oj mrJudge
Toggle navigation
  • Login
    • Forget Password
      Login
User Image

Hello, Stranger

Guest
  • Analysis Mode
  • Problems
    • All Problems
    • Latest Problems
  • Join Us Now
  • Registration
  • Contact Us
  • Infomation
  • About
    • Terms of Use
    • Technical Specifications
    • Credits

longedge Batch , stdin/stdout

Registered Users Only

Please login to utilize this feature.

Do note that this website only supports submissions in C++.

longedge.html

Title

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 ai and vertex bi with a distance of ci.
Here, a self-loop is an edge where ai = bi (1≤i≤M), and double edges are two edges where (ai,bi)=(aj,bj) or (ai,bi)=(bj,aj) (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≤ai,bi≤N
  • 1≤ci≤1000
  • ci 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  
a1 b1 c1  
a2 b2 c2
:  
aM bM cM  

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.

Tags

Subtasks and Limits

Subtask Score #TC Time Memory Scoring
1100191s256MBAverage
2021s256MBMinimum

Judge Compile Command

g++-8 ans.cpp -o longedge -Wall -Wshadow -static -O2 -lm -m64 -s -w -std=gnu++17 -fmax-errors=512

Accepted Submissions

subIDUserTimeMax Time

Past Submissions

subIDUserTimeScore
mrJudge 09.05.20
Copyright © 2020 mrJudge. All rights reserved.