結果

問題 No.1690 Power Grid
コンテスト
ユーザー ntuda
提出日時 2025-08-10 22:31:38
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 468 ms / 3,000 ms
コード長 2,785 bytes
コンパイル時間 305 ms
コンパイル使用メモリ 82,712 KB
実行使用メモリ 80,436 KB
最終ジャッジ日時 2025-08-10 22:31:45
合計ジャッジ時間 6,228 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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ファイルパターン 結果
sample AC * 3
other AC * 25
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 typing


class DSU:
    '''
    Implement (union by size) + (path halving)

    Reference:
    Zvi Galil and Giuseppe F. Italiano,
    Data structures and algorithms for disjoint set union problems
    '''

    def __init__(self, n: int = 0) -> None:
        self._n = n
        self.parent_or_size = [-1] * n

    def merge(self, a: int, b: int) -> int:
        assert 0 <= a < self._n
        assert 0 <= b < self._n

        x = self.leader(a)
        y = self.leader(b)

        if x == y:
            return x

        if -self.parent_or_size[x] < -self.parent_or_size[y]:
            x, y = y, x

        self.parent_or_size[x] += self.parent_or_size[y]
        self.parent_or_size[y] = x

        return x

    def same(self, a: int, b: int) -> bool:
        assert 0 <= a < self._n
        assert 0 <= b < self._n

        return self.leader(a) == self.leader(b)

    def leader(self, a: int) -> int:
        assert 0 <= a < self._n

        parent = self.parent_or_size[a]
        while parent >= 0:
            if self.parent_or_size[parent] < 0:
                return parent
            self.parent_or_size[a], a, parent = (
                self.parent_or_size[parent],
                self.parent_or_size[parent],
                self.parent_or_size[self.parent_or_size[parent]]
            )

        return a

    def size(self, a: int) -> int:
        assert 0 <= a < self._n

        return -self.parent_or_size[self.leader(a)]

    def groups(self) -> typing.List[typing.List[int]]:
        leader_buf = [self.leader(i) for i in range(self._n)]

        result: typing.List[typing.List[int]] = [[] for _ in range(self._n)]
        for i in range(self._n):
            result[leader_buf[i]].append(i)

        return list(filter(lambda r: r, result))

from itertools import combinations
N,M,K = map(int,input().split())
A = list(map(int,input().split()))
XYZ = [list(map(int,input().split())) for _ in range(M)]
INF = 10 ** 11
cost = [[INF] * N for _ in range(N)]
for i in range(N):
    cost[i][i] = 0
for x,y,z in XYZ:
    x -= 1
    y -= 1
    cost[x][y] = z
    cost[y][x] = z
for k in range(N):
    for i in range(N):
        for j in range(N):
            if cost[i][k]!=INF and cost[k][j]!=INF:
                cost[i][j] = min(cost[i][j], cost[i][k] + cost[k][j])
Q = []
for i in range(N):
    for j in range(i+1,N):
        Q.append((cost[i][j],i,j))
Q.sort()

ans = INF
for C in combinations(range(N),K):
    tmp = 0
    C = set(C)
    for c in C:
        tmp += A[c]
    dsu = DSU(N)
    cnt = 0
    for c,a,b in Q:
        if a in C and b in C:
            if dsu.same(a,b):
                continue
            dsu.merge(a,b)
            tmp += c
            cnt += 1
            if cnt == K:
                break
    ans = min(ans,tmp)

print(ans)
0