結果
問題 | No.2604 Initial Motion |
ユーザー | nikoro256 |
提出日時 | 2024-01-12 22:59:02 |
言語 | PyPy3 (7.3.15) |
結果 |
AC
|
実行時間 | 2,831 ms / 3,000 ms |
コード長 | 4,628 bytes |
コンパイル時間 | 257 ms |
コンパイル使用メモリ | 81,700 KB |
実行使用メモリ | 113,808 KB |
最終ジャッジ日時 | 2024-01-12 22:59:55 |
合計ジャッジ時間 | 46,710 ms |
ジャッジサーバーID (参考情報) |
judge13 / judge15 |
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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 | 61 ms
68,096 KB |
testcase_01 | AC | 60 ms
68,096 KB |
testcase_02 | AC | 70 ms
70,176 KB |
testcase_03 | AC | 221 ms
79,152 KB |
testcase_04 | AC | 264 ms
79,896 KB |
testcase_05 | AC | 251 ms
79,332 KB |
testcase_06 | AC | 260 ms
79,816 KB |
testcase_07 | AC | 252 ms
79,716 KB |
testcase_08 | AC | 234 ms
79,800 KB |
testcase_09 | AC | 243 ms
79,656 KB |
testcase_10 | AC | 235 ms
79,292 KB |
testcase_11 | AC | 241 ms
79,984 KB |
testcase_12 | AC | 223 ms
79,448 KB |
testcase_13 | AC | 1,723 ms
96,112 KB |
testcase_14 | AC | 1,131 ms
88,060 KB |
testcase_15 | AC | 849 ms
85,824 KB |
testcase_16 | AC | 1,380 ms
92,956 KB |
testcase_17 | AC | 2,036 ms
101,988 KB |
testcase_18 | AC | 1,899 ms
99,608 KB |
testcase_19 | AC | 1,875 ms
99,200 KB |
testcase_20 | AC | 1,573 ms
92,212 KB |
testcase_21 | AC | 1,228 ms
88,712 KB |
testcase_22 | AC | 1,822 ms
98,652 KB |
testcase_23 | AC | 1,257 ms
88,912 KB |
testcase_24 | AC | 1,652 ms
95,304 KB |
testcase_25 | AC | 2,383 ms
103,884 KB |
testcase_26 | AC | 1,470 ms
92,064 KB |
testcase_27 | AC | 1,096 ms
86,536 KB |
testcase_28 | AC | 1,304 ms
90,080 KB |
testcase_29 | AC | 1,743 ms
93,680 KB |
testcase_30 | AC | 1,106 ms
88,088 KB |
testcase_31 | AC | 1,380 ms
91,724 KB |
testcase_32 | AC | 1,498 ms
92,956 KB |
testcase_33 | AC | 139 ms
80,588 KB |
testcase_34 | AC | 1,437 ms
95,496 KB |
testcase_35 | AC | 2,201 ms
113,808 KB |
testcase_36 | AC | 2,323 ms
112,144 KB |
testcase_37 | AC | 137 ms
80,172 KB |
testcase_38 | AC | 134 ms
78,904 KB |
testcase_39 | AC | 141 ms
78,776 KB |
testcase_40 | AC | 2,831 ms
104,224 KB |
testcase_41 | AC | 2,813 ms
103,772 KB |
ソースコード
from typing import NamedTuple, Optional, List, Tuple, cast 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 = 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 import sys from collections import defaultdict input=sys.stdin.readline K,N,M=map(int,input().split()) A=list(map(int,input().split())) B=list(map(int,input().split())) #初期化 mf=MCFGraph(N+2) dic=defaultdict(int) for i in range(K): dic[A[i]]+=1 for k in dic.keys(): mf.add_edge(0,k,dic[k],0) for i in range(N): mf.add_edge(i+1,N+1,B[i],0) for i in range(M): u,v,d=map(int,input().split()) mf.add_edge(u,v,10**9,d) mf.add_edge(v,u,10**9,d) #flowを流す。返り値は(流れの量,費用)。O(F(N+M)log(N+M)) print(mf.flow(0,N+1,K)[1])