（Java数据结构和算法）最小生成树---Kruskal算法（并查集）

该文章利用prime算法求得连通图的最小生成树对应的边权最小和，prime算法是从顶点的角度思考和解决问题。本文介绍的Kruskal算法将从边的角度考虑并解决问题，利用了并查集方便地解决了最小生成树的问题。

本文参考博文

//并查集
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("请输入边数：");
		int n = scan.nextInt();
	
		EdgeNode[] edges = new EdgeNode[n];
		for(int i = 0; i < n; i++){
			System.out.println("请输入第"+(i+1)+"条边的两个顶点及权重：");
			edges[i] = new EdgeNode();
			edges[i].st = scan.nextInt();
			edges[i].en = scan.nextInt();
			edges[i].weight = scan.nextInt();
		}
		System.out.println("最小生成树边权之和："+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;
	}
}