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 JAVA (judge verdict: Accepted)

import java.io.BufferedReader;
import java.util.ArrayList;
import java.util.HashMap;
import java.io.InputStreamReader;

public class Main {
	public static void main(String[] args){
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		
		int V, E;
		
		
		String line;
		try{
			line = br.readLine();
			String[] data = line.split(" ");
			V = Integer.parseInt(data[0]);
			E = Integer.parseInt(data[1]);
			
			ArrayList<ArrayList<PairValue>> graph = new ArrayList<ArrayList<PairValue>>();
			
			
			for(int i=0; i<V; i++){
				graph.add(new ArrayList<PairValue>());
			}
			
			for(int i=0; i<E; i++){
				data = br.readLine().split(" ");
				int s = Integer.valueOf(data[0]);
				int t = Integer.valueOf(data[1]);
				int w = Integer.valueOf(data[2]);
				graph.get(s).add(new PairValue(t, w));
				graph.get(t).add(new PairValue(s,w));
				
				
			}
			
			int mst = solve(V,E,graph);
			System.out.println(mst);
			
		}catch(Exception ex){
			ex.printStackTrace();
		}  
	}
	
	private static int solve(int V, int E, ArrayList<ArrayList<PairValue>> graph){
		// create s set mstSet that keeps track of vertices already include in MST
		boolean[] mstSet = new boolean[V];
		
		
		// assign key values to all vertices in the graph, initial all key values as INFINITE
		int[] key = new int[V];
		for(int i=0; i<V; i++){
			key[i] = Integer.MAX_VALUE;
			mstSet[i] = false;
		}
		
		// assign 0 to the first vertex so that it will be picked first
		key[0] = 0;
		
		// while mstSet does not include all vertices
		/**
		 * 1. Pick a vertex u which is not there in the mstSet and has min key value
		 * 2. include u to the mstSet
		 * 3. update key values adjacent vertices of u
		 * **/
		
		int count = 0;
		int sum = 0;
		while(count < V){
			PairValue pair = minKey(key, mstSet);
			int u = pair.index;
			//System.out.println("u: "+u);
			sum += pair.weight;
			mstSet[u] = true;
			
			
			// get all adj nodes
			ArrayList<PairValue> neighbours = graph.get(u);
			for(int v=0; v<neighbours.size(); v++){
				int neighbourVertex = neighbours.get(v).index;
				int w = neighbours.get(v).weight;
				if(!mstSet[neighbourVertex] && key[neighbourVertex] > w){
					key[neighbourVertex] = w;
				}
			}
			
			
			count ++;
		}
		
				
		return sum;
	}
	
	// return min key index;
	private static PairValue minKey(int[] key, boolean[] mstSet){
		int min = Integer.MAX_VALUE;
		int index = -1;
		
		for(int i=0; i<key.length; i++){
			if(min > key[i] && !mstSet[i]){
				min = key[i];
				index = i;
			}
		}
		return new PairValue(index, min);
	}
}



class PairValue{
	int index, weight;
	public PairValue(int a, int b){
		index = a;
		weight = b;
	}
}