思路分析

代码实现

package com.atguigu.floyd;import java.util.Arrays;public class FloydAlgorithm {public static void main(String[] args) {//测试看看图是否创建成功char[] vertex={'A','B','C','D','E','F','G'};//创建邻接矩阵int[][] matrix=new int[vertex.length][vertex.length];final int N=65535;matrix[0] = new int[] { 0, 5, 7, N, N, N, 2 };matrix[1] = new int[] { 5, 0, N, 9, N, N, 3 };matrix[2] = new int[] { 7, N, 0, N, 8, N, N };matrix[3] = new int[] { N, 9, N, 0, N, 4, N };matrix[4] = new int[] { N, N, 8, N, 0, 5, 4 };matrix[5] = new int[] { N, N, N, 4, 5, 0, 6 };matrix[6] = new int[] { 2, 3, N, N, 4, 6, 0 };//创建Graph对象Graph graph = new Graph(vertex.length, matrix, vertex);//调用弗洛伊德算法graph.floyd();graph.show();}}//创建图
class Graph{private char[] vertex;//存放顶点的数组private int[][] dis;//保存，从各个顶点出发到其他顶点的距离，最后的结果，也是保留在该数组private int[][] pre;//保存到达目标顶点的前驱顶点//构造器/**** @param length 大小* @param matrix 邻接矩阵* @param vertex 顶点数组*/public Graph(int length,int[][] matrix,char[] vertex){this.vertex=vertex;this.dis=matrix;this.pre=new int[length][length];//对pre数组初始化,注意存放的是前驱顶点的下标for (int i = 0; i < length; i++) {Arrays.fill(pre[i],i);}}//显示pre数组和dis数组public void show(){//为了显示便于阅读，我们优化一下输出char[] vertex={'A','B','C','D','E','F','G'};for (int k = 0; k < dis.length; k++) {//先将pre数组输出的一行for (int i = 0; i < dis.length; i++) {System.out.print(pre[k][i]+" ");}System.out.println();//将dis数组输出的一行for (int i = 0; i < dis.length; i++) {System.out.print(vertex[k]+"到"+vertex[i]+"的最短路径是"+dis[k][i]+"   ");}System.out.println();System.out.println();}}//佛罗伊德算法,比较容易理解，而且容易实现public void floyd(){int len=0;//变量保存距离//对中间顶点的遍历，k就是中间顶点的下标for (int k = 0; k < dis.length; k++) {//[A, B, C, D, E, F, G]//从i顶点开始出发[A, B, C, D, E, F, G]for (int i = 0; i < dis.length; i++) {//到达j顶点[A, B, C, D, E, F, G]for (int j = 0; j < dis.length; j++) {len=dis[i][k]+dis[k][j];//求出从i顶点出发，经过k中间顶点，到达j顶点距离if(len<dis[i][j]){//如果len小于dis[i][j]dis[i][j]=len;//更新距离pre[i][j]=pre[k][j];//更新前驱顶点}}}}}}