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47 changes: 45 additions & 2 deletions dynamic_programming/floyd_warshall.py
Original file line number Diff line number Diff line change
Expand Up @@ -12,19 +12,58 @@ def __init__(self, n=0): # a graph with Node 0,1,...,N-1
] # 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)
Expand All @@ -38,5 +77,9 @@ def show_min(self, u, v):
graph.add_edge(4, 2, 4)
graph.add_edge(4, 3, 9)
graph.floyd_warshall()
graph.show_min(1, 4)
graph.show_min(0, 3)
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