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)
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。