結果

問題 No.2604 Initial Motion
ユーザー mkawa2mkawa2
提出日時 2024-11-04 22:56:47
言語 PyPy3
(7.3.15)
結果
TLE  
実行時間 -
コード長 5,803 bytes
コンパイル時間 467 ms
コンパイル使用メモリ 82,448 KB
実行使用メモリ 199,704 KB
最終ジャッジ日時 2024-11-04 22:56:57
合計ジャッジ時間 9,366 ms
ジャッジサーバーID
(参考情報)
judge1 / judge3
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 69 ms
76,980 KB
testcase_01 AC 66 ms
69,744 KB
testcase_02 AC 65 ms
69,608 KB
testcase_03 AC 340 ms
83,172 KB
testcase_04 AC 326 ms
83,296 KB
testcase_05 AC 309 ms
82,640 KB
testcase_06 AC 336 ms
82,868 KB
testcase_07 AC 370 ms
83,336 KB
testcase_08 AC 364 ms
83,300 KB
testcase_09 AC 329 ms
83,212 KB
testcase_10 AC 363 ms
83,432 KB
testcase_11 AC 354 ms
83,608 KB
testcase_12 AC 320 ms
83,020 KB
testcase_13 TLE -
testcase_14 -- -
testcase_15 -- -
testcase_16 -- -
testcase_17 -- -
testcase_18 -- -
testcase_19 -- -
testcase_20 -- -
testcase_21 -- -
testcase_22 -- -
testcase_23 -- -
testcase_24 -- -
testcase_25 -- -
testcase_26 -- -
testcase_27 -- -
testcase_28 -- -
testcase_29 -- -
testcase_30 -- -
testcase_31 -- -
testcase_32 -- -
testcase_33 -- -
testcase_34 -- -
testcase_35 -- -
testcase_36 -- -
testcase_37 -- -
testcase_38 -- -
testcase_39 -- -
testcase_40 -- -
testcase_41 -- -
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 #

import sys

sys.setrecursionlimit(200005)
# 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 << 62)

md = 10**9+7
# md = 998244353

from heapq import *

def dijkstra(to, root=0):
    n = len(to)
    dist = [inf]*n
    dist[root] = 0
    hp = [(0, root)]
    while hp:
        d, u = heappop(hp)
        if d > dist[u]: continue
        for v, c in to[u]:
            nd = d+c
            if dist[v] <= nd: continue
            dist[v] = nd
            heappush(hp, (nd, v))

    return dist

# コストが負だと失敗するかも

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

from collections import Counter

k,n,m=LI()
aa=LI1()
bb=LI()
to=[[] for _ in range(n)]
for _ in range(m):
    u,v,c=LI1()
    c+=1
    to[u].append((v,c))
    to[v].append((u,c))

cnt=Counter()
for a in aa:
    if bb[a]:
        bb[a]-=1
    else:
        cnt[a]+=1

vv=[v for v in range(n) if bb[v]]
an=len(cnt)
bn=len(vv)
mf=MCFGraph(an+bn+2)
s=an+bn
t=s+1

i=0
for a in cnt:
    dist=dijkstra(to,a)
    mf.add_edge(s,i,cnt[a],0)
    for j,v in enumerate(vv,an):
        mf.add_edge(i,j,k,dist[v])
    i+=1
for j,v in enumerate(vv,an):
    mf.add_edge(j,t,bb[v],0)

f=mf.flow(s,t)
print(f[1])
0