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package com.eh.ftd.dsa.ds;
import com.google.common.collect.Lists;
import java.util.Arrays;
import java.util.Collections;
import java.util.List;
/**
* Kruskal算法
*
* @author David Li
* @create 2020/07/05 14:12
*/
public class Kruskal {
/**
* 图的邻接矩阵表现形式
* 0表示自己指向自己，值为Integer.MAX_VALUE表示无穷远
*/
private int[][] matrix;
/**
* 顶点的表现形式
*/
private List<String> vertexNames;
/**
* 保存最小生成树连通信息
*/
private Edge[] mstEdges;
class Edge implements Comparable<Edge> {
int s; // 边的起始坐标
int t; // 边的末端坐标
public Edge(int s, int t) {
this.s = s;
this.t = t;
}
@Override
public int compareTo(Edge o) {
return matrix[s][t] - matrix[o.s][o.t];
}
}
/**
* 表示顶点是否被访问过， 如果是则表明已经加入到最小生成树中
*/
private boolean[] visited;
public Kruskal(List<String> vertexNames) {
this.matrix = new int[vertexNames.size()][vertexNames.size()];
this.vertexNames = vertexNames;
this.visited = new boolean[vertexNames.size()];
mstEdges = new Edge[vertexNames.size() - 1];
for (int i = 0; i < vertexNames.size(); i++) {
for (int j = 0; j < vertexNames.size(); j++) {
if (i != j) {
matrix[i][j] = Integer.MAX_VALUE;
}
}
}
}
public void buildEdge(String v1, String v2, int weight) {
int idx1 = getIndexByVertexName(v1);
int idx2 = getIndexByVertexName(v2);
matrix[idx1][idx2] = weight;
matrix[idx2][idx1] = weight;
}
public void buildMSTWithKruskal() {
// 1. 获取所有排序后的边
List<Edge> edges = getAllSortedEdges();
// 2. 将这个边的两个顶点加入到连通网中
DisjointSet disjointSet = new DisjointSet(vertexNames.size());
int count = 0;
while (true) {
Edge edge = edges.get(0);
System.out.printf("当前边：%s,%s\n", vertexNames.get(edge.s), vertexNames.get(edge.t));
int mergeRes = disjointSet.merge(edge.s, edge.t);
// 如果没有构成环路则保存连通信息，直到所有的顶点都加入到MST
if (mergeRes == 1) {
mstEdges[count++] = edge;
}
// 继续下一条边
edges.remove(edge);
if (count == vertexNames.size() - 1) {
// 构成n-1条边说明mst已经生成
break;
}
}
}
/**
* 获取所有的边并从小到大排序
*
* @return
*/
private List<Edge> getAllSortedEdges() {
List<Edge> edges = Lists.newArrayList();
for (int i = 0; i < vertexNames.size(); i++) {
for (int j = 0; j < vertexNames.size(); j++) {
// i<=j 是因为这个图是无向图， i->j和j->i是一样的
if (matrix[i][j] == Integer.MAX_VALUE || i >= j) {
// 过滤无意义的边
continue;
}
edges.add(new Edge(i, j));
}
}
Collections.sort(edges);
return edges;
}
/**
* 获取最小生成树权值和
*
* @return
*/
public int getMinimumWeight() {
int res = 0;
for (Edge e : mstEdges) {
res += matrix[e.s][e.t];
}
return res;
}
/**
* 打印最小生成树的连通信息
*/
public void printPrimeMST() {
for (Edge edge : mstEdges) {
System.out.printf("{%s,%s}", vertexNames.get(edge.s), vertexNames.get(edge.t));
}
}
/**
* 获得顶点对应下标
*
* @param vertexName
* @return
*/
private int getIndexByVertexName(String vertexName) {
for (int i = 0; i < vertexNames.size(); i++) {
if (vertexName.equals(vertexNames.get(i))) {
return i;
}
}
throw new RuntimeException();
}
public static void main(String[] args) {
List cites = Lists.newArrayList("A", "B", "C", "D", "E", "F", "G");
Kruskal kruskal = new Kruskal(cites);
kruskal.buildEdge("A", "B", 12);
kruskal.buildEdge("A", "F", 16);
kruskal.buildEdge("A", "G", 14);
kruskal.buildEdge("B", "C", 10);
kruskal.buildEdge("B", "F", 7);
kruskal.buildEdge("C", "D", 3);
kruskal.buildEdge("C", "E", 5);
kruskal.buildEdge("C", "F", 6);
kruskal.buildEdge("D", "E", 4);
kruskal.buildEdge("E", "F", 2);
kruskal.buildEdge("E", "G", 8);
kruskal.buildEdge("F", "G", 9);
kruskal.buildMSTWithKruskal();
System.out.printf("最小生成树的权值和为: %d\n", kruskal.getMinimumWeight()); // 39
System.out.println("最小生成树的连通信息:");
kruskal.printPrimeMST();
}
}
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依次类推，直到连通网中没有孤岛
代码实现：