mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-27 15:01:08 +00:00
f4b4ac159a
* Ruff test resolution * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
86 lines
2.2 KiB
Python
86 lines
2.2 KiB
Python
import math
|
|
|
|
|
|
class Graph:
|
|
def __init__(self, n=0): # a graph with Node 0,1,...,N-1
|
|
self.n = n
|
|
self.w = [
|
|
[math.inf for j in range(n)] for i in range(n)
|
|
] # adjacency matrix for weight
|
|
self.dp = [
|
|
[math.inf for j in range(n)] for i in range(n)
|
|
] # dp[i][j] stores minimum distance from i to j
|
|
|
|
def add_edge(self, u, v, w):
|
|
"""
|
|
Adds a directed edge from node u
|
|
to node v with weight w.
|
|
|
|
>>> g = Graph(3)
|
|
>>> g.add_edge(0, 1, 5)
|
|
>>> g.dp[0][1]
|
|
5
|
|
"""
|
|
self.dp[u][v] = w
|
|
|
|
def floyd_warshall(self):
|
|
"""
|
|
Computes the shortest paths between all pairs of
|
|
nodes using the Floyd-Warshall algorithm.
|
|
|
|
>>> g = Graph(3)
|
|
>>> g.add_edge(0, 1, 1)
|
|
>>> g.add_edge(1, 2, 2)
|
|
>>> g.floyd_warshall()
|
|
>>> g.show_min(0, 2)
|
|
3
|
|
>>> g.show_min(2, 0)
|
|
inf
|
|
"""
|
|
for k in range(self.n):
|
|
for i in range(self.n):
|
|
for j in range(self.n):
|
|
self.dp[i][j] = min(self.dp[i][j], self.dp[i][k] + self.dp[k][j])
|
|
|
|
def show_min(self, u, v):
|
|
"""
|
|
Returns the minimum distance from node u to node v.
|
|
|
|
>>> g = Graph(3)
|
|
>>> g.add_edge(0, 1, 3)
|
|
>>> g.add_edge(1, 2, 4)
|
|
>>> g.floyd_warshall()
|
|
>>> g.show_min(0, 2)
|
|
7
|
|
>>> g.show_min(1, 0)
|
|
inf
|
|
"""
|
|
return self.dp[u][v]
|
|
|
|
|
|
if __name__ == "__main__":
|
|
import doctest
|
|
|
|
doctest.testmod()
|
|
|
|
# Example usage
|
|
graph = Graph(5)
|
|
graph.add_edge(0, 2, 9)
|
|
graph.add_edge(0, 4, 10)
|
|
graph.add_edge(1, 3, 5)
|
|
graph.add_edge(2, 3, 7)
|
|
graph.add_edge(3, 0, 10)
|
|
graph.add_edge(3, 1, 2)
|
|
graph.add_edge(3, 2, 1)
|
|
graph.add_edge(3, 4, 6)
|
|
graph.add_edge(4, 1, 3)
|
|
graph.add_edge(4, 2, 4)
|
|
graph.add_edge(4, 3, 9)
|
|
graph.floyd_warshall()
|
|
print(
|
|
graph.show_min(1, 4)
|
|
) # Should output the minimum distance from node 1 to node 4
|
|
print(
|
|
graph.show_min(0, 3)
|
|
) # Should output the minimum distance from node 0 to node 3
|