結果

問題 No.2604 Initial Motion
ユーザー nikoro256nikoro256
提出日時 2024-01-12 22:59:02
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 2,878 ms / 3,000 ms
コード長 4,628 bytes
コンパイル時間 265 ms
コンパイル使用メモリ 82,124 KB
実行使用メモリ 113,924 KB
最終ジャッジ日時 2024-09-27 23:46:23
合計ジャッジ時間 50,659 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge2
このコードへのチャレンジ
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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 68 ms
68,608 KB
testcase_01 AC 72 ms
68,608 KB
testcase_02 AC 72 ms
68,864 KB
testcase_03 AC 239 ms
79,172 KB
testcase_04 AC 282 ms
80,152 KB
testcase_05 AC 238 ms
79,660 KB
testcase_06 AC 299 ms
79,572 KB
testcase_07 AC 276 ms
79,840 KB
testcase_08 AC 251 ms
80,076 KB
testcase_09 AC 255 ms
80,180 KB
testcase_10 AC 233 ms
79,436 KB
testcase_11 AC 249 ms
79,988 KB
testcase_12 AC 239 ms
79,712 KB
testcase_13 AC 1,959 ms
96,364 KB
testcase_14 AC 1,196 ms
88,644 KB
testcase_15 AC 896 ms
85,816 KB
testcase_16 AC 1,533 ms
93,228 KB
testcase_17 AC 2,237 ms
101,864 KB
testcase_18 AC 2,111 ms
99,932 KB
testcase_19 AC 2,025 ms
99,204 KB
testcase_20 AC 1,713 ms
92,220 KB
testcase_21 AC 1,356 ms
89,248 KB
testcase_22 AC 2,011 ms
98,976 KB
testcase_23 AC 1,333 ms
89,156 KB
testcase_24 AC 1,833 ms
95,648 KB
testcase_25 AC 2,723 ms
104,532 KB
testcase_26 AC 1,618 ms
92,724 KB
testcase_27 AC 1,199 ms
86,656 KB
testcase_28 AC 1,512 ms
90,568 KB
testcase_29 AC 1,890 ms
94,468 KB
testcase_30 AC 1,219 ms
87,892 KB
testcase_31 AC 1,564 ms
91,400 KB
testcase_32 AC 1,708 ms
93,060 KB
testcase_33 AC 158 ms
81,004 KB
testcase_34 AC 1,496 ms
95,080 KB
testcase_35 AC 2,349 ms
113,924 KB
testcase_36 AC 2,394 ms
112,292 KB
testcase_37 AC 150 ms
80,512 KB
testcase_38 AC 147 ms
79,104 KB
testcase_39 AC 150 ms
78,856 KB
testcase_40 AC 2,855 ms
104,284 KB
testcase_41 AC 2,878 ms
103,464 KB
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 # 

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])
0