def criticalPathAnalysis(g):
"""
(Digraph) -> DigraphAsLists
Computes the critical path in an event-node graph.
"""
n = g.numberOfVertices
earliestTime = Array(n)
earliestTime[0] = 0
g.topologicalOrderTraversal(
Algorithms.EarliestTimeVisitor(earliestTime))
latestTime = Array(n)
latestTime[n - 1] = earliestTime[n - 1]
g.depthFirstTraversal(PostOrder(
Algorithms.LatestTimeVisitor(latestTime)), 0)
slackGraph = DigraphAsLists(n)
for v in xrange(n):
slackGraph.addVertex(v)
for e in g.edges:
slack = latestTime[e.v1.number] - \
earliestTime[e.v0.number] - e.weight
slackGraph.addEdge(
e.v0.number, e.v1.number, slack)
return Algorithms.DijkstrasAlgorithm(slackGraph, 0)
def DijkstrasAlgorithm(g, s):
"""
(Digraph, int) -> DigraphAsLists
Dijkstra's algorithm to solve the single-source, shortest path problem
for the given edge-weighted, directed graph.
"""
n = g.numberOfVertices
table = Array(n)
for v in xrange(n):
table[v] = Algorithms.Entry()
table[s].distance = 0
queue = BinaryHeap(g.numberOfEdges)
queue.enqueue(Association(0, g[s]))
while not queue.isEmpty:
assoc = queue.dequeueMin()
v0 = assoc.value
if not table[v0.number].known:
table[v0.number].known = True
for e in v0.emanatingEdges:
v1 = e.mateOf(v0)
d = table[v0.number].distance + e.weight
if table[v1.number].distance > d:
table[v1.number].distance = d
table[v1.number].predecessor = v0.number
queue.enqueue(Association(d, v1))
result = DigraphAsLists(n)
for v in xrange(n):
result.addVertex(v, table[v].distance)
for v in xrange(n):
if v != s:
result.addEdge(v, table[v].predecessor)
return result
def main(*argv):
"Demostration program number 10."
print Demo10.main.__doc__
GraphAsMatrix.main([])
DigraphAsMatrix.main([])
GraphAsLists.main([])
DigraphAsLists.main([])
return 0
def criticalPathAnalysis(g):
"""
(Digraph) -> DigraphAsLists
Computes the critical path in an event-node graph.
"""
n = g.numberOfVertices
earliestTime = Array(n)
earliestTime[0] = 0
g.topologicalOrderTraversal(
Algorithms.EarliestTimeVisitor(earliestTime))
latestTime = Array(n)
latestTime[n - 1] = earliestTime[n - 1]
g.depthFirstTraversal(
PostOrder(Algorithms.LatestTimeVisitor(latestTime)), 0)
slackGraph = DigraphAsLists(n)
for v in range(n):
slackGraph.addVertex(v)
for e in g.edges:
slack = latestTime[e.v1.number] - \
earliestTime[e.v0.number] - e.weight
slackGraph.addEdge(e.v0.number, e.v1.number, slack)
return Algorithms.DijkstrasAlgorithm(slackGraph, 0)
def DijkstrasAlgorithm(g, s):
"""
(Digraph, int) -> DigraphAsLists
Dijkstra's algorithm to solve the single-source, shortest path problem
for the given edge-weighted, directed graph.
"""
n = g.numberOfVertices
table = Array(n)
for v in range(n):
table[v] = Algorithms.Entry()
table[s].distance = 0
queue = BinaryHeap(g.numberOfEdges)
queue.enqueue(Association(0, g[s]))
while not queue.isEmpty:
assoc = queue.dequeueMin()
v0 = assoc.value
if not table[v0.number].known:
table[v0.number].known = True
for e in v0.emanatingEdges:
v1 = e.mateOf(v0)
d = table[v0.number].distance + e.weight
if table[v1.number].distance > d:
table[v1.number].distance = d
table[v1.number].predecessor = v0.number
queue.enqueue(Association(d, v1))
result = DigraphAsLists(n)
for v in range(n):
result.addVertex(v, table[v].distance)
for v in range(n):
if v != s:
result.addEdge(v, table[v].predecessor)
return result
