def FloydsAlgorithm(g):
"""
(Digraph) -> DigraphAsMatrix
Floyd's algorithm to solve the all-pairs, shortest path problem
for the given edge-weighted, directed graph.
"""
n = g.numberOfVertices
distance = DenseMatrix(n, n)
for v in xrange(n):
for w in xrange(n):
distance[v, w] = sys.maxint
for e in g.edges:
distance[e.v0.number, e.v1.number] = e.weight
for i in xrange(n):
for v in xrange(n):
for w in xrange(n):
if distance[v, i] != sys.maxint and \
distance[i, w] != sys.maxint:
d = distance[v, i] + distance[i, w]
if distance[v, w] > d:
distance[v, w] = d
result = DigraphAsMatrix(n)
for v in xrange(n):
result.addVertex(v)
for v in xrange(n):
for w in xrange(n):
if distance[v, w] != sys.maxint:
result.addEdge(v, w, distance[v, w])
return result
def main(*argv):
"Demostration program number 10."
print Demo10.main.__doc__
GraphAsMatrix.main([])
DigraphAsMatrix.main([])
GraphAsLists.main([])
DigraphAsLists.main([])
return 0
def FloydsAlgorithm(g):
"""
(Digraph) -> DigraphAsMatrix
Floyd's algorithm to solve the all-pairs, shortest path problem
for the given edge-weighted, directed graph.
"""
n = g.numberOfVertices
distance = DenseMatrix(n, n)
for v in range(n):
for w in range(n):
distance[v, w] = sys.maxsize
for e in g.edges:
distance[e.v0.number, e.v1.number] = e.weight
for i in range(n):
for v in range(n):
for w in range(n):
if distance[v, i] != sys.maxsize and \
distance[i, w] != sys.maxsize:
d = distance[v, i] + distance[i, w]
if distance[v, w] > d:
distance[v, w] = d
result = DigraphAsMatrix(n)
for v in range(n):
result.addVertex(v)
for v in range(n):
for w in range(n):
if distance[v, w] != sys.maxsize:
result.addEdge(v, w, distance[v, w])
return result
