該文章利用prime演算法求得連通圖的最小生成樹對應的邊權最小和，prime演算法是從頂點的角度思考和解決問題。本文介紹的Kruskal演算法將從邊的角度考慮並解決問題，利用了並查集方便地解決了最小生成樹的問題。

本文參考博文

//並查集
class UnionSameSet{
	public int[] parent;
	public int[] rank;
	public int n;

	public UnionSameSet(int n){
		this.n = n;
		parent = new int[n];
		rank = new int[n];
	}
	
	public
 
 void init(){
		for(int i = 0; i < n; i++){
			parent[i] = i;
			rank[i] = 1;
		}
	}
	public int findRoot(int v){
		if(v == parent[v]){
			return v;
		}else{
			return findRoot(parent[v]);
		}
	}
	public void unite(int x, int y){
		x = findRoot(x);
		y = findRoot(y);
		if(x == y){
			return;
		}else
 
 if(rank[x] < rank[y]){
			parent[x] = y;
			if(rank[y] < rank[x] + 1){
				rank[y] = rank[x] + 1;
			}
		}else{
			parent[y] = x;
			if(rank[x] < rank[y] + 1){
				rank[x] = rank[y] + 1;
			}
		}
	}
}

class EdgeNode{
	public int st;
	public int en;
	public int weight;
}

class MyComparator
 
 implements java.util.Comparator{
	public int compare(Object ee1, Object ee2){
		EdgeNode e1 = (EdgeNode)ee1;
		EdgeNode e2 = (EdgeNode)ee2;
		if(e1.weight < e2.weight){
			return -1;
		}else if(e1.weight > e2.weight){
			return 1;
		}else{
			return 0;
		}
	}
}

public class Main {

	public static void main(String[] args){
		java.util.Scanner scan = new java.util.Scanner(System.in);		

		System.out.print("請輸入邊數：");
		int n = scan.nextInt();
	
		EdgeNode[] edges = new EdgeNode[n];
		for(int i = 0; i < n; i++){
			System.out.println("請輸入第"+(i+1)+"條邊的兩個頂點及權重：");
			edges[i] = new EdgeNode();
			edges[i].st = scan.nextInt();
			edges[i].en = scan.nextInt();
			edges[i].weight = scan.nextInt();
		}
		System.out.println("最小生成樹邊權之和："+kruskal(n, edges));
	}
	
	public static int kruskal(int n, EdgeNode[] edges){
		int sum = 0;
		UnionSameSet uss = new UnionSameSet(n);
		uss.init();
		java.util.Arrays.sort(edges, new MyComparator());
		for(int i = 0; i < n; i++){
			if(uss.findRoot(edges[i].st) != uss.findRoot(edges[i].en)){
				uss.unite(edges[i].st, edges[i].en);
				sum += edges[i].weight;
			}
		}
		return sum;
	}
}