結果
| 問題 |
No.2713 Just Solitaire
|
| コンテスト | |
| ユーザー |
 budou
|
| 提出日時 | 2024-04-12 20:40:15 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 121 ms / 2,000 ms |
| コード長 | 9,477 bytes |
| コンパイル時間 | 303 ms |
| コンパイル使用メモリ | 82,152 KB |
| 実行使用メモリ | 79,616 KB |
| 最終ジャッジ日時 | 2024-10-02 22:51:40 |
| 合計ジャッジ時間 | 4,964 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 32 |
ソースコード
import typing
import sys
from collections import deque, defaultdict
input = lambda: sys.stdin.readline().strip()
inf = 10**18
mod = 998244353
from typing import NamedTuple, Optional, List, Tuple, cast
from heapq import heappush, heappop
from typing import NamedTuple, Optional, List, cast
class MFGraph:
class Edge(NamedTuple):
src: int
dst: int
cap: int
flow: int
class _Edge:
def __init__(self, dst: int, cap: int) -> None:
self.dst = dst
self.cap = cap
self.rev: Optional[MFGraph._Edge] = None
def __init__(self, n: int) -> None:
self._n = n
self._g: List[List[MFGraph._Edge]] = [[] for _ in range(n)]
self._edges: List[MFGraph._Edge] = []
def add_edge(self, src: int, dst: int, cap: int) -> int:
assert 0 <= src < self._n
assert 0 <= dst < self._n
assert 0 <= cap
m = len(self._edges)
e = MFGraph._Edge(dst, cap)
re = MFGraph._Edge(src, 0)
e.rev = re
re.rev = e
self._g[src].append(e)
self._g[dst].append(re)
self._edges.append(e)
return m
def get_edge(self, i: int) -> Edge:
assert 0 <= i < len(self._edges)
e = self._edges[i]
re = cast(MFGraph._Edge, e.rev)
return MFGraph.Edge(
re.dst,
e.dst,
e.cap + re.cap,
re.cap
)
def edges(self) -> List[Edge]:
return [self.get_edge(i) for i in range(len(self._edges))]
def change_edge(self, i: int, new_cap: int, new_flow: int) -> None:
assert 0 <= i < len(self._edges)
assert 0 <= new_flow <= new_cap
e = self._edges[i]
e.cap = new_cap - new_flow
assert e.rev is not None
e.rev.cap = new_flow
def flow(self, s: int, t: int, flow_limit: Optional[int] = None) -> int:
assert 0 <= s < self._n
assert 0 <= t < self._n
assert s != t
if flow_limit is None:
flow_limit = cast(int, sum(e.cap for e in self._g[s]))
current_edge = [0] * self._n
level = [0] * self._n
def fill(arr: List[int], value: int) -> None:
for i in range(len(arr)):
arr[i] = value
def bfs() -> bool:
fill(level, self._n)
queue = []
q_front = 0
queue.append(s)
level[s] = 0
while q_front < len(queue):
v = queue[q_front]
q_front += 1
next_level = level[v] + 1
for e in self._g[v]:
if e.cap == 0 or level[e.dst] <= next_level:
continue
level[e.dst] = next_level
if e.dst == t:
return True
queue.append(e.dst)
return False
def dfs(lim: int) -> int:
stack = []
edge_stack: List[MFGraph._Edge] = []
stack.append(t)
while stack:
v = stack[-1]
if v == s:
flow = min(lim, min(e.cap for e in edge_stack))
for e in edge_stack:
e.cap -= flow
assert e.rev is not None
e.rev.cap += flow
return flow
next_level = level[v] - 1
while current_edge[v] < len(self._g[v]):
e = self._g[v][current_edge[v]]
re = cast(MFGraph._Edge, e.rev)
if level[e.dst] != next_level or re.cap == 0:
current_edge[v] += 1
continue
stack.append(e.dst)
edge_stack.append(re)
break
else:
stack.pop()
if edge_stack:
edge_stack.pop()
level[v] = self._n
return 0
flow = 0
while flow < flow_limit:
if not bfs():
break
fill(current_edge, 0)
while flow < flow_limit:
f = dfs(flow_limit - flow)
flow += f
if f == 0:
break
return flow
def min_cut(self, s: int) -> List[bool]:
visited = [False] * self._n
stack = [s]
visited[s] = True
