广度优先算法BFS

package myalgorithm;

import java.util.Arrays;
import java.util.LinkedList;
import java.util.Queue;
/*BFS用于记录的位置和值的结构*/
class node
{
    node(int xparam,int yparam,int valparam)
    {
        this.x = xparam;
        this.y = yparam;
        this.value = valparam;
    }
    int x,y,value;
}
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}
    };
  /*BFS算法*/
    public void BFS(node startPoint)
    {
        //起始点装入队列
        Queue<node> queue = new LinkedList<node>();
        startPoint.value = 1;//确保起始步数为1
        queue.offer(startPoint);
        
        node t1;
        int tx,ty;
        top:
        while(!queue.isEmpty())
        {
            //取队首，出队后不再入队，value也自此固定
            t1 = queue.poll();
            mark[t1.x][t1.y] = t1.value;//标记步数
            for(int i=0;i<4;i++)
            {
                tx = t1.x + choose[i][0];
                ty = t1.y + choose[i][1];
                
                //找到美女，肯定是最短的，可以立即返回
                if(graph[tx][ty] == 'M')
                {
                    stepnum = t1.value + 1;//下一步可到
                    mark[tx][ty] = stepnum;
                    break top;
                }
                //继续接着找，把空路径添加到队列末尾
                //不是炸弹和围墙,并且没有被标记
                if(graph[tx][ty] != '#' 
                        && graph[tx][ty] != '*'
                        &&mark[tx][ty] == 0)
                {
                    queue.offer(new node(tx,ty,t1.value+1));
                }
            }
        }
    }
    /*BFS回溯路径*/
    private void getPath(node target) {

        int beforex = 0,beforey = 0;
        int x = target.x;
        int y = target.y;
        for(int i=0;i<4;i++)
        {
            beforex = x + choose[i][0];
            beforey = y + choose[i][1];
            //找到英雄的出发点，函数结束
            if (beforex == 1 && beforey == 1)
            {
                return;
            }
            if(mark[x][y] - 1 == mark[beforex][beforey])
            {
                System.out.print("("+beforex+","+beforey+")<--");
                break;
            }
        }
        getPath(new node(beforex,beforey,0));
        return;
    }
    /*main函数*/
    public static void main(String[] args) {
        ShortPath my = new ShortPath();
        
        long start = System.currentTimeMillis();
        my.BFS(new node(1,1,0));
        long end = System.currentTimeMillis();
        System.out.println("BFS step: " + my.stepnum + " time:" + (end-start));
        //打印标记结果
        for (int m = 0;m<my.graph.length;m++)
            System.out.println(Arrays.toString(my.mark[m]));
        //打印巡回路径
        my.getPath(new node(6,8,0));       
    }

}

BFS step: 13 time:4
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 1, 2, 3, 0, 7, 8, 0, 10, 11, 0]
[0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0]
[0, 3, 0, 5, 6, 7, 0, 9, 10, 11, 0]
[0, 4, 5, 6, 0, 8, 9, 10, 11, 0, 0]
[0, 5, 6, 7, 8, 9, 10, 0, 12, 0, 0]
[0, 6, 0, 8, 9, 10, 11, 0, 13, 0, 0]
[0, 0, 10, 9, 0, 11, 0, 0, 0, 0, 0]
[0, 0, 11, 10, 11, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(5,8)<--(4,8)<--(4,7)<--(4,6)<--(4,5)<--(3,5)<--(3,4)<--(3,3)<--(2,3)<--(2,2)<--(2,1)

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扩展：

PhotoShop中的魔术棒选择工具的原理，就是从鼠标选中的点作为种子，并加入队列；依次查找周边的点，如果颜色与种子颜色相近，则加入队列；对队列中的元素依次进行类似扩展，这样就选取了与最初种子颜色相同的点的集合。