深度优先算法DFS

英雄要从H点出发，去解救位于M点的美女。

迷宫的围墙用#表示，带*号的位置表示有杀手埋伏，这些点都是不能走的，

那么英雄要最少走多少步才能解救美女呢？

package myalgorithm;
import java.util.Arrays;
import java.util.LinkedList;
import java.util.Queue;
public class ShortPath {
    /*全局最短路径*/
    public int stepnum = 999;
    /*构建11*11的迷宫,英雄H在(1,1)的位置出发，去解救美女M(6,8)*/
    char[][] graph = {
            {'#','#','#','#','#','#','#','#','#','#','#'},
            {'#','H','_','_','*','_','_','*','_','_','#'},
            {'#','_','_','_','_','_','_','_','_','_','#'},
            {'#','_','*','_','_','_','*','_','_','_','#'},
            {'#','_','_','_','*','_','_','_','_','*','#'},
            {'#','_','_','_','_','_','_','*','_','*','#'},
            {'#','_','*','_','_','_','_','_','M','_','#'},
            {'#','*','_','_','*','_','_','_','_','_','#'},
            {'#','_','_','_','_','_','_','_','_','_','#'},
            {'#','_','_','_','*','_','_','_','_','_','#'},
            {'#','#','#','#','#','#','#','#','#','#','#'},
    };
    /*初始标记数组都为0*/
    public int[][] mark = new int[graph.length][graph.length];
    /*每一个位置有四种选择：右下左上*/
    public int[][] choose = {
            {0,1},
            {1,0},
            {0,-1},
            {-1,0}
    };
    /*采用递归的DFS算法*/
    public void DFS(int x,int y, int step) {
        /*找到美女M*/
        if (graph[x][y] == 'M')
        {
            if(step < stepnum)
            {
                stepnum = step;
            }
            return;//找到之后立即返回，不再继续
        }
 
        //新位置
        int tx = 0;
        int ty = 0;
        for(int i=0;i<4;i++)
        {
            tx = x + choose[i][0];
            ty = y + choose[i][1];
            if(graph[tx][ty] != '#'
                    && graph[tx][ty] != '*'
                    && mark[tx][ty] == 0)
            {
                mark[tx][ty] = 1;//标记该点已经走过
                DFS(tx,ty,step+1);
                mark[tx][ty] = 0;//取消该点的标记
            }
        }
        return;
    }
   public static void main(String[] args) {
        ShortPath my = new ShortPath();long start1 = System.currentTimeMillis();
        my.mark[1][1] = 1;
        my.DFS(1,1,0);long end1 = System.currentTimeMillis();
        System.out.println("DFS step: " + my.stepnum + " time:" + (end1-start1));
    }
 
}

非常耗时：DFS step: 12 time:109830