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 Kotlin (1.0.0) (judge verdict: Accepted)

import java.util.*
import kotlin.*

import java.io.InputStream
import java.lang.NumberFormatException
import java.lang.StringBuilder


fun main(args: Array<String>) {
    Program().solve()
}

class Program {
    fun solve() {
        val sc = FastScanner()
        val n = sc.nextInt()
        val m = sc.nextInt()
        val edges = Array(m) { Triple(sc.nextInt() - 1, sc.nextInt() - 1, sc.nextInt()) }

        val dist = Array(n) { Array(n) { Int.MAX_VALUE / 2 } }

        edges.forEach {
            dist[it.first][it.second] = it.third
            dist[it.second][it.first] = it.third
        }

        for (k in 0 until n)
            for (i in 0 until n)
                for (j in 0 until n)
                    dist[i][j] = Math.min(dist[i][j], dist[i][k] + dist[k][j])

        println(edges.count { dist[it.first][it.second] != it.third })
    }
}


class FastScanner {
    companion object {
        val input: InputStream = System.`in`
        val buffer = ByteArray(1024) { 0 }
        fun isPrintableChar(c: Int): Boolean = c in 33..126
    }

    var ptr = 0
    var buflen = 0
    private fun hasNextByte(): Boolean {
        if (ptr < buflen) {
            return true
        } else {
            ptr = 0
            buflen = input.read(buffer)
            if (buflen <= 0) {
                return false
            }
        }
        return true
    }

    private fun readByte(): Int = if (hasNextByte()) buffer[ptr++].toInt() else -1

    private fun skipUnprintable() {
        while (hasNextByte() && !isPrintableChar(buffer[ptr].toInt())) ptr++
    }

    fun hasNext(): Boolean {
        skipUnprintable()
        return hasNextByte()
    }

    fun next(): String {
        if (!hasNext()) throw NoSuchElementException()
        val sb = StringBuilder()
        var b = readByte()
        while (isPrintableChar(b)) {
            sb.appendCodePoint(b)
            b = readByte()
        }
        return sb.toString()
    }

    fun nextInt(): Int {
        if (!hasNext()) throw NoSuchElementException()
        var n = 0
        var b = readByte()
        // '-' = 45
        val minus = b == 45
        if (minus) {
            b = readByte()
        }

        // '0' = 48 '9' = 57
        if (b !in 48..57) {
            throw NumberFormatException()
        }

        while (true) {
            if (b in 48..57) {
                n *= 10
                n += b - 48
            } else if (b == -1 || !isPrintableChar(b)) {
                return if (minus) -n else n
            } else {
                throw NumberFormatException()
            }
            b = readByte()
        }
    }

    fun nextLong(): Long {
        if (!hasNext()) throw NoSuchElementException()
        var n = 0L
        var b = readByte()
        // '-' = 45
        val minus = b == 45
        if (minus) {
            b = readByte()
        }

        // '0' = 48 '9' = 57
        if (b !in 48..57) {
            throw NumberFormatException()
        }

        while (true) {
            if (b in 48..57) {
                n *= 10
                n += b - 48
            } else if (b == -1 || !isPrintableChar(b)) {
                return if (minus) -n else n
            } else {
                throw NumberFormatException()
            }
            b = readByte()
        }
    }

    fun nextDouble(): Double = next().toDouble()
}