結果

問題 No.3050 Prefix Removal
ユーザー とりゐ
提出日時 2025-03-07 23:27:54
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,915 ms / 2,000 ms
コード長 5,910 bytes
コンパイル時間 511 ms
コンパイル使用メモリ 82,472 KB
実行使用メモリ 268,720 KB
最終ジャッジ日時 2025-03-07 23:28:38
合計ジャッジ時間 41,391 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge4
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ファイルパターン 結果
other AC * 55
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 # 

def naive(N, K, A):
    mx = -1 << 60
    cand = []
    for bit in range(1 << N):
        res = []
        tmp = 1
        for i in range(N):
            if (bit >> i) & 1:
                tmp += 1
            res.append(tmp)
        if tmp < K or res[0] != 1:
            continue
        val = 0
        for i in range(N):
            if res[i] <= K:
                val += res[i] * A[i]
        if val > mx:
            mx = val
            cand = []
        while res[-1] > K:
            res.pop()
        if val == mx:
            cand.append(res)
    return mx


import math
from bisect import bisect_left, bisect_right, insort
from typing import Generic, Iterable, Iterator, TypeVar, Union, List

T = TypeVar("T")


class SortedMultiset(Generic[T]):
    BUCKET_RATIO = 50
    REBUILD_RATIO = 170

    def _build(self, a=None) -> None:
        "Evenly divide `a` into buckets."
        if a is None:
            a = list(self)
        size = self.size = len(a)
        bucket_size = int(math.ceil(math.sqrt(size / self.BUCKET_RATIO)))
        self.a = [a[size * i // bucket_size : size * (i + 1) // bucket_size] for i in range(bucket_size)]

    def __init__(self, a: Iterable[T] = []) -> None:
        "Make a new SortedMultiset from iterable. / O(N) if sorted / O(N log N)"
        a = list(a)
        if not all(a[i] <= a[i + 1] for i in range(len(a) - 1)):
            a = sorted(a)
        self._build(a)

    def __iter__(self) -> Iterator[T]:
        for i in self.a:
            for j in i:
                yield j

    def __reversed__(self) -> Iterator[T]:
        for i in reversed(self.a):
            for j in reversed(i):
                yield j

    def __len__(self) -> int:
        return self.size

    def __repr__(self) -> str:
        return "SortedMultiset" + str(self.a)

    def __str__(self) -> str:
        s = str(list(self))
        return "{" + s[1 : len(s) - 1] + "}"

    def _find_bucket(self, x: T) -> List[T]:
        "Find the bucket which should contain x. self must not be empty."
        for a in self.a:
            if x <= a[-1]:
                return a
        return a

    def __contains__(self, x: T) -> bool:
        if self.size == 0:
            return False
        a = self._find_bucket(x)
        i = bisect_left(a, x)
        return i != len(a) and a[i] == x

    def count(self, x: T) -> int:
        "Count the number of x."
        return self.index_right(x) - self.index(x)

    def add(self, x: T) -> None:
        "Add an element. / O(√N)"
        if self.size == 0:
            self.a = [[x]]
            self.size = 1
            return
        a = self._find_bucket(x)
        insort(a, x)
        self.size += 1
        if len(a) > len(self.a) * self.REBUILD_RATIO:
            self._build()

    def discard(self, x: T) -> bool:
        "Remove an element and return True if removed. / O(√N)"
        if self.size == 0:
            return False
        a = self._find_bucket(x)
        i = bisect_left(a, x)
        if i == len(a) or a[i] != x:
            return False
        a.pop(i)
        self.size -= 1
        if len(a) == 0:
            self._build()
        return True

    def lt(self, x: T) -> Union[T, None]:
        "Find the largest element < x, or None if it doesn't exist."
        for a in reversed(self.a):
            if a[0] < x:
                return a[bisect_left(a, x) - 1]

    def le(self, x: T) -> Union[T, None]:
        "Find the largest element <= x, or None if it doesn't exist."
        for a in reversed(self.a):
            if a[0] <= x:
                return a[bisect_right(a, x) - 1]

    def gt(self, x: T) -> Union[T, None]:
        "Find the smallest element > x, or None if it doesn't exist."
        for a in self.a:
            if a[-1] > x:
                return a[bisect_right(a, x)]

    def ge(self, x: T) -> Union[T, None]:
        "Find the smallest element >= x, or None if it doesn't exist."
        for a in self.a:
            if a[-1] >= x:
                return a[bisect_left(a, x)]

    def __getitem__(self, x: int) -> T:
        "Return the x-th element, or IndexError if it doesn't exist."
        if x < 0:
            x += self.size
        if x < 0:
            raise IndexError
        for a in self.a:
            if x < len(a):
                return a[x]
            x -= len(a)
        raise IndexError

    def index(self, x: T) -> int:
        "Count the number of elements < x."
        ans = 0
        for a in self.a:
            if a[-1] >= x:
                return ans + bisect_left(a, x)
            ans += len(a)
        return ans

    def index_right(self, x: T) -> int:
        "Count the number of elements <= x."
        ans = 0
        for a in self.a:
            if a[-1] > x:
                return ans + bisect_right(a, x)
            ans += len(a)
        return ans


def solve(N, K, A):
    cum = [0]
    for i in range(N - 1, -1, -1):
        cum.append(cum[-1] + A[i])
    must = cum.pop()
    ans = -1 << 100
    B = cum.copy()
    B.sort(reverse=True)
    big = SortedMultiset(B[: K - 1])
    small = SortedMultiset(B[K - 1 :])
    big_sm = sum(B[: K - 1])
    cum = cum[::-1]
    for i in range(N - 1, K - 2, -1):
        off = cum[i]
        if off in big:
            big.discard(off)
            big_sm -= off
            mx = small[-1]
            big_sm += mx
            big.add(mx)
            small.discard(mx)
        else:
            small.discard(off)
        # print(big, small, big_sm)
        val = -off * K + big_sm + must
        ans = max(ans, val)
    return ans


N, K = map(int, input().split())
A = list(map(int, input().split()))
print(solve(N, K, A))
exit()

import random

while False:
    N = random.randint(1, 10)
    K = random.randint(1, N)
    A = [random.randint(-3, 3) for i in range(N)]
    ans1 = solve(N, K, A)
    ans2 = naive(N, K, A)
    print(N, K, A)
    print(ans1, ans2)
    assert ans1 == ans2
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