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うさぎでもわかる離散数学(グラフ理論) 第15羽 最大フロー・最小カットの求め方 | 工業大学生ももやまのうさぎ塾 https://www.momoyama-usagi.com/entry/math-risan15#i-7
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from collections import deque | |
class Dinic: | |
def __init__(self, max_v): | |
self.n = max_v | |
self.G = [[] for _ in range(self.n)] | |
def add_edge(self, fr, to, cap): # frからtoへ向かう容量capの辺を追加する | |
self.G[fr].append([to, cap, len(self.G[to])]) | |
self.G[to].append([fr, 0, len(self.G[fr]) - 1]) | |
def bfs(self, s): # sからの最短距離をBFSで計算する | |
self.level = [-1 for _ in range(self.n)] # sからの距離 | |
que = deque() | |
self.level[s] = 0 | |
que.append(s) | |
while que: | |
v = que.popleft() | |
for i in range(len(self.G[v])): | |
e = self.G[v][i] | |
if e[1] > 0 and self.level[e[0]] < 0: | |
self.level[e[0]] = self.level[v] + 1 | |
que.append(e[0]) | |
def dfs(self, v, t, f): # 増加パスをDFSで探す | |
if v == t: | |
return f | |
for i in range(self.iter[v], len(self.G[v])): | |
self.iter[v] = i | |
e = self.G[v][i] | |
if e[1] > 0 and self.level[v] < self.level[e[0]]: | |
d = self.dfs(e[0], t, min(f, e[1])) | |
if d > 0: | |
e[1] -= d | |
self.G[e[0]][e[2]][1] += d | |
return d | |
return 0 | |
def max_flow(self, s, t): | |
flow = 0 | |
while True: | |
self.bfs(s) | |
if self.level[t] < 0: | |
return flow | |
self.iter = [0 for _ in range(self.n)] # どこまで調べ終わったか | |
f = self.dfs(s, t, float("inf")) | |
while f > 0: | |
flow += f | |
f = self.dfs(s, t, float("inf")) | |
N = 7 | |
g = Dinic(N) | |
g.add_edge(0, 1, 12) # (0)渋谷 -> (1)新宿 12 | |
g.add_edge(0, 2, 25) # (0)渋谷 -> (2)表参道 25 | |
g.add_edge(2, 1, 3) # (2)表参道 -> (1)新宿 3 | |
g.add_edge(1, 3, 25) # (1)新宿 -> (3)御茶ノ水 25 | |
g.add_edge(2, 4, 18) # (2)表参道 -> (4)霞が関 18 | |
g.add_edge(2, 5, 2) # (2)表参道 -> (5)赤坂見附 2 | |
g.add_edge(5, 1, 3) # (5)赤坂見附 -> (1)新宿 3 | |
g.add_edge(5, 3, 2) # (5)赤坂見附 -> (3)御茶ノ水 2 | |
g.add_edge(4, 5, 2) # (4)霞が関 -> (5)赤坂見附 2 | |
g.add_edge(4, 3, 8) # (4)霞が関 -> (3)御茶ノ水 8 | |
g.add_edge(3, 6, 21) # (3)御茶ノ水 -> (6)東京 21 | |
g.add_edge(4, 6, 17) # (4)霞が関 -> (6)東京 17 | |
print(g.max_flow(0, 6)) |
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実行結果
35