"""
Description:
(1) Start with initial flow as 0;
(2) Choose augmenting path from source to sink and add path to flow;
"""
def bfs(graph, s, t, parent):
visited = [False] * len(graph)
queue = []
queue.append(s)
visited[s] = True
while queue:
u = queue.pop(0)
for ind in range(len(graph[u])):
if visited[ind] is False and graph[u][ind] > 0:
queue.append(ind)
visited[ind] = True
parent[ind] = u
return visited[t]
def ford_fulkerson(graph, source, sink):
parent = [-1] * (len(graph))
max_flow = 0
while bfs(graph, source, sink, parent):
path_flow = float("Inf")
s = sink
while s != source:
path_flow = min(path_flow, graph[parent[s]][s])
s = parent[s]
max_flow += path_flow
v = sink
while v != source:
u = parent[v]
graph[u][v] -= path_flow
graph[v][u] += path_flow
v = parent[v]
return max_flow
graph = [
[0, 16, 13, 0, 0, 0],
[0, 0, 10, 12, 0, 0],
[0, 4, 0, 0, 14, 0],
[0, 0, 9, 0, 0, 20],
[0, 0, 0, 7, 0, 4],
[0, 0, 0, 0, 0, 0],
]
source, sink = 0, 5
print(ford_fulkerson(graph, source, sink))