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 | 1,915 ms / 3,000 ms |
コード長 | 4,572 bytes |
コンパイル時間 | 343 ms |
コンパイル使用メモリ | 87,096 KB |
実行使用メモリ | 279,776 KB |
最終ジャッジ日時 | 2023-10-10 21:29:59 |
合計ジャッジ時間 | 52,559 ms |
ジャッジサーバーID (参考情報) |
judge12 / judge13 |
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テストケース
テストケース表示入力 | 結果 | 実行時間 実行使用メモリ |
---|---|---|
testcase_00 | AC | 163 ms
80,528 KB |
testcase_01 | AC | 163 ms
80,552 KB |
testcase_02 | AC | 1,596 ms
271,916 KB |
testcase_03 | AC | 1,415 ms
255,216 KB |
testcase_04 | AC | 1,912 ms
273,624 KB |
testcase_05 | AC | 1,521 ms
272,068 KB |
testcase_06 | AC | 1,877 ms
270,180 KB |
testcase_07 | AC | 1,614 ms
270,272 KB |
testcase_08 | AC | 1,359 ms
256,752 KB |
testcase_09 | AC | 1,212 ms
255,064 KB |
testcase_10 | AC | 1,192 ms
251,924 KB |
testcase_11 | AC | 1,549 ms
271,176 KB |
testcase_12 | AC | 1,603 ms
271,800 KB |
testcase_13 | AC | 1,356 ms
273,456 KB |
testcase_14 | AC | 1,803 ms
268,900 KB |
testcase_15 | AC | 1,224 ms
255,640 KB |
testcase_16 | AC | 1,739 ms
273,500 KB |
testcase_17 | AC | 1,748 ms
270,712 KB |
testcase_18 | AC | 1,718 ms
269,620 KB |
testcase_19 | AC | 1,344 ms
269,432 KB |
testcase_20 | AC | 1,566 ms
270,332 KB |
testcase_21 | AC | 1,621 ms
270,952 KB |
testcase_22 | AC | 1,748 ms
271,812 KB |
testcase_23 | AC | 1,362 ms
271,040 KB |
testcase_24 | AC | 1,682 ms
270,024 KB |
testcase_25 | AC | 1,653 ms
271,808 KB |
testcase_26 | AC | 1,575 ms
270,884 KB |
testcase_27 | AC | 1,335 ms
270,420 KB |
testcase_28 | AC | 1,398 ms
270,508 KB |
testcase_29 | AC | 1,915 ms
270,000 KB |
testcase_30 | AC | 1,420 ms
271,400 KB |
testcase_31 | AC | 1,654 ms
271,188 KB |
testcase_32 | AC | 172 ms
80,552 KB |
testcase_33 | AC | 1,073 ms
269,912 KB |
testcase_34 | AC | 1,494 ms
279,776 KB |
ソースコード
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()