克鲁斯卡尔算法介绍

克鲁斯卡尔(Kruskal)算法，是用来求加权连通图的最小生成树的算法。
基本思想：按照权值从小到大的顺序选择n-1条边，并保证这n-1条边不构成回路
具体做法：首先构造一个只含n个顶点的森林，然后依权值从小到大从连通网中选择边加入到森林中，并使森林中不产生回路，直至森林变成一棵树为止

public class KruskalAlgorithm {/*** 边的个数*/public int edgeNum;/*** 顶点数组*/public char[] vertexs;/***邻街矩阵*/public int[][] matrix;/***用INF表示两点之前不连通*/public static final int INF = Integer.MAX_VALUE;public static void main(String[] args) {char[] vertexs = {'A', 'B', 'C', 'D', 'E', 'F', 'G'};int[][] matrix = {/*A*//*B*//*C*//*D*//*E*//*F*//*G*//*A*/ {0, 12, INF, INF, INF, 16, 14},/*B*/ {12, 0, 10, INF, INF, 7, INF},/*C*/ {INF, 10, 0, 3, 5, 6, INF},/*D*/ {INF, INF, 3, 0, 4, INF, INF},/*E*/ {INF, INF, 5, 4, 0, 2, 8},/*F*/ {16, 7, 6, INF, 2, 0, 9},/*G*/ {14, INF, INF, INF, 8, 9, 0}};KruskalAlgorithm kruskalAlgorithm = new KruskalAlgorithm(vertexs, matrix);kruskalAlgorithm.show();kruskalAlgorithm.kruskal();}/*** 克鲁斯卡尔算法**/public void kruskal() {int index = 0;int[] ends = new int[edgeNum];EData[] result = new EData[edgeNum];// 获取所有的边并排序EData[] edges = getEdges();// 对所有的边排序sortEdges(edges);// 遍历edges 数组，将边添加到最小生成树中时，判断是准备加入的边否形成了回路，如果没有，就加入 result, 否则不能加入for (int i = 0; i < edgeNum; i++) {// 获取到第i条边的第一个顶点(起点)int index1 = getIndex(edges[i].start);// 获取到第i条边的第2个顶点int index2 = getIndex(edges[i].end);// 获取index1这个顶点在已有最小生成树中的终点int end1 = getEnd(ends, index1);// 获取index2这个顶点在已有最小生成树中的终点int end2 = getEnd(ends, index2);// 是否构成回路if (end1 != end2) {// 没有构成回路// 设置m 在"已有最小生成树"中的终点 <E,F> [0,0,0,0,5,0,0,0,0,0,0,0]ends[end1] = end2;// 有一条边加入到result数组result[index++] = edges[i];}}System.out.println("最小生成树为：");for (int i = 0; i < index; i++) {System.out.println(result[i]);}}public KruskalAlgorithm(char[] vertexs, int[][] matrix) {int len = vertexs.length;this.matrix = matrix;this.vertexs = vertexs;for (int i = 0; i < len; i++) {// 不统计顶点自身for (int j = i + 1; j < len; j++) {if (matrix[i][j] != INF) {edgeNum++;}}}}/*** 遍历邻接矩阵*/public void show() {System.out.println("邻接矩阵为：");for (int i = 0; i < matrix.length; i++) {for (int j = 0; j < matrix[0].length; j++) {System.out.printf("%12d", matrix[i][j]);}System.out.println();}}/*** 获得所有的边* @return*/public EData[] getEdges() {int index = 0;EData[] edges = new EData[edgeNum];for (int i = 0; i < vertexs.length; i++) {for (int j = i + 1; j < vertexs.length; j++) {if (matrix[i][j] != INF) {edges[index++] = new EData(vertexs[i], vertexs[j], matrix[i][j]);}}}return edges;}/*** 使用冒泡排序对所有的边按权值从小到大排序* @param edges*/public void sortEdges(EData[] edges) {for (int i = 0; i < edges.length - 1; i++) {for (int j = 0; j < edges.length - 1 - i; j++) {if (edges[j].weight > edges[j + 1].weight) {EData temp = edges[j];edges[j] = edges[j + 1];edges[j + 1] = temp;}}}}/*** 获取顶点对应的下标，如果没找到就返回-1* @param ch* @return*/public int getIndex(char ch) {for (int i = 0; i < vertexs.length; i++) {if (ch == vertexs[i]) {return i;}}return -1;}/*** 获取下标为i的顶点的终点, 用于后面判断两个顶点的终点是否相同* @param ends* @param i* @return*/public int getEnd(int[] ends, int i) {while (ends[i] != 0) {i = ends[i];}return i;}
}class EData {char start;char end;int weight;public EData(char start, char end, int weight) {this.start = start;this.end = end;this.weight = weight;}@Overridepublic String toString() {return "EData{" +"<" + start +", " + end + ">" +", weight=" + weight+ '}';}
}