克鲁斯卡尔（Kruskal）算法 Java实现

判断是否为回路的机制没有理解

代码所示图和边集数组



代码

public class MiniSpanTreeKruskal {

/** 邻接矩阵 */
private int[][] matrix;
/** 表示正无穷 */
private int MAX_WEIGHT = Integer.MAX_VALUE;
/**边集数组*/
private List<Edge> edgeList = new ArrayList<Edge>();

/**
* 创建图
*/
private void createGraph(int index) {
matrix = new int[index][index];
int[] v0 = { 0, 10, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 11, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT };
int[] v1 = { 10, 0, 18, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 16, MAX_WEIGHT, 12 };
int[] v2 = { MAX_WEIGHT, 18, 0, 22, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 8 };
int[] v3 = { MAX_WEIGHT, MAX_WEIGHT, 22, 0, 20, MAX_WEIGHT, MAX_WEIGHT, 16, 21 };
int[] v4 = { MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 20, 0, 26, MAX_WEIGHT, 7, MAX_WEIGHT };
int[] v5 = { 11, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 26, 0, 17, MAX_WEIGHT, MAX_WEIGHT };
int[] v6 = { MAX_WEIGHT, 16, MAX_WEIGHT, 24, MAX_WEIGHT, 17, 0, 19, MAX_WEIGHT };
int[] v7 = { MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 16, 7, MAX_WEIGHT, 19, 0, MAX_WEIGHT };
int[] v8 = { MAX_WEIGHT, 12, 8, 21, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 0 };
matrix[0] = v0;
matrix[1] = v1;
matrix[2] = v2;
matrix[3] = v3;
matrix[4] = v4;
matrix[5] = v5;
matrix[6] = v6;
matrix[7] = v7;
matrix[8] = v8;
}

/**
* 创建边集数组，并且对他们按权值从小到大排序（顺序存储结构也可以认为是数组吧）
*/
public void createEdages() {

Edge v0 = new Edge(4, 7, 7);
Edge v1 = new Edge(2, 8, 8);
Edge v2 = new Edge(0, 1, 10);
Edge v3 = new Edge(0, 5, 11);
Edge v4 = new Edge(1, 8, 12);
Edge v5 = new Edge(3, 7, 16);
Edge v6 = new Edge(1, 6, 16);
Edge v7 = new Edge(5, 6, 17);
Edge v8 = new Edge(1, 2, 18);
Edge v9 = new Edge(6, 7, 19);
Edge v10 = new Edge(3, 4, 20);
Edge v11 = new Edge(3, 8, 21);
Edge v12 = new Edge(2, 3, 22);
Edge v13 = new Edge(3, 6, 24);
Edge v14 = new Edge(4, 5, 26);

edgeList.add(v0);
edgeList.add(v1);
edgeList.add(v2);
edgeList.add(v3);
edgeList.add(v4);
edgeList.add(v5);
edgeList.add(v6);
edgeList.add(v7);
edgeList.add(v8);
edgeList.add(v9);
edgeList.add(v10);
edgeList.add(v11);
edgeList.add(v12);
edgeList.add(v13);
edgeList.add(v14);
}

// 克鲁斯卡尔算法
public void kruskal() {
//创建图和边集数组
createGraph(9);
//可以由图转出边集数组并按权从小到大排序，这里为了方便观察直接写出来了
createEdages();

//定义一个数组用来判断边与边是否形成环路
int[] parent = new int[9];

/**权值总和*/
int sum = 0;

int n, m;

//遍历边
for (int i = 0; i < edgeList.size(); i++) {
Edge edge= edgeList.get(i);
n = find(parent, edge.getBegin());
m = find(parent, edge.getEnd());

//说明形成了环路或者两个结点都在一棵树上
//注：书上没有讲解为什么这种机制可以保证形成环路，思考了半天，百度了也没有什么好的答案，研究的时间不多，就暂时就放一放吧
if (n != m) {
parent
= m;
System.out.println("(" + edge.getBegin() + "," + edge.getEnd() + ")" +edge.getWeight());

sum += edge.getWeight();
}
}

System.out.println("权值总和为：" + sum);
}

public int find(int[] parent, int index) {
while (parent[index] > 0) {
index = parent[index];
}
return index;
}

public static void main(String[] args) {
MiniSpanTreeKruskal graph = new MiniSpanTreeKruskal();
graph.kruskal();
}

}

class Edge {

private int begin;
private int end;
private int weight;

public Edge(int begin, int end, int weight) {
super();
this.begin = begin;
this.end = end;
this.weight = weight;
}

public int getBegin() {
return begin;
}

public void setBegin(int begin) {
this.begin = begin;
}

public int getEnd() {
return end;
}

public void setEnd(int end) {
this.end = end;
}

public int getWeight() {
return weight;
}

public void setWeight(int weight) {
this.weight = weight;
}

@Override
public String toString() {
return "Edge [begin=" + begin + ", end=" + end + ", weight=" + weight + "]";
}

}结果：