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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.*;
import java.util.*;
 
 
public class Main implements Runnable {
 
  public static final int MOD = 1000000007;

  public void run() {
    Scanner scanner = new Scanner(System.in);

    int n = scanner.nextInt();
    int m = scanner.nextInt();

    List<Integer>[] paths = new List[n];
    List<Integer>[] costs = new List[n];
    boolean[][] used = new boolean[n][n];
    for (int i = 0 ; i < n ; i ++) {
      paths[i] = new ArrayList();
      costs[i] = new ArrayList();
    }
    for (int i = 0 ; i < m ; i ++) {
      int a = scanner.nextInt() - 1;
      int b = scanner.nextInt() - 1;
      int c = scanner.nextInt();
      paths[a].add(b);
      costs[a].add(c);
      paths[b].add(a);
      costs[b].add(c);
      used[a][b] = true;
      used[b][a] = true;
    }

    for (int i = 0 ; i < n ; i ++) {
      dijkstra(n, paths, costs, used, i);
    }

    int res = 0;
    for (int i = 0 ; i < n ; i ++) {
      for (int j = 0 ; j < n ; j ++) {
        if (used[i][j]) {
          res ++;
        }
      }
    }

    System.out.println(res / 2);
  }

  public void dijkstra(int n, List<Integer>[] paths, List<Integer>[] costs, boolean[][] used, int first) {
    int[] dd = new int[n];
    int[] prevs = new int[n];
    for (int i = 0 ; i < n ; i ++) {
      dd[i] = (i == first) ? 0 : Integer.MAX_VALUE;
      prevs[i] = -1;
    }
    Queue<Integer> queue = new PriorityQueue<Integer>((n1, n2) -> dd[n1.intValue()] - dd[n2.intValue()]);
    for (int i = 0 ; i < n ; i ++) {
      queue.offer(i);
    }
    while (!queue.isEmpty()) {
      int c = queue.poll();
      for (int j = 0 ; j < paths[c].size() ; j ++) {
        int b = paths[c].get(j);
        int cost = costs[c].get(j);
        if (dd[b] > dd[c] + cost) {
          dd[b] = dd[c] + cost;
          prevs[b] = c;
          if (queue.remove(b)) {
            queue.offer(b);
          }
        }
      }
    }
    for (int end = 0 ; end < n ; end ++) {
      int c = end;
      while (c != first) {
        int nc = prevs[c];
        used[c][nc] = false;
        used[nc][c] = false;
        c = nc;
      }
    }
  }

  public static void main(String[] args) {
    Main main = new Main();
    main.run();
  }
 
  // scanner slightly faster than usual ones
  public static class BetterScanner {
 
    private InputStream stream;
    private byte[] buffer = new byte[1024];
    private int pointer = 0;
    private int bufferLength = 0;
 
    public BetterScanner(InputStream stream) {
      this.stream = stream;
    }
 
    private boolean updateBuffer() {
      if (pointer >= bufferLength) {
        pointer = 0;
        try {
          bufferLength = stream.read(buffer);
        } catch (IOException exception) {
          exception.printStackTrace();
        }
        return bufferLength > 0;
      } else {
        return true;
      }
    }
 
    private int read() {
      if (updateBuffer()) {
        return buffer[pointer ++];
      } else {
        return -1;
      }
    }
 
    public boolean hasNext() {
      skipUnprintable();
      return updateBuffer();
    }
 
    private void skipUnprintable() { 
      while (updateBuffer() && !isPrintableChar(buffer[pointer])) {
        pointer ++;
      }
    }
 
    public String next() {
      if (hasNext()) {
        StringBuilder builder = new StringBuilder();
        int codePoint = read();
        while (isPrintableChar(codePoint)) {
          builder.appendCodePoint(codePoint);
          codePoint = read();
        }
        return builder.toString();
      } else {
        throw new NoSuchElementException();
      }
    }
 
    public long nextLong() {
      if (hasNext()) {
        long number = 0;
        boolean minus = false;
        int codePoint = read();
        if (codePoint == '-') {
          minus = true;
          codePoint = read();
        }
        if (codePoint >= '0' && codePoint <= '9') {
          while (true) {
            if (codePoint >= '0' && codePoint <= '9') {
              number *= 10;
              number += codePoint - '0';
            } else if (codePoint < 0 || !isPrintableChar(codePoint)) {
              return (minus) ? -number : number;
            } else {
              throw new NumberFormatException();
            }
            codePoint = read();
          }
        } else {
          throw new NumberFormatException();
        }
      } else {
        throw new NoSuchElementException();
      }
    }
 
    public int nextInt() {
      long number = nextLong();
      if (number >= Integer.MIN_VALUE && number <= Integer.MAX_VALUE) {
        return (int)number;
      } else {
        throw new NumberFormatException();
      }
    }
 
    private boolean isPrintableChar(int codePoint) {
      return codePoint >= 33 && codePoint <= 126;
    }
 
  }
 
}