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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Comparator;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.List;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.Set;
import java.util.StringTokenizer;
import java.util.TreeMap;

public class Main {

	public static void main(String[] args) throws IOException {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskX solver = new TaskX();
		solver.solve(1, in, out);
		out.close();
	}

	static class TaskX {
		public void solve(int testNumber, InputReader in, PrintWriter out) {

			// input
			int n = in.nextInt();
			int myN = 101;
			List<Edge>[] list = new ArrayList[myN];
			int m = in.nextInt();
			for (int i = 0; i < myN; i++) {
				list[i] = new ArrayList<>();
			}
			int[][] edge = new int[myN][myN];
			Node[] nodes = new Node[myN];
			Set<Integer> s = new HashSet<>();
			for (int i = 0; i < m; i++) {
				int a = in.nextInt()-1;
				int b = in.nextInt()-1;
				int c = in.nextInt();
				list[a].add(new Edge(b, c));
				list[b].add(new Edge(a, c));
				edge[a][b] = c;
				s.add((a+1)*1000+(b+1));
			}

			// solve
			int[][] dist = new int[myN][myN];
			for (int l = 0; l < n; l++) {
				for (int i = 0; i < n; i++) {
					nodes[i] = new Node(i, Integer.MAX_VALUE);
				}

				PriorityQueue<Node> pq = new PriorityQueue<Node>(new MyComparator());

				nodes[l].cost = 0;
				pq.add(nodes[l]);

				while (!pq.isEmpty()) {
					Node node = pq.remove();

					for (int i = 0; i < list[node.nodeNum].size(); i++) {
						int toNodeNum = list[node.nodeNum].get(i).toNodeNum;
						int moveWeight = list[node.nodeNum].get(i).weight;
						if (node.cost + moveWeight < nodes[toNodeNum].cost) {
							nodes[toNodeNum].cost = node.cost + moveWeight;
							pq.add(nodes[toNodeNum]);
						}
					}
				}

				for (int i = 0; i < n; i++) {
					dist[l][i] = nodes[i].cost;
				}
			}

			for (int k = 0; k < n; k++) {
				for (int i = 0; i < n; i++) {
					for (int j = 0; j < n; j++) {
						if (dist[k][i] + edge[i][j] == dist[k][j]) {
							s.remove((i+1)*1000+(j+1));
						}
					}
				}
			}
			out.println(s.size());

		}
	}

	@SuppressWarnings("rawtypes")
	/**
	 * 昇順ソート
	 * */
	static class MyComparator implements Comparator {

		public int compare(Object o1, Object o2) {

			Node n1 = (Node) o1;
			Node n2 = (Node) o2;

			int cost1 = n1.cost;
			int cost2 = n2.cost;

			if (cost1 > cost2) {
				return 1;
			} else if (cost1 < cost2) {
				return -1;
			} else {
				return 0;
			}
		}
	}

	static class Node {
		int nodeNum;
		int cost;

		public Node(int nodeNum, int weight) {
			this.nodeNum = nodeNum;
			this.cost = weight;
		}
	}
	static class Edge {
		int toNodeNum;
		int weight;

		public Edge(int nodeNum, int weight) {
			this.toNodeNum = nodeNum;
			this.weight = weight;
		}
	}

	static class ArrayUtils {
		public static Map<Integer, Integer> getCountMap(int[] array) {
			Map<Integer, Integer> map = new TreeMap<>();
			for (int x : array)
				map.merge(x, 1, Integer::sum);
			return map;
		}
	}

	static class InputReader {
		BufferedReader in;
		StringTokenizer tok;

		public String nextString() {
			while (!tok.hasMoreTokens()) {
				try {
					tok = new StringTokenizer(in.readLine(), " ");
				} catch (IOException e) {
					throw new InputMismatchException();
				}
			}
			return tok.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(nextString());
		}

		public long nextLong() {
			return Long.parseLong(nextString());
		}

		public int[] nextIntArray(int n) {
			int[] res = new int[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextInt();
			}
			return res;
		}

		public long[] nextLongArray(int n) {
			long[] res = new long[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextLong();
			}
			return res;
		}

		public InputReader(InputStream inputStream) {
			in = new BufferedReader(new InputStreamReader(inputStream));
			tok = new StringTokenizer("");
		}

	}

}