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)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;
using static System.Convert;
using static System.Math;
//using Debug;
//using static System.Globalization.CultureInfo;
using System.Text;
class Program
{
    static void Main(string[] args)
    {
        Solve();
        //WriteLine(Solve());
    }
    static void Solve()
    {
        var ve = Input.ar;
        var ps = new Pair<long, Pair<int, int>>[ve[1]];
        var uf = UnionFind<int>.Make(ve[0]);
        for(var i = 0; i < ve[1]; i++)
        {
            var stw = Input.ar;
            ps[i] = new Pair<long, Pair<int, int>>(stw[2], new Pair<int, int>(stw[0], stw[1]));
        }var res = 0L;
        Array.Sort(ps);
        foreach (var p in ps)
            if (!uf.IsSame(p.v2.v1, p.v2.v2))
            {
                uf.Union(p.v2.v1, p.v2.v2);
                res += p.v1;
            }
        WriteLine(res);
    }
}

public class Input
{
    public static string read => ReadLine();
    public  static int[] ar => Array.ConvertAll(read.Split(' '), int.Parse);
    public  static int num => ToInt32(read);
    public static long[] arL => Array.ConvertAll(read.Split(' '), long.Parse);
    public  static long numL => ToInt64(read);
    public static char[][] gred(int h) 
        => Enumerable.Repeat(0, h).Select(v => read.ToCharArray()).ToArray();
    public static int[][] ar2D(int num)
        => Enumerable.Repeat(0, num).Select(v => ar).ToArray();
    public static long[][] arL2D(int num)
        => Enumerable.Repeat(0, num).Select(v => arL).ToArray();
    public const long Inf = (long)1e18;
    public const double eps = 1e-6;
    public  const string Alfa = "abcdefghijklmnopqrstuvwxyz";
    public  const int MOD = 1000000007;
}

public class UnionFind<T>
{
    private class Vertex
    {
        public T Key { get; set; }
        public Vertex Parent { get; set; }
        public int Rank { get; set; }
        public int Size { get; set; }
        public Vertex(T key, Vertex Parent = null, int rank = 0)
        {
            this.Key = key;
            this.Parent = Parent;
            this.Rank = rank;
        }
    }
    private readonly Dictionary<T, Vertex> dics;

    public UnionFind()
    {
        dics = new Dictionary<T, Vertex>();
    }
    
    public T Parent(T key)
        => FindSet(dics[key].Parent).Key;
    public int Size(T key)
        => FindSet(dics[key].Parent).Size;

    public bool IsSame(T key1, T key2)
    {
        if (!dics.ContainsKey(key1) || !dics.ContainsKey(key2))
            return false;
        return ReferenceEquals(FindSet(dics[key1]),FindSet(dics[key2]));
    }

    public bool MakeSet(T key)
    {
        if (dics.ContainsKey(key))
            return false;
        dics[key] = new Vertex(key);
        dics[key].Parent = dics[key];
        dics[key].Size = 1;
        return true;
    }

    public bool Union(T key1, T key2)
    {
        if (!dics.ContainsKey(key1) || !dics.ContainsKey(key2))
            return false;
        if (IsSame(key1, key2)) return false;
        Link(FindSet(dics[key1]), FindSet(dics[key2]));
        return true;
    }

    public static UnionFind<int> Make(int num, int eg = 0)
    {
        var uf = new UnionFind<int>();
        for (var i = 0; i < num; i++)
            uf.MakeSet(i);
        for (var i = 0; i < eg; i++)
        {
            var inp = Input.ar;
            inp[0]--;inp[1]--;
            uf.Union(inp[0], inp[1]);
        }
        return uf;
    }

    private void Link(Vertex vex1, Vertex vex2)
    {
        if (vex1.Rank > vex2.Rank)
        {
            vex2.Parent = vex1;
            vex1.Size += vex2.Size;
        }
        else
        {
            vex1.Parent = vex2;
            vex2.Size += vex1.Size;
            if (vex1.Rank == vex2.Rank)
                vex2.Rank++;
        }
    }

    private Vertex FindSet(Vertex vex)
    {
        if (!ReferenceEquals(vex.Parent, vex))
            vex.Parent = FindSet(vex.Parent);
        return vex.Parent;
    }
}

public class Pair<T1,T2>:IComparable<Pair<T1,T2>>
{
    public T1 v1;
    public T2 v2;
    public Pair():this(default(T1),default(T2)) { }
    public Pair(T1 v1,T2 v2)
    {
        this.v1 = v1;
        this.v2 = v2;
    }

    public int CompareTo(Pair<T1,T2> p)
    {
        int c = Comparer<T1>.Default.Compare(v1, p.v1);
        if (c == 0)
            c = Comparer<T2>.Default.Compare(v2, p.v2);
        return c;
    }
}