << "1 "; break;
case 2:cout << "→"; break;
case 3:cout << "↓"; break;
case 4:cout << "←"; break;
case 5:cout << "↑"; break;
default:break;
}
//cout << maze2[i][j]<<" ";
}
cout << endl;
}
}
else cout << "No path"<<endl;
return 0;
}
输入:
1 1 1 1 1 1 1 1 1 1
1 0 0 1 0 0 0 1 0 1
1 0 0 1 0 0 0 1 0 1
1 0 0 0 0 1 1 0 0 1
1 0 1 1 1 0 0 0 0 1
1 0 0 0 1 0 0 0 0 1
1 0 1 0 0 0 1 0 0 1
1 0 1 1 1 0 1 1 0 1
1 1 0 0 0 0 0 0 0 1
1 1 1 1 1 1 1 1 1 1
输出:
(8,7)
(8,6)
(8,5)
(7,5)
(6,5)
(6,4)
(6,3)
(5,3)
(5,2)
(5,1)
(4,1)
(3,1)
(3,2)
(2,2)
(1,2)
(1,1)
1 1 1 1 1 1 1 1 1 1
1 →↓1 0 0 0 1 0 1
1 0 ↓1 0 0 0 1 0 1
1 ↓←0 0 1 1 0 0 1
1 ↓1 1 1 0 0 0 0 1
1 →→↓1 0 0 0 0 1
1 0 1 →→↓1 0 0 1
1 0 1 1 1 ↓1 1 0 1
1 1 0 0 0 →→→0 1
1 1 1 1 1 1 1 1 1 1