#1190705 (PyPy3) No.3097 Azuki Kurai

• 問題: No.3097 Azuki Kurai
• ユーザー: daikusutora
• 提出日時: 2026-09-28 20:35:09
• 言語: PyPy3 (7.3.23 + ACL)
• 結果: TLE
• 実行時間: -
• コード長: 5,666 bytes
• コンパイル時間: 81 ms
• コンパイル使用メモリ: 82,960 KB
• 実行使用メモリ: 311,484 KB
• 最終ジャッジ日時: 2026-09-28 20:35:40
• 合計ジャッジ時間: 15,042 ms
• ジャッジサーバーID （参考情報）: judge1_0 / judge2_0

ファイルパターン	結果
other	TLE * 1 -- * 31

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


N, M, K = map(int, input().split())
A = list(map(int, input().split()))
B = list(map(int, input().split()))

INF = float("inf")
for m in range(1, M + 1):
    # 0 ~ N*(m+1)-1: 各日にちに対応する頂点の番号
    # N*(m+1) ~ N*(m+1)+N*m-1: 分配器頂点
    # N*(2*m+1): 始点
    # N*(2*m+1)+1: 終点
    graph = MCFGraph(N * (2 * m + 1) + 2)
    # 始点 -> 0日目の家頂点に対して辺を張る
    for i in range(N):
        graph.add_edge(N * (2 * m + 1), i, A[i], 0)
    # j日目~j+1日目に対して辺を張る
    for j in range(m + 1):
        for i in range(N):
            if j > 0:
                if j == m and j - 1 < M and B[j - 1] != i + 1:
                    graph.add_edge(i + j * N, N * (2 * m + 1) + 1, INF, 0)
                if j - 1 < M and B[j - 1] == i + 1:
                    graph.add_edge(i + j * N, N * (2 * m + 1) + 1, INF, 1)
            if j < m:
                # 自分の家に小豆を残す辺 OK
                graph.add_edge(i + j * N, i + (j + 1) * N, INF, 0)
                if j == 0 or (j > 0 and B[j - 1] != i + 1):
                    # 自分の家から分配器への辺 OK
                    graph.add_edge(i + j * N, (i + j * N) + (N * (m + 1)), K, 0)
                    # 分配器から次のj+1日目の左隣の家と右隣の家への辺 OK
                    graph.add_edge(
                        (i + j * N) + (N * (m + 1)), (i - 1) % N + (j + 1) * N, INF, 0
                    )
                    graph.add_edge(
                        (i + j * N) + (N * (m + 1)), (i + 1) % N + (j + 1) * N, INF, 0
                    )
    print(sum(A) - graph.flow(N * (2 * m + 1), N * (2 * m + 1) + 1)[1])