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March 20, 2024 01:05
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040 - Get More Money(★7) https://atcoder.jp/contests/typical90/tasks/typical90_an
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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, W = map(int, input().split()) | |
g = Dinic(N + 2) | |
source, sink = 0, N + 1 | |
sum = 0 | |
A = list(map(int, input().split())) | |
for i in range(N): # source -> A[i], A[i] -> sink | |
g.add_edge(source, i + 1, A[i]) | |
sum += A[i] | |
g.add_edge(i + 1, sink, W) | |
for i in range(N): | |
k, *c = map(int, input().split()) | |
for j in range(k): | |
g.add_edge(c[j], i + 1, float("inf")) | |
print(sum - g.max_flow(source, sink)) |
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