結果

問題 No.14 最小公倍数ソート
ユーザー Mao-betaMao-beta
提出日時 2024-02-29 02:02:38
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 603 ms / 5,000 ms
コード長 7,126 bytes
コンパイル時間 814 ms
コンパイル使用メモリ 81,828 KB
実行使用メモリ 91,960 KB
最終ジャッジ日時 2024-02-29 02:02:52
合計ジャッジ時間 11,249 ms
ジャッジサーバーID
（参考情報） 		judge13 / judge15
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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 89 ms
78,388 KB
testcase_01 AC 90 ms
78,516 KB
testcase_02 AC 89 ms
78,388 KB
testcase_03 AC 277 ms
82,740 KB
testcase_04 AC 584 ms
91,316 KB
testcase_05 AC 443 ms
88,120 KB
testcase_06 AC 447 ms
87,864 KB
testcase_07 AC 528 ms
89,144 KB
testcase_08 AC 496 ms
89,656 KB
testcase_09 AC 553 ms
90,808 KB
testcase_10 AC 511 ms
90,168 KB
testcase_11 AC 590 ms
90,424 KB
testcase_12 AC 559 ms
90,424 KB
testcase_13 AC 573 ms
90,680 KB
testcase_14 AC 603 ms
91,320 KB
testcase_15 AC 527 ms
91,960 KB
testcase_16 AC 463 ms
88,120 KB
testcase_17 AC 402 ms
87,352 KB
testcase_18 AC 367 ms
86,204 KB
testcase_19 AC 511 ms
90,040 KB
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ソースコード

diff # 

import sys
import math
import bisect
from heapq import heapify, heappop, heappush
from collections import deque, defaultdict, Counter
from functools import lru_cache
from itertools import accumulate, combinations, permutations, product

sys.setrecursionlimit(1000000)
MOD = 10 ** 9 + 7
MOD99 = 998244353

input = lambda: sys.stdin.readline().strip()
NI = lambda: int(input())
NMI = lambda: map(int, input().split())
NLI = lambda: list(NMI())
SI = lambda: input()
SMI = lambda: input().split()
SLI = lambda: list(SMI())
EI = lambda m: [NLI() for _ in range(m)]


# 高速エラストテネス　sieve[n]はnの最小の素因数
def make_prime_table(n):
    sieve = list(range(n + 1))
    sieve[0] = -1
    sieve[1] = -1
    for i in range(4, n + 1, 2):
        sieve[i] = 2
    for i in range(3, int(n ** 0.5) + 1, 2):
        if sieve[i] != i:
            continue
        for j in range(i * i, n + 1, i * 2):
            if sieve[j] == j:
                sieve[j] = i
    return sieve

prime_table = make_prime_table(1000)
# 素数列挙
primes = [p for i, p in enumerate(prime_table) if i == p]

# 素因数分解　上のprime_tableと組み合わせて使う
def prime_factorize(n):
    result = []
    while n != 1:
        p = prime_table[n]
        e = 0
        while n % p == 0:
            n //= p
            e += 1
        result.append((p, e))
    return result


# Nの素因数分解を辞書で返す(単体)
def prime_fact(n):
    root = int(n**0.5) + 1
    prime_dict = {}
    for i in range(2, root):
        cnt = 0
        while n % i == 0:
            cnt += 1
            n = n // i
        if cnