#!/usr/bin/env python3.3
# -*- coding:utf-8 -*-
# Copyright 2013
'''
最大流：沿增广路径反复增加流，直到找不到增广路径
1）残留网络：Gf由可以容纳更多网络流的边所组成
2）增广路径：为残留网络Gf上从s到t的一条简单路径p，其中p中所的边的最小权值为该增广路径的残留容量
3）最大流最小割：对G的某个割(S,T)，有|f|=c(S,T)
'''
def edmonds_karp(graph, graph_size, s, t):
# 初始化所有边的流
flow = [[0] * graph_size for i in range(graph_size)]
while True:
# 查找增广路径
path = augmenting_path(graph, graph_size, flow, s, t)
if path is not None:
f = min(graph[u][v]-flow[u][v] for u, v in path)
for u, v in path:
flow[u][v] += f
flow[v][u] -= f
else:
break
return sum(flow[s])
def augmenting_path(graph, graph_size, flow, s, t):
visit_q = [s]
visit_path = {s:[]}
while visit_q:
# 广度优先搜索
u = visit_q.pop(0)
for v in range(graph_size):
if v not in visit_path and graph[u][v] is not None:
# 是否还有残留容量
if graph[u][v] - flow[u][v] > 0:
visit_path[v] = visit_path[u] + [(u, v)]
if v == t:
return visit_path[v]
visit_q.append(v)
return None
