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@Ceasar
Created April 23, 2012 23:34
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Simple implementation of floyd-warhsall algorithm in Python.
def adj(g):
"""
Convert a directed graph to an adjacency matrix.
Note: The distance from a node to itself is 0 and distance from a node to
an unconnected node is defined to be infinite.
>>> g = {1: {2: 3, 3: 8, 5: -4},
... 2: {4: 1, 5: 7},
... 3: {2: 4},
... 4: {1: 2, 3: -5},
... 5: {4: 6}}
>>> adj(g) # doctest: +NORMALIZE_WHITESPACE
{1: {1: 0, 2: 3, 3: 8, 4: inf, 5: -4},
2: {1: inf, 2: 0, 3: inf, 4: 1, 5: 7},
3: {1: inf, 2: 4, 3: 0, 4: inf, 5: inf},
4: {1: 2, 2: inf, 3: -5, 4: 0, 5: inf},
5: {1: inf, 2: inf, 3: inf, 4: 6, 5: 0}}
"""
vertices = g.keys()
return {v1: {v2: 0 if v1 == v2 else g[v1].get(v2, float('inf'))
for v2 in vertices}
for v1 in vertices}
def costs_of_shortest_paths(g):
"""
Find the cost of the shortest path between every pair of vertices in a
weighted graph.
Uses the Floyd-Warshall algorithm.
:param g: An adjacency matrix.
>>> inf = float('inf')
>>> g = {0: {0: 0, 1: 1, 2: 4},
... 1: {0: inf, 1: 0, 2: 2},
... 2: {0: inf, 1: inf, 2: 0}}
>>> fw(g) # doctest: +NORMALIZE_WHITESPACE
{0: {0: 0, 1: 1, 2: 3},
1: {0: inf, 1: 0, 2: 2},
2: {0: inf, 1: inf, 2: 0}}
>>> h = {1: {2: 3, 3: 8, 5: -4},
... 2: {4: 1, 5: 7},
... 3: {2: 4},
... 4: {1: 2, 3: -5},
... 5: {4: 6}}
>>> fw(adj(h)) # doctest: +NORMALIZE_WHITESPACE
{1: {1: 0, 2: 1, 3: -3, 4: 2, 5: -4},
2: {1: 3, 2: 0, 3: -4, 4: 1, 5: -1},
3: {1: 7, 2: 4, 3: 0, 4: 5, 5: 3},
4: {1: 2, 2: -1, 3: -5, 4: 0, 5: -2},
5: {1: 8, 2: 5, 3: 1, 4: 6, 5: 0}}
"""
vertices = g.keys()
d = g
for v2 in vertices:
d = {v1: {v3: min(d[v1][v3], d[v1][v2] + d[v2][v3])
for v3 in vertices}
for v1 in vertices}
return d
if __name__ == "__main__":
import doctest
doctest.testmod()
@DavidCain
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Nice implementation, but you're missing the doctest result for fw(adj(h)). I included it.

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