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PushRelabel.py
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import numpy as np
class Edge:
def __init__(self, flow, capacity, u, v):
self.flow = flow
self.capacity = capacity
self.u = u
self.v = v
class Vertex:
def __init__(self, h, e_flow):
self.h = h
self.e_flow = e_flow
class Graph:
def __init__(self, graph):
graph = np.array(graph)
cities = [graph[i, i] for i in range(np.shape(graph)[0])]
streets = []
streetsName = []
self.streetsName = streetsName
for i in range(np.shape(graph)[0]):
for j in range(np.shape(graph)[0]):
if j > i and graph[i, j] > 0:
streets.append(graph[i, j])
streetsName.append((i, j))
self.V = len(cities) + len(streets) + 2
self.edge = []
self.ver = []
for i in range(self.V):
self.ver.append(Vertex(0, 0))
for i in range(len(streets)):
self.addEdge(0, i + 1, streets[i])
for i in range(len(cities)):
self.addEdge(len(streets) + i + 1, len(self.ver) - 1, cities[i])
for i in range(len(streetsName)):
self.addEdge(i + 1, len(streets) + 1 + streetsName[i][0], np.inf)
self.addEdge(i + 1, len(streets) + 1 + streetsName[i][1], np.inf)
def addEdge(self, u, v, capacity):
self.edge.append(Edge(0, capacity, u, v))
def preflow(self, s):
self.ver[s].h = len(self.ver)
for i in range(len(self.edge)):
if (self.edge[i].u == s):
self.edge[i].flow = self.edge[i].capacity
self.ver[self.edge[i].v].e_flow += self.edge[i].flow
self.edge.append(
Edge(-self.edge[i].flow, 0, self.edge[i].v, s))
def overFlowVertex(self):
for i in range(1, len(self.ver)-1):
if (self.ver[i].e_flow > 0):
return i
return -1
def updateReverseEdgeFlow(self, i, flow):
u = self.edge[i].v
v = self.edge[i].u
for j in range(0, len(self.edge)):
if (self.edge[j].v == v and self.edge[j].u == u):
self.edge[j].flow -= flow
return
e = Edge(0, flow, u, v)
self.edge.append(e)
def push(self, u):
for i in range(0, len(self.edge)):
if (self.edge[i].u == u):
if (self.edge[i].flow == self.edge[i].capacity):
continue
if (self.ver[u].h > self.ver[self.edge[i].v].h):
flow = min(self.edge[i].capacity -
self.edge[i].flow, self.ver[u].e_flow)
self.ver[u].e_flow -= flow
self.ver[self.edge[i].v].e_flow += flow
self.edge[i].flow += flow
self.updateReverseEdgeFlow(i, flow)
return True
return False
def relabel(self, u):
mh = 2100000
for i in range(len(self.edge)):
if (self.edge[i].u == u):
if (self.edge[i].flow == self.edge[i].capacity):
continue
if (self.ver[self.edge[i].v].h < mh):
mh = self.ver[self.edge[i].v].h
self.ver[u].h = mh + 1
def getMaxFlow(self, s, t):
self.preflow(s)
while (self.overFlowVertex() != -1):
u = self.overFlowVertex()
if (self.push(u) == False):
self.relabel(u)
return self.ver[len(self.ver)-1].e_flow
# gx = [[50, 150, 0, 100],
# [150, 70, 50, 0],
# [0, 50, 60, 0],
# [100, 0, 0, 10]]
# g = Graph(gx)
# print(g.getMaxFlow(0, len(g.ver) - 1))
# for item in g.edge:
# print(item.u, item.v, item.capacity - item.flow)