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86import 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