結果

問題 No.1301 Strange Graph Shortest Path
ユーザー mkawa2mkawa2
提出日時 2023-11-30 23:31:37
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,146 ms / 3,000 ms
コード長 5,019 bytes
コンパイル時間 447 ms
コンパイル使用メモリ 81,828 KB
実行使用メモリ 208,432 KB
最終ジャッジ日時 2023-11-30 23:33:28
合計ジャッジ時間 28,781 ms
ジャッジサーバーID
（参考情報） 		judge15 / judge12
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 62 ms
68,224 KB
testcase_01 AC 60 ms
68,224 KB
testcase_02 AC 1,146 ms
199,452 KB
testcase_03 AC 767 ms
184,696 KB
testcase_04 AC 942 ms
206,112 KB
testcase_05 AC 896 ms
201,928 KB
testcase_06 AC 939 ms
194,380 KB
testcase_07 AC 844 ms
193,748 KB
testcase_08 AC 797 ms
186,420 KB
testcase_09 AC 693 ms
185,408 KB
testcase_10 AC 676 ms
185,736 KB
testcase_11 AC 848 ms
198,056 KB
testcase_12 AC 795 ms
198,476 KB
testcase_13 AC 700 ms
197,392 KB
testcase_14 AC 911 ms
189,188 KB
testcase_15 AC 668 ms
185,848 KB
testcase_16 AC 840 ms
204,912 KB
testcase_17 AC 848 ms
203,304 KB
testcase_18 AC 863 ms
189,384 KB
testcase_19 AC 719 ms
190,252 KB
testcase_20 AC 786 ms
191,672 KB
testcase_21 AC 807 ms
199,796 KB
testcase_22 AC 931 ms
195,556 KB
testcase_23 AC 694 ms
198,668 KB
testcase_24 AC 904 ms
194,872 KB
testcase_25 AC 836 ms
204,640 KB
testcase_26 AC 824 ms
193,776 KB
testcase_27 AC 692 ms
195,892 KB
testcase_28 AC 690 ms
193,140 KB
testcase_29 AC 1,000 ms
206,104 KB
testcase_30 AC 761 ms
201,912 KB
testcase_31 AC 821 ms
202,504 KB
testcase_32 AC 61 ms
68,224 KB
testcase_33 AC 533 ms
195,296 KB
testcase_34 AC 791 ms
208,432 KB
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ソースコード

diff # 

import sys

# sys.setrecursionlimit(1000005)
# sys.set_int_max_str_digits(200005)
int1 = lambda x: int(x)-1
pDB = lambda *x: print(*x, end="\n", file=sys.stderr)
p2D = lambda x: print(*x, sep="\n", end="\n\n", file=sys.stderr)
def II(): return int(sys.stdin.readline())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def LI1(): return list(map(int1, sys.stdin.readline().split()))
def LLI1(rows_number): return [LI1() for _ in range(rows_number)]
def SI(): return sys.stdin.readline().rstrip()

dij = [(0, 1), (-1, 0), (0, -1), (1, 0)]
# dij = [(0, 1), (-1, 0), (0, -1), (1, 0), (1, 1), (1, -1), (-1, 1), (-1, -1)]
# inf = -1-(-1 << 31)
inf = -1-(-1 << 63)
# md = 10**9+7
md = 998244353

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=LI()
mf=MCFGraph(n)
for _ in range(m):
    u,v,c,d=LI()
    u,v=u-1,v-1
    mf.add_edge(u,v,1,c)
    mf.add_edge(v,u,1,c)
    mf.add_edge(u,v,1,d)
    mf.add_edge(v,u,1,d)

ans=mf.flow(0,n-1,2)
print(ans[1])
0