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 Rust (1.15.1) (judge verdict: Accepted)

use std::collections::{HashMap, HashSet};

fn main() {
    let mut input = String::new();
    let _ = std::io::stdin().read_line(&mut input).unwrap();
    let mut input = input
        .trim()
        .split_whitespace()
        .map(|x| x.parse::<usize>().unwrap());

    let n = input.next().unwrap();
    let m = input.next().unwrap();

    let mut routes: HashMap<usize, HashMap<usize, usize>> = (0..n)
        .into_iter()
        .map(|node| (node, HashMap::new()))
        .collect();
    let mut unused_routes: HashSet<(usize, usize)> = HashSet::new();

    for _ in 0..m {
        let mut input = String::new();
        let _ = std::io::stdin().read_line(&mut input).unwrap();
        let mut input = input
            .trim()
            .split_whitespace()
            .map(|x| x.parse::<usize>().unwrap());
        let a = input.next().unwrap() - 1;
        let b = input.next().unwrap() - 1;
        let cost = input.next().unwrap();
        if let Some(x) = routes.get_mut(&a) {
            x.insert(b, cost);
        }
        if let Some(x) = routes.get_mut(&b) {
            x.insert(a, cost);
        }
        unused_routes.insert((a, b));
    }
    // println!("{:?}", routes);

    let mut graph: Vec<Vec<Option<usize>>> = (0..n)
        .into_iter()
        .map(|node| {
            (0..n)
                .into_iter()
                .map(|i| routes.get(&node).unwrap().get(&i).map(|x| *x))
                .collect()
        })
        .collect();
    // println!("{:?}", graph);

    let next = warshall_floyd(&mut graph);
    // println!("{:?}", graph);
    // println!("{:?}", next);

    for s in 0..n {
        for e in 0..n {
            if s != e {
                if let Some((_, route)) = shortest_path(&graph, &next, s, e) {
                    for items in route.windows(2) {
                        unused_routes.remove(&(items[0], items[1]));
                        unused_routes.remove(&(items[1], items[0]));
                    }
                }
            }
        }
    }
    println!("{}", unused_routes.len());
}

fn warshall_floyd(dist: &mut Vec<Vec<Option<usize>>>) -> Vec<Vec<usize>> {
    let n = dist.len();
    let mut next = vec![];

    for _ in 0..n {
        next.push((0..n).map(|j| j).collect::<Vec<usize>>());
    }

    for k in 0..n {
        for i in 0..n {
            for j in 0..n {
                if let (Some(dik), Some(dkj)) = (dist[i][k], dist[k][j]) {
                    if dist[i][j].is_none() || dist[i][j].unwrap() > dik + dkj {
                        dist[i][j] = Some(dik + dkj);
                        next[i][j] = next[i][k];
                    }
                }
            }
        }
    }
    next
}

fn shortest_path(
    dist: &Vec<Vec<Option<usize>>>,
    next: &Vec<Vec<usize>>,
    start: usize,
    goal: usize,
) -> Option<(usize, Vec<usize>)> {
    if dist[start][goal].is_none() {
        return None;
    }

    let mut path = vec![start];
    let mut node = start;
    while node != goal {
        path.push(next[node][goal]);
        node = next[node][goal];
    }
    Some((dist[start][goal].unwrap(), path))
}