結果

問題 No.1301 Strange Graph Shortest Path
ユーザー Kite_kuma
提出日時 2020-10-30 22:20:50
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,878 ms / 3,000 ms
コード長 4,572 bytes
コンパイル時間 543 ms
コンパイル使用メモリ 82,344 KB
実行使用メモリ 275,560 KB
最終ジャッジ日時 2024-09-13 00:24:56
合計ジャッジ時間 49,394 ms
ジャッジサーバーID
(参考情報)
judge2 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 2
other AC * 33
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

from __future__ import annotations
from typing import NamedTuple, Optional, List
from heapq import heappush, heappop
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 = 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) -> (int, int):
return self.slope(s, t, flow_limit)[-1]
def slope(self, s: int, t: int, flow_limit: Optional[int] = None) -> List[(int, int)]:
assert 0 <= s < self._n
assert 0 <= t < self._n
assert s != t
if flow_limit is None:
flow_limit = sum(e.cap for e in self._g[s])
dual = [0] * self._n
prev: List[Optional[(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] -= dist_t - 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) = prev[v]
f = min(f, e.cap)
v = u
v = t
while prev[v] is not None:
(u, e) = prev[v]
e.cap -= f
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
# https://atcoder.jp/contests/practice2/tasks/practice2_e
def main() -> None:
n, m = map(int, input().split())
s, t = 0, n - 1
graph = MCFGraph(n + m)
for i in range(m):
u, v, c, d = map(int, input().split())
assert 1 <= u <= n and 1 <= v <= n and c <= d
u -= 1
v -= 1
mid = n + i
graph.add_edge(u, mid, 2, c)
graph.add_edge(mid, v, 1, 0)
graph.add_edge(mid, v, 1, d - c)
graph.add_edge(v, mid, 2, c)
graph.add_edge(mid, u, 1, 0)
graph.add_edge(mid, u, 1, d - c)
flow, cost = graph.flow(s, t, 2)
assert flow == 2
print(cost)
if __name__ == '__main__':
main()
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