Problem:
Score : 400 points

Problem Statement

You are given an undirected connected weighted graph with N vertices and M edges that contains neither self-loops nor double edges.

The i-th (1≤i≤M) edge connects vertex a_i and vertex b_i with a distance of c_i.

Here, a self-loop is an edge where a_i = b_i (1≤i≤M), and double edges are two edges where (a_i,b_i)=(a_j,b_j) or (a_i,b_i)=(b_j,a_j) (1≤i<j≤M).

A connected graph is a graph where there is a path between every pair of different vertices.

Find the number of the edges that are not contained in any shortest path between any pair of different vertices.

Constraints

2≤N≤100

N-1≤M≤min(N(N-1)/2,1000)

1≤a_i,b_i≤N

1≤c_i≤1000

c_i is an integer.

The given graph contains neither self-loops nor double edges.

The given graph is connected.

Input

The input is given from Standard Input in the following format:

N M
a_1 b_1 c_1
a_2 b_2 c_2
:
a_M b_M c_M

Output

Print the number of the edges in the graph that are not contained in any shortest path between any pair of different vertices.

Sample Input 1

3 3
1 2 1
1 3 1
2 3 3

Sample Output 1

1

In the given graph, the shortest paths between all pairs of different vertices are as follows:

The shortest path from vertex 1 to vertex 2 is: vertex 1 → vertex 2, with the length of 1.

The shortest path from vertex 1 to vertex 3 is: vertex 1 → vertex 3, with the length of 1.

The shortest path from vertex 2 to vertex 1 is: vertex 2 → vertex 1, with the length of 1.

The shortest path from vertex 2 to vertex 3 is: vertex 2 → vertex 1 → vertex 3, with the length of 2.

The shortest path from vertex 3 to vertex 1 is: vertex 3 → vertex 1, with the length of 1.

The shortest path from vertex 3 to vertex 2 is: vertex 3 → vertex 1 → vertex 2, with the length of 2.

Thus, the only edge that is not contained in any shortest path, is the edge of length 3 connecting vertex 2 and vertex 3, hence the output should be 1.

Sample Input 2

3 2
1 2 1
2 3 1

Sample Output 2

0

Every edge is contained in some shortest path between some pair of different vertices.

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;

class TEST{
	static void Main(){
		Sol mySol =new Sol();
		mySol.Solve();
	}
}

class Sol{
	public void Solve(){
		
		int Inf = (int)1e9;
		
		List<Pair>[] E = new List<Pair>[N];
		for(int i=0;i<N;i++){
			E[i] = new List<Pair>();
		}
		int[][] WF = new int[N][];
		
		for(int i=0;i<N;i++){
			WF[i] = new int[N];
			for(int j=0;j<N;j++) WF[i][j] = i == j ? 0 : Inf;
		}
		
		for(int i=0;i<M;i++){
			E[A[i]].Add(new Pair(B[i],C[i],i));
			E[B[i]].Add(new Pair(A[i],C[i],i));
			WF[A[i]][B[i]] = C[i];
			WF[B[i]][A[i]] = C[i];
		}
		
		for(int k=0;k<N;k++){
			for(int i=0;i<N;i++){
				for(int j=0;j<N;j++){
					WF[i][j] = Math.Min(WF[i][j],WF[i][k] + WF[k][j]);
				}
			}
		}
		
		bool[] used = new bool[M];
		for(int s=0;s<N;s++){
			int[] min = new int[N];
			for(int i=0;i<N;i++) min[i] = WF[s][i];
			bool[] done = new bool[N];
			for(int i=0;i<N;i++){
				int mm = Inf;
				int idx = -1;
				for(int j=0;j<N;j++){
					if(done[j])continue;
					if(mm > min[j]){
						idx = j;
						mm = min[j];
					}
				}
				
				done[idx] = true;
				foreach(var e in E[idx]){
					if(WF[s][e.To] == WF[s][idx] + e.Cost){
						used[e.Idx] = true;
					}
				}
			}
		}
		
		
		int ans = used.Count(v => v == false);
		Console.WriteLine(ans);
		
		
		
		
		
		
	}
	
	class Pair{
		public int To,Cost,Idx;
		public Pair(int t,int c,int i){
			To = t; Cost = c; Idx = i;
		}
	}
	
	
	
	int N,M;
	int[] A,B,C;
	
	public Sol(){
		var d = ria();
		N = d[0]; M = d[1];
		A = new int[M];
		B = new int[M];
		C = new int[M];
		for(int i=0;i<M;i++){
			d = ria();
			A[i] = d[0] - 1;
			B[i] = d[1] - 1;
			C[i] = d[2];
			
		}
	}

	static String rs(){return Console.ReadLine();}
	static int ri(){return int.Parse(Console.ReadLine());}
	static long rl(){return long.Parse(Console.ReadLine());}
	static double rd(){return double.Parse(Console.ReadLine());}
	static String[] rsa(char sep=' '){return Console.ReadLine().Split(sep);}
	static int[] ria(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>int.Parse(e));}
	static long[] rla(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>long.Parse(e));}
	static double[] rda(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>double.Parse(e));}
}