結果

問題 No.1301 Strange Graph Shortest Path
ユーザー shotoyooshotoyoo
提出日時 2020-11-27 23:18:51
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,063 ms / 3,000 ms
コード長 4,510 bytes
コンパイル時間 842 ms
コンパイル使用メモリ 86,556 KB
実行使用メモリ 211,636 KB
最終ジャッジ日時 2023-10-09 22:08:20
合計ジャッジ時間 32,151 ms
ジャッジサーバーID
（参考情報） 		judge11 / judge15
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 162 ms
80,228 KB
testcase_01 AC 162 ms
80,428 KB
testcase_02 AC 1,046 ms
202,276 KB
testcase_03 AC 916 ms
185,132 KB
testcase_04 AC 1,057 ms
209,284 KB
testcase_05 AC 1,003 ms
202,028 KB
testcase_06 AC 939 ms
197,920 KB
testcase_07 AC 889 ms
195,352 KB
testcase_08 AC 853 ms
186,820 KB
testcase_09 AC 720 ms
189,000 KB
testcase_10 AC 799 ms
186,852 KB
testcase_11 AC 943 ms
202,436 KB
testcase_12 AC 855 ms
202,036 KB
testcase_13 AC 805 ms
199,912 KB
testcase_14 AC 1,027 ms
192,960 KB
testcase_15 AC 805 ms
189,152 KB
testcase_16 AC 946 ms
207,704 KB
testcase_17 AC 916 ms
205,756 KB
testcase_18 AC 948 ms
192,036 KB
testcase_19 AC 743 ms
194,736 KB
testcase_20 AC 857 ms
194,908 KB
testcase_21 AC 884 ms
202,896 KB
testcase_22 AC 1,046 ms
199,356 KB
testcase_23 AC 789 ms
201,832 KB
testcase_24 AC 954 ms
197,760 KB
testcase_25 AC 918 ms
208,224 KB
testcase_26 AC 870 ms
196,388 KB
testcase_27 AC 786 ms
198,480 KB
testcase_28 AC 812 ms
193,364 KB
testcase_29 AC 1,063 ms
209,340 KB
testcase_30 AC 909 ms
204,684 KB
testcase_31 AC 894 ms
205,500 KB
testcase_32 AC 147 ms
80,532 KB
testcase_33 AC 632 ms
196,976 KB
testcase_34 AC 866 ms
211,636 KB
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ソースコード

diff # 

import sys
input = lambda : sys.stdin.readline().rstrip()
sys.setrecursionlimit(max(1000, 10**9))
write = lambda x: sys.stdout.write(x+"\n")

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

# グラフの読み込み
n,m = map(int, input().split())
g = MCFGraph(n)
for _ in range(m):
    u,v,c,d = map(int, input().split())
    u -= 1
    v -= 1
    g.add_edge(u,v,1, c)
    g.add_edge(u,v,1, d)
    g.add_edge(v,u,1, c)
    g.add_edge(v,u,1, d)
    
val = g.flow(0,n-1,2)
# d[u][v]: (u,v)の流量
ans = val[1]
print(ans)
0