結果
問題 | No.1301 Strange Graph Shortest Path |
ユーザー |
![]() |
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 |
(要ログイン)
ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 33 |
ソースコード
from __future__ import annotationsfrom typing import NamedTuple, Optional, Listfrom heapq import heappush, heappopclass MCFGraph:class Edge(NamedTuple):src: intdst: intcap: intflow: intcost: intclass _Edge:def __init__(self, dst: int, cap: int, cost: int) -> None:self.dst = dstself.cap = capself.cost = costself.rev: Optional[MCFGraph._Edge] = Nonedef __init__(self, n: int) -> None:self._n = nself._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._nassert 0 <= dst < self._nassert 0 <= capm = len(self._edges)e = MCFGraph._Edge(dst, cap, cost)re = MCFGraph._Edge(src, 0, -cost)e.rev = rere.rev = eself._g[src].append(e)self._g[dst].append(re)self._edges.append(e)return mdef get_edge(self, i: int) -> Edge:assert 0 <= i < len(self._edges)e = self._edges[i]re = e.revreturn 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._nassert 0 <= t < self._nassert s != tif flow_limit is None:flow_limit = sum(e.cap for e in self._g[s])dual = [0] * self._nprev: List[Optional[(int, MCFGraph._Edge)]] = [None] * self._ndef refine_dual() -> bool:pq = [(0, s)]visited = [False] * self._ndist: List[Optional[int]] = [None] * self._ndist[s] = 0while pq:(dist_v, v) = heappop(pq)if visited[v]:continuevisited[v] = Trueif v == t:breakdual_v = dual[v]for e in self._g[v]:w = e.dstif visited[w] or e.cap == 0:continuereduced_cost = e.cost - dual[w] + dual_vnew_dist = dist_v + reduced_costdist_w = dist[w]if dist_w is None or new_dist < dist_w:dist[w] = new_distprev[w] = (v, e)heappush(pq, (new_dist, w))else:return Falsedist_t = dist[t]for v in range(self._n):if visited[v]:dual[v] -= dist_t - dist[v]return Trueflow = 0cost = 0prev_cost_per_flow: Optional[int] = Noneresult = [(flow, cost)]while flow < flow_limit:if not refine_dual():breakf = flow_limit - flowv = twhile prev[v] is not None:(u, e) = prev[v]f = min(f, e.cap)v = uv = twhile prev[v] is not None:(u, e) = prev[v]e.cap -= fe.rev.cap += fv = uc = -dual[s]flow += fcost += f * cif c == prev_cost_per_flow:result.pop()result.append((flow, cost))prev_cost_per_flow = creturn result# https://atcoder.jp/contests/practice2/tasks/practice2_edef main() -> None:n, m = map(int, input().split())s, t = 0, n - 1graph = 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 <= du -= 1v -= 1mid = n + igraph.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 == 2print(cost)if __name__ == '__main__':main()