# initialize graph
graph = [{} for i in xrange(numVertices)]
vertexnames = csv_f.next()[0].split(' ')
# sink
for i in xrange(numVertices-1):
vertexname = csv_f.next()[0]
vertexindex = vertexnames.index(vertexname)
s1 = csv_f.next()[0]
s2 = csv_f.next()[0]
s3 = csv_f.next()[0]
neighborindices = [vertexnames.index(elt) for elt in s1.split(' ')]
neighborcaps = [int(elt) for elt in s2.split(' ')]
neighborcosts = [int(elt) for elt in s3.split(' ')]
for v in xrange(len(neighborindices)):
graph[vertexindex][neighborindices[v]] = (neighborcaps[v], neighborcosts[v])
# assume source and sink already added, last two vertices
source = numVertices - 2
sink = source + 1
F, maxflow, matching = edmond_karp.edmonds_karp(graph, source, sink)
print "\nSolution:"
print "flow = %i" % maxflow
print "Matching:"
for a in matching.keys():
print "%s <--> %s" % (vertexnames[a], vertexnames[matching[a]])
data.close()
os.system("python menu.py")
def cycle_cancel(G, source, sink):
# number of vertices
n = len(G)
# find feasible maxflow
F, maxflow, matching = edmond_karp.edmonds_karp(G, source, sink)
# convert flow graph the from the maxflow to a residual graph
# remove used flow edges in F
for u in xrange(n):
for v in G[u].keys():
if F[u][v][0] > 0:
F[u][v] = (0,0)
# add unused edges from G to F
for u in xrange(n-2):
for v in G[u].keys():
if F[v][u] == (0,0):
F[u][v] = G[u][v]
# convert now residual graph F into list of dicts
resG = [{} for i in xrange(n)]
for u in xrange(n):
for v in xrange(n):
if F[u][v] != (0, 0):
resG[u][v] = (abs(F[u][v][0]), F[u][v][1])
# use Bellman-Ford to find cycles reachable from sink in residual graph
# augment along this cycle and keep doing so until no more cycles
while True:
cycle = bellman_ford(resG, sink)
if not cycle:
break
# smallest capacity of the cycle
flow = min(resG[u][v][0] for u,v in cycle)
# agument along cycle, updating flow graph and TODO residual graph
for u,v in cycle:
# update residual graph
temp = resG[u][v]
# update reverse edge
if u in resG[v].keys():
resG[v][u] = (resG[v][u][0] + flow, resG[v][u][1])
else:
resG[v][u] = (flow, -resG[u][v][1])
# update forward edge
if temp[0] == flow:
# remove edge if no more capacity
del resG[u][v]
else:
resG[u][v] = (resG[u][v][0] - flow, resG[u][v][1])
cost = 0
assignment = {}
# initialize all demand nodes
for v in resG[sink].keys():
assignment[v] = []
for u in xrange(n):
for v in resG[u].keys():
edge = resG[u][v]
if edge[1] < 0:
cost -= edge[1]
assignment[u].append(v)
return maxflow, cost, assignment
graph = [{} for i in xrange(numVertices)]
vertexnames = csv_f.next()[0].split(' ')
# sink
for i in xrange(numVertices - 1):
vertexname = csv_f.next()[0]
vertexindex = vertexnames.index(vertexname)
s1 = csv_f.next()[0]
s2 = csv_f.next()[0]
s3 = csv_f.next()[0]
neighborindices = [vertexnames.index(elt) for elt in s1.split(' ')]
neighborcaps = [int(elt) for elt in s2.split(' ')]
neighborcosts = [int(elt) for elt in s3.split(' ')]
for v in xrange(len(neighborindices)):
graph[vertexindex][neighborindices[v]] = (neighborcaps[v],
neighborcosts[v])
# assume source and sink already added, last two vertices
source = numVertices - 2
sink = source + 1
F, maxflow, matching = edmond_karp.edmonds_karp(graph, source, sink)
print "\nSolution:"
print "flow = %i" % maxflow
print "Matching:"
for a in matching.keys():
print "%s <--> %s" % (vertexnames[a], vertexnames[matching[a]])
data.close()
os.system("python menu.py")
def cycle_cancel(G, source, sink):
# number of vertices
n = len(G)
# find feasible maxflow
F, maxflow, matching = edmond_karp.edmonds_karp(G, source, sink)
# convert flow graph the from the maxflow to a residual graph
# remove used flow edges in F
for u in xrange(n):
for v in G[u].keys():
if F[u][v][0] > 0:
F[u][v] = (0,0)
# add unused edges from G to F
for u in xrange(n-2):
for v in G[u].keys():
if F[v][u] == (0,0):
F[u][v] = G[u][v]
# convert now residual graph F into list of dicts
resG = [{} for i in xrange(n)]
for u in xrange(n):
for v in xrange(n):
if F[u][v] != (0, 0):
resG[u][v] = (abs(F[u][v][0]), F[u][v][1])
# use Bellman-Ford to find cycles reachable from sink in residual graph
# augment along this cycle and keep doing so until no more cycles
while True:
cycle = bellman_ford(resG, sink)
if not cycle:
break
# smallest capacity of the cycle
flow = min(resG[u][v][0] for u,v in cycle)
# agument along cycle, updating flow graph and TODO residual graph
for u,v in cycle:
# update residual graph
temp = resG[u][v]
# update reverse edge
if u in resG[v].keys():
resG[v][u] = (resG[v][u][0] + flow, resG[v][u][1])
else:
resG[v][u] = (flow, -resG[u][v][1])
# update forward edge
if temp[0] == flow:
# remove edge if no more capacity
del resG[u][v]
else:
resG[u][v] = (resG[u][v][0] - flow, resG[u][v][1])
cost = 0
assignment = {}
# initialize all demand nodes
for v in resG[sink].keys():
assignment[v] = []
for u in xrange(n):
for v in resG[u].keys():
edge = resG[u][v]
if edge[1] < 0:
cost -= edge[1]
assignment[u].append(v)
return maxflow, cost, assignment
