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 C++ (judge verdict: Accepted)

#include<iostream>
#include<algorithm>
#include<vector>
#include<stack>
#include<queue>
#include<list>
#include<string>
#include<cstring>
#include<cstdlib>
#include<cstdio>
#include<cmath>
#include<ctime>
using namespace std;

typedef long long ll;

bool debug = false;
const int NIL = -1;
const int INF = 1000000000;
const int NUM = 100010;
clock_t START, END;

int u[NUM], v[NUM], w[NUM], p[NUM], r[NUM];
int V, E;

int cmp(const int i, const int j) {
	return w[i] < w[j];
}

int find(int x) {
	return p[x] == x ? x : p[x] = find(p[x]);
}

int Kruskal() {
	int ans = 0;
	for (int i = 0; i < V; i++)
		p[i] = i;
	for (int i = 0; i < E; i++)
		r[i] = i;
	sort(r, r + E, cmp);
	for (int i = 0; i < E; i++) {
		int e = r[i];
		int x = find(u[e]);
		int y = find(v[e]);
		if (x != y) {
			ans += w[e];
			p[x] = y;
		}
	}
	return ans;
}

int main(void)
{
	if (debug) {
		START = clock();
		freopen("in29.txt", "r", stdin);
		freopen("out.txt", "w", stdout);
	}
	int ans;
	cin >> V >> E;
	for (int i = 0; i < E; i++)
		scanf("%d%d%d", &u[i], &v[i], &w[i]);
	ans = Kruskal();
	cout << ans << endl;
	if (debug) {
		END = clock();
		double endtime = (double)(END - START) / 1000;
		printf("total time = %lf s", endtime);
	}
	return 0;
}