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>
#define rep(i, to) for (int i = 0; i < (to); i++)
#define rrep(i, to) for (int i = (to) - 1; i >= 0; i--)
#define repf(i, from, to) for (int i = (from); i < (to); i++)
#define all(v) v.begin(), v.end()
#define unless(cond) if (!(cond))
using namespace std;
using ll = long long;
template <typename T>
using V = vector<T>;
template <typename T, typename U>
using P = pair<T, U>;

struct UnionFind {
  V<int> p;

  // make set
  UnionFind(int n) {
    p.resize(n);
    rep(i, n) p[i] = i;
  }

  // union
  void unite(int a, int b) {
    int root_a = root(a);
    int root_b = root(b);

    p[root_a] = root_b;
  }

  // find
  int root(int i) {
    if(p[i] == i) {
      return i;
    }
    return p[i] = root(p[i]);
  }

  bool same(int a, int b) {
    return root(a) == root(b);
  }
};

struct Edge {
  int from, to;
  int cost;

  bool operator <(const Edge &other) const {
    return cost < other.cost;
  }
};

int main() {
  int v, e;

  cin >> v >> e;

  V<Edge> edges(e);
  rep(i, e) {
    int s, t, w;
    cin >> s >> t >> w;
    edges[i] = {s, t, w};
  }

  UnionFind uf(v);

  sort(edges.begin(), edges.end());

  int sum = 0;
  rep(i, e) {
    Edge edge = edges[i];

    if(uf.same(edge.from, edge.to)) {
      continue;
    }
    sum += edge.cost;
    uf.unite(edge.from, edge.to);
  }

  cout << sum << endl;
}