結果

問題 No.3219 Ruler to Maximize
ユーザー しもりん
提出日時 2025-08-01 22:09:47
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 91 ms / 2,000 ms
コード長 4,489 bytes
コンパイル時間 255 ms
コンパイル使用メモリ 82,292 KB
実行使用メモリ 79,532 KB
最終ジャッジ日時 2025-08-01 22:09:53
合計ジャッジ時間 3,943 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 2
other AC * 32
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 # 

from collections import defaultdict
import sys
import os
from typing import Any, Callable


IS_LOCAL = os.environ.get("LOCAL") == "true"


def debug(*args, sep=" ", end="\n", flush=False) -> None:
    if IS_LOCAL:
        print(*args, sep=sep, end=end, file=sys.stderr, flush=flush)


def yn(flg: bool) -> bool:
    print('Yes' if flg else 'No')
    return flg


def gcd(a, b):
    a = abs(a); b = abs(b)
    if a < b: a, b = b, a
    while b > 0:
        a, b = b, a % b
    return a


def lcm(a, b):
    return a * b // gcd(a, b)


class monoid_super:
    Base: type                          # ベースの型
    identity: Any                       # 単位元
    combine: Callable[[Any, Any], Any]  # モノイド演算

    def __init__(self, *args):
        if not args:
            self.value = self.identity
        elif len(args) == 1 and isinstance(args[0], monoid_super):
            self.value = args[0].value
        else:
            raw = args[0] if len(args) == 1 else args
            self.value = self.Base(raw)

    def __mul__(self, other):
        if not isinstance(other, type(self)):
            return NotImplemented
        new_val = self.combine(self.value, other.value)
        return type(self)(new_val)

    def __getitem__(self, x):
        return self.value[x]

    def __iter__(self):
        return self.value

    def __repr__(self):
        return f'{self.value}'


class monoid(monoid_super):

    Base = int
    identity = 0

    @staticmethod
    def combine(a, b):
        return a | b


class UnionFind_with_Value:
    def __init__(self, n) -> None:
        self.n = n
        self.parents = [-1 for _ in range(n)]
        self.value = [monoid() for _ in range(n)]
        self.potential = [0 for _ in range(n)]

    def find(self, x):
        path = []
        while self.parents[x] >= 0:
            path.append(x)
            x = self.parents[x]
        p = 0
        for y in path[::-1]:
            self.parents[y] = x
            p += self.potential[y]
            self.potential[y] = p
        return x

    def union(self, x, y, d=0):
        self.find(x); self.find(y)
        px = self.potential[x]
        py = self.potential[y]
        x = self.find(x)
        y = self.find(y)
        if x == y:
            return False
        d += px - py
        if self.parents[x] > self.parents[y]:
            x, y = y, x
            d *= -1
        self.parents[x] += self.parents[y]
        self.value[x] *= self.value[y]
        self.parents[y] = x
        self.value[y] = None
        self.potential[y] = d
        return True

    def apply(self, x, m):
        if isinstance(m, monoid):
            self.value[self.find(x)] *= m
        elif isinstance(m, monoid.Base):
            self.value[self.find(x)] *= monoid(m)
        else:
            NotImplemented

    def size(self, x):
        return -self.parents[self.find(x)]

    def prod(self, x):
        return self.value[self.find(x)].value

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def diff(self, x, y):
        assert self.same(x, y)
        return self.potential[y] - self.potential[x]

    def members(self, x):
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        group_members = defaultdict(list)
        for member in range(self.n):
            group_members[self.find(member)].append(member)
        return group_members

    def __str__(self):
        return '\n'.join(
            f'{r}: {m} {self.prod(r)}' for r, m in self.all_group_members().items()
        )


def main():
    readline = sys.stdin.readline
    float("inf")

    N = int(input())
    A = list(map(int, readline().split()))
    U = UnionFind_with_Value(N)
    for i, a in enumerate(A):
        U.apply(i, monoid(a))
    for i, a in enumerate(A):
        for j in range(i + 1, N):
            aa = A[j]
            if a & aa > 0:
                U.union(i, j)
    S = [(U.prod(i), i) for i in U.roots()]
    S.sort(reverse=True)
    W = S[0][0]
    B = sum(s for s, _ in S[1::])
    print(W * B)
    ans = [None] * N
    r = S[0][1]
    for i in range(N):
        if U.find(i) == r:
            ans[i] = 'W'
        else:
            ans[i] = 'B'
    print(''.join(ans))
    debug(W, B)
    debug(U)


if __name__ == "__main__":
    main()
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