結果

問題 No.119 旅行のツアーの問題
ユーザー 👑 colognecologne
提出日時 2022-02-08 23:18:36
言語 Python3
(3.12.2 + numpy 1.26.4 + scipy 1.12.0)
結果
AC  
実行時間 24 ms / 5,000 ms
コード長 3,349 bytes
コンパイル時間 386 ms
コンパイル使用メモリ 11,012 KB
実行使用メモリ 9,240 KB
最終ジャッジ日時 2023-09-06 00:00:17
合計ジャッジ時間 2,589 ms
ジャッジサーバーID
（参考情報） 		judge13 / judge14
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 21 ms
8,892 KB
testcase_01 AC 22 ms
8,940 KB
testcase_02 AC 20 ms
8,852 KB
testcase_03 AC 21 ms
8,820 KB
testcase_04 AC 21 ms
8,948 KB
testcase_05 AC 20 ms
9,028 KB
testcase_06 AC 24 ms
8,948 KB
testcase_07 AC 20 ms
8,868 KB
testcase_08 AC 21 ms
8,968 KB
testcase_09 AC 20 ms
8,800 KB
testcase_10 AC 20 ms
8,992 KB
testcase_11 AC 20 ms
8,932 KB
testcase_12 AC 20 ms
8,984 KB
testcase_13 AC 20 ms
9,024 KB
testcase_14 AC 21 ms
9,016 KB
testcase_15 AC 21 ms
8,876 KB
testcase_16 AC 24 ms
9,240 KB
testcase_17 AC 20 ms
9,028 KB
testcase_18 AC 21 ms
9,040 KB
testcase_19 AC 20 ms
8,988 KB
testcase_20 AC 22 ms
8,916 KB
testcase_21 AC 23 ms
9,152 KB
testcase_22 AC 24 ms
9,236 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 collections import deque
from math import inf
import sys
sys.setrecursionlimit(10**6)


class MaxFlow:

    def __init__(self, N: int):
        self.__N = N
        self.__G = [[] for _ in range(N)]
        self.__E = []

    def add_edge(self, from_: int, to: int, cap: int) -> int:
        """
        Adds an edge oriented from vertex from_ to vertex to with capacity cap.
        Returns edge index.
        """
        assert 0 <= from_ < self.__N
        assert 0 <= to < self.__N
        assert 0 <= cap

        from_edge = [to, None, cap]
        to_edge = [from_, from_edge, 0]
        from_edge[1] = to_edge

        self.__E.append((from_edge, to_edge))
        self.__G[from_].append(from_edge)
        self.__G[to].append(to_edge)

        return len(self.__E) - 1

    def get_edge(self, i: int):
        """
        Returns i-th edge state as tuple (from_, to, cap, flow)
        """
        (to, _, flow), (from_, _, remain) = self.__E[i]
        return (from_, to, flow+remain, flow)

    def flow(self, source: int, sink: int, flow_limit: int = inf) -> float:
        """
        Returns maximum-flow from vertex source to vertex sink,
        bounded with flow_limit.
        """
        assert 0 <= source < self.__N
        assert 0 <= sink < self.__N
        assert source != sink
        assert flow_limit >= 0

        level = []
        cnt = []

        def bfs():
            level[source] = 0
            Q = deque([source])
            while len(Q) != 0:
                u = Q.popleft()
                for edg in self.__G[u]:
                    to, _, cap = edg
                    if cap > 0 and level[to] == -1:
                        level[to] = level[u] + 1
                        if to == sink:
                            return True
                        Q.append(to)
            return False

        def flow(e, f):
            if e == sink:
                return f

            while cnt[e] < len(self.__G[e]):
                edg = self.__G[e][cnt[e]]
                to, rev, cap = edg

                if cap <= 0 or level[to] <= level[e]:
                    cnt[e] += 1
                    continue

                flowed = flow(to, min(f, cap))
                if flowed > 0:
                    edg[2] -= flowed
                    rev[2] += flowed
                    return flowed

            level[e] = -1
            return 0

        answer = 0
        while flow_limit > 0:
            level = [-1] * self.__N
            cnt = [0] * self.__N

            if not bfs():
                break

            while True:
                flowed = flow(source, flow_limit)
                if flowed <= 0:
                    break

                answer += flowed
                flow_limit -= flowed

        return answer


def main():
    N = int(input())
    BC = [tuple(map(int, input().split())) for i in range(N)]
    M = int(input())
    DE = [tuple(map(int, input().split())) for i in range(M)]

    G = MaxFlow(2*N+2)
    ans = 0
    for i in range(N):
        B, C = BC[i]
        ans += max(B, C)
        G.add_edge(2*N, 2*i, max(B, C) - C)
        G.add_edge(2*i, 2*i+1, max(B, C))
        G.add_edge(2*i+1, 2*N+1, max(B, C) - B)

    for d, e in DE:
        G.add_edge(2*d+1, 2*e, inf)

    ans -= G.flow(2*N, 2*N+1)

    print(ans)


if __name__ == '__main__':
    main()
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