while stack:
v = stack.pop()
for e in self._g[v]:
if e.cap > 0 and not visited[e.dst]:
visited[e.dst] = True
stack.append(e.dst)
return visited
class MCFGraph:
class Edge(NamedTuple):
src: int
dst: int
cap: int
flow: int
cost: int
class _Edge:
def __init__(self, dst: int, cap: int, cost: int) -> None:
self.dst = dst
self.cap = cap
self.cost = cost
self.rev: Optional[MCFGraph._Edge] = None
def __init__(self, n: int) -> None:
self._n = n
self._g: List[List[MCFGraph._Edge]] = [[] for _ in range(n)]
self._edges: List[MCFGraph._Edge] = []
def add_edge(self, src: int, dst: int, cap: int, cost: int) -> int:
assert 0 <= src < self._n
assert 0 <= dst < self._n
assert 0 <= cap
m = len(self._edges)
e = MCFGraph._Edge(dst, cap, cost)
re = MCFGraph._Edge(src, 0, -cost)
e.rev = re
re.rev = e
self._g[src].append(e)
self._g[dst].append(re)
self._edges.append(e)
return m
def get_edge(self, i: int) -> Edge:
assert 0 <= i < len(self._edges)
e = self._edges[i]
re = cast(MCFGraph._Edge, e.rev)
return MCFGraph.Edge(
re.dst,
e.dst,
e.cap + re.cap,
re.cap,
e.cost
)
def edges(self) -> List[Edge]:
return [self.get_edge(i) for i in range(len(self._edges))]
def flow(self, s: int, t: int,
flow_limit: Optional[int] = None) -> Tuple[int, int]:
return self.slope(s, t, flow_limit)[-1]
def slope(self, s: int, t: int,
flow_limit: Optional[int] = None) -> List[Tuple[int, int]]:
assert 0 <= s < self._n
assert 0 <= t < self._n
assert s != t
if flow_limit is None:
flow_limit = cast(int, sum(e.cap for e in self._g[s]))
dual = [0] * self._n
prev: List[Optional[Tuple[int, MCFGraph._Edge]]] = [None] * self._n
def refine_dual() -> bool:
pq = [(0, s)]
visited = [False] * self._n
dist: List[Optional[int]] = [None] * self._n
dist[s] = 0
while pq:
dist_v, v = heappop(pq)
if visited[v]:
continue
visited[v] = True
if v == t:
break
dual_v = dual[v]
for e in self._g[v]:
w = e.dst
if visited[w] or e.cap == 0:
continue
reduced_cost = e.cost - dual[w] + dual_v
new_dist = dist_v + reduced_cost
dist_w = dist[w]
if dist_w is None or new_dist < dist_w:
dist[w] = new_dist
prev[w] = v, e
heappush(pq, (new_dist, w))
else:
return False
dist_t = dist[t]
for v in range(self._n):
if visited[v]:
dual[v] -= cast(int, dist_t) - cast(int, dist[v])
return True
flow = 0
cost = 0
prev_cost_per_flow: Optional[int] = None
result = [(flow, cost)]
while flow < flow_limit:
if not refine_dual():
break
f = flow_limit - flow
v = t
while prev[v] is not None:
u, e = cast(Tuple[int, MCFGraph._Edge], prev[v])
f = min(f, e.cap)
v = u
v = t
while prev[v] is not None:
u, e = cast(Tuple[int, MCFGraph._Edge], prev[v])
e.cap -= f
assert e.rev is not None
e.rev.cap += f
v = u
c = -dual[s]
flow += f
cost += f * c
if c == prev_cost_per_flow:
result.pop()
result.append((flow, cost))
prev_cost_per_flow = c
return result
def solve():
# https://yukicoder.me/problems/no/2713
N, M = map(int, input().split())
A = list(map(int, input().split()))
B = list(map(int, input().split()))
g = MFGraph(N+M+2)
# 燃やす埋める問題
# 0: 使わない(S)
# N+M+1: 使う(T)
# iを使うとx円の罰金
# Sからiにxの辺
for i in range(N):
g.add_edge(0, i+1, A[i])
g.add_edge(i+1, N+M+1,0)
# c1~ckを使うとP円の賞金 -> 1つでも使わないとP円の罰金
# cからKにinfの辺
# SからKに0, KからTにPの辺
for m in range(M):
c = list(map(int, input().split()))[1:]
for x in c:
g.add_edge(x, N+1+m, inf)
g.add_edge(0, N+1+m, 0)
g.add_edge(N+1+m, N+M+1, B[m])
print(sum(B)-g.flow(0, N+M+1))
def main():
t = 1
for _ in range(t):
solve()
main()