Description
Given a directed graph G = (V,E) with edge length l(e) and a source vertex s. Find out if there is a negative cycle in G. A negative cycle in a graph is a cycle with negative length.
# Input
The graph has `n` vertices and `m` edges.
There are m + 1 lines, the first line gives three numbers `n`,`m` and `s`(1 <= s <=n), describing the number of vertices, the number of edges and the source vertex. Each of the following lines contains three integers `a`, `b` and `c`, meaning there is an edge (a,b) belong to E and the length of the edge is c. All the numbers in a line are separated by space. (`1 <= a,b <= n`)
1 <= `n` <= 1000, 1 <= `m` <= 5000, and the length of `edge` is in the range of [-1000, 1000]. You can assume that all the vertices are reachable from `s`.
Your code should read the input from standard input (e.g.
using functions `input()/raw_input()` in Python and `cin/scanf` in C++).
# Output
One line, if there is a negative cycle, output should be ‘True’. If not, output should be ‘False’.
Your code should write the output to standard output (e.g. using functions `print` in Python and `cout/printf` in C++).
# Requirement
Your algorithm should run in O(nm) time.
Time limtation: 5 seconds.
Memory limitation: 1.0 GB.
# Environment
Your code will be running on Ubuntu 18.04.5.
Now only accept C++ and Python2/Python3 code, g++ version 7.5.0 and Python versions are Python 2.7.17 and Python 3.6.9.
# Examples and Testing
Some examples (e.g., input-x.txt and output-x.txt, x = 1, 2) are provided.
A figure corresponding input-1 can be found in this repo too.
For Python code, try the following to test your code
“`
python ./solution.py < input-x.txt > my-output-x.txt
“`
For C++ code, try the following to test your code
“`
g++ -o mybinary solution.cpp
./mybinary < input-x.txt > my-output-x.txt
“`
Your output `my-output-x.txt` needs to be *match exactly* to the given `output-x.txt`.
On Unix-based systems you can use `diff` to compare them:
“`
diff my-output-x.txt output-x.txt
“`
On Windows you can use `fc` to compare them:
“`
fc my-output-x.txt output-x.txt
“`
