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++14 (judge verdict: Accepted)

#include <cmath>
#include <cstdio>
#include <vector>
#include <iostream>
#include <algorithm>
#include <queue>
#include <string>
#include <set>
#include <map>
#define REP(i,n) for(ll i = 0; i < (ll)n; i++)
#define INF 1000000000000000
using namespace std;
typedef long long ll;
typedef double db;
typedef string str;

struct UnionFind{
  vector<ll> par;
  vector<ll> rank;
  vector<ll> sizes;

  UnionFind(ll n){
    init(n);
  }

  void init(ll n){
    par.resize(n);
    rank.resize(n);
    sizes.resize(n);
    REP(i,n){
      par[i] = i;
      rank[i] = 0;
      sizes[i] = 1;
    }
  }

  ll find(ll x){
    if(par[x] == x){
      return x;
    }else{
      return par[x] = find(par[x]);
    }
  }

  void unite(ll x, ll y){
    x = find(x);
    y = find(y);
    if(x==y) return;
    if(rank[x]<rank[y]){
      par[x] = y;
      sizes[y] += sizes[x];
    }else{
      par[y] = x;
      sizes[x] += sizes[y];
      if(rank[x]==rank[y]) rank[x]++;
    }
  }

  bool same(ll x, ll y){
    return find(x)==find(y);
  }

  ll size(ll x){
    return sizes[find(x)];
  }
};
struct edge{ll from, to, cost;};
bool compare_edge(const edge& e1, const edge& e2){
  return e1.cost<e2.cost;
}
struct graph{
  vector<edge> es;
  ll V;
  graph(ll n){
    init(n);
  }
  void init(ll n){
    V = n;
  }
  void add_edge(ll from, ll to, ll cost){
    edge e;
    e.from = from, e.to = to, e.cost = cost;
    es.push_back(e);
  }
  ll kruskal(){
    sort(es.begin(),es.end(),compare_edge);
    UnionFind uf(V);
    ll res = 0;
    for(auto e : es){
      if(!uf.same(e.from,e.to)){
        uf.unite(e.from,e.to);
        res += e.cost;
      }
    }
    return res;
  }
};

int main(){
  ll V, E;
  cin >> V >> E;
  graph g(V);
  REP(i,E){
    ll s,t,w;
    cin >> s >> t >> w;
    g.add_edge(s,t,w);
  }
  cout << g.kruskal() << endl;
  return 0;
}