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<bits/stdc++.h>
using namespace std;
using Int = long long;
//BEGIN CUT HERE
template<typename T>
struct Kruskal{
  
  struct edge{
    int from,to;
    T cost;
    int used;
    edge(int from,int to,T cost):
      from(from),to(to),cost(cost),used(0){}
    bool operator<(const edge& e) const{
      return cost<e.cost;
    }
  };

  int n;
  vector<int> r,p;
  vector<edge> es;

  Kruskal(){}
  Kruskal(int n):n(n),r(n,1),p(n){
    iota(p.begin(),p.end(),0);
  }
  
  int find(int x){
    if(x!=p[x]) p[x]=find(p[x]);
    return p[x];
  }

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

  void unite(int x,int y){
    x=find(x);y=find(y);
    if(x==y) return;
    if(r[x]<r[y]) swap(x,y);
    r[x]+=r[y];
    p[y]=x;
  }

  void add_edge(int u,int v,T c){
    es.emplace_back(u,v,c);
  }
  
  T build(){
    sort(es.begin(),es.end());
    T res=0;
    for(auto &e:es){
      if(!same(e.from,e.to)){
        res+=e.cost;
        unite(e.from,e.to);
        e.used=1;
      }
    }
    return res;
  }
};
//END CUT HERE
int main(){
  int V,E;
  scanf("%d %d",&V,&E);
  Kruskal<int> ksk(V);
  for(int i=0;i<E;i++){
    int a,b,c;
    scanf("%d %d %d",&a,&b,&c);
    ksk.add_edge(a,b,c);
  }
  printf("%d\n",ksk.build());
  return 0;
}

/*
  verified on 2018/10/22
  http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_2_A&lang=jp
*/