#944593 (PyPy3) No.2604 Initial Motion

• 問題: No.2604 Initial Motion
• ユーザー: rlangevin
• 提出日時: 2024-01-19 12:14:02
• 言語: PyPy3 (7.3.15)
• 結果: TLE
• 実行時間: -
• コード長: 4,583 bytes
• コンパイル時間: 319 ms
• コンパイル使用メモリ: 82,296 KB
• 実行使用メモリ: 115,156 KB
• 最終ジャッジ日時: 2024-09-28 03:24:10
• 合計ジャッジ時間: 66,185 ms
• ジャッジサーバーID （参考情報）: judge5 / judge2

ファイルパターン	結果
sample	AC * 3
other	AC * 38 TLE * 1

ソースコード

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import sys
input = sys.stdin.readline
#https://github.com/not522/ac-library-python/blob/master/atcoder/mincostflow.py
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
    
    
K, N, M = map(int, input().split())
A = list(map(int, input().split()))
B = list(map(int, input().split()))
G = MCFGraph(N + 2)
s, g = 0, N + 1
for i in range(M):
    u, v, d = map(int, input().split())
    G.add_edge(u, v, K, d)
    G.add_edge(v, u, K, d)
    
for i in range(K):
    G.add_edge(s, A[i], 1, 0)
for i in range(N):
    G.add_edge(i + 1, g, B[i], 0)
    
print(G.flow(s, g, K)[1])
 
 
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