Problem:
Minimum Spanning Tree

Find the sum of weights of edges of the Minimum Spanning Tree for a given weighted undirected graph G = (V, E).

Input

|V| |E|
s0 t0 w0
s1 t1 w1
:
s|E|-1 t|E|-1 w|E|-1

, where |V| is the number of vertices and |E| is the number of edges in the graph. The graph vertices are named with the numbers 0, 1,..., |V|-1 respectively.

si and ti represent source and target verticess of i-th edge (undirected) and wi represents the weight of the i-th edge.

Output

Print the sum of the weights of the Minimum Spanning Tree.

Constraints

1 ≤ |V| ≤ 10,000

0 ≤ |E| ≤ 100,000

0 ≤ wi ≤ 10,000

The graph is connected

There are no parallel edges

There are no self-loops

Sample Input 1

4 6
0 1 2
1 2 1
2 3 1
3 0 1
0 2 3
1 3 5

Sample Output 1

3

Sample Input 2

6 9
0 1 1
0 2 3
1 2 1
1 3 7
2 4 1
1 4 3
3 4 1
3 5 1
4 5 6

Sample Output 2

5

Solution in JAVA (judge verdict: Accepted)

import java.io.*;
import java.util.*;
import java.util.Map.Entry;

@SuppressWarnings("unused")
public class Main {
	
	//final boolean isDebug = true;
	final boolean isDebug = false;
	String fileName = "input.txt";
	FastScanner sc;
	PrintWriter out;
	final int MOD = (int)1e9+7;
	final int INF = Integer.MAX_VALUE / 2;
	
	void solve() throws Exception{
		int V = sc.nextInt();
		int E = sc.nextInt();
		ArrayList<Edge> edgeList = new ArrayList<>();
		for(int i = 0; i < E; i++){
			int s = sc.nextInt();
			int t = sc.nextInt();
			long w = sc.nextLong();
			edgeList.add(new Edge(s, t, w));
		}
		System.out.println(kruskal(V, edgeList));
	}
	
	long kruskal(int V, ArrayList<Edge> edgeList){
		Collections.sort(edgeList);
		UnionFind uf = new UnionFind(V);
		long cost = 0;
		ArrayList<Edge> res = new ArrayList<>();
		for(Edge e : edgeList){
			if(!uf.isSame(e.from, e.to)){
				uf.union(e.from, e.to);
				cost += e.cost;
				res.add(e);
			}
		}
		return cost;
	}
	
	/* end solve */
	
	/* main */
	public static void main(String[] args) throws Exception {
		new Main().m();
	}
	
	void m() throws Exception {
		long S = System.currentTimeMillis();
		sc = (isDebug) ? new FastScanner(new FileInputStream(fileName)) : new FastScanner(System.in);
		out = new PrintWriter(System.out);
		solve();
		out.flush();
		long G = System.currentTimeMillis();
		if(isDebug){
			System.out.println("---Debug---");
			System.out.printf("%8d ms", (G-S));
		}
	}
	/* end main */
}
/* end Main */

class Edge implements Comparable<Edge>{
	int from;
	int to;
	long cost;
	public Edge(int f, int t, long c){
		from = f;
		to = t;
		cost = c;
	}
	@Override
	public int compareTo(Edge o) {
		if(this.cost == o.cost) return 0;
		else{
			return (this.cost < o.cost) ? -1 : 1;
		}
	}
}

class UnionFind{
	int[] par;
	int[] rank;
	int[] size;
	int group;
	
	UnionFind(int n){
		par = new int[n];
		rank = new int[n];
		size = new int[n];
		group = n;
		for(int i = 0; i < n; i++){
			par[i] = i;
			rank[i] = 0;
			size[i] = 1;
		}
	}
	
	//経路圧縮しながらrootを求める
	int find(int x){
		if(par[x] == x){
			return x;
		}else{
			int f = find(par[x]);
			return par[x] = f;
		}
	}
	
	//ランクの小さいほうにつなげる
	boolean union(int x, int y, int w){
		x = find(x);
		y = find(y);
		if(x == y) return false;
		
		if(rank[x] < rank[y]){
			int tmp = x; x = y; y = tmp;
			w = -w;
		}
		
		//y(のroot)をx(のroot)の下にくっつける
		//yのほうが重くなる(ポテンシャルが高くなる)
		if(rank[x] == rank[y]) rank[x]++;
		group--;
		par[y] = x;
		size[x] += size[y];
		
		return true;
	}
	
	boolean union(int x, int y){
		return union(x, y, 0);
	}
	
	boolean isSame(int x, int y){
		return find(x) == find(y);
	}
}

class FastScanner {
    private InputStream in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    public FastScanner(InputStream in) {
		this.in = in;
	}
    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        }else{
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }
    private int readByte() {
    	if (hasNextByte()) return buffer[ptr++];
    	else return -1;
    }
    private static boolean isPrintableChar(int c){
    	return 33 <= c && c <= 126;
    }
    public boolean hasNext() {
    	while(hasNextByte() && !isPrintableChar(buffer[ptr]))
    		ptr++; return hasNextByte();
    }
    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    public String nextLine() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(b != 10) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b)){
                return minus ? -n : n;
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }
    public double nextDouble() {
    	return Double.parseDouble(next());
    }
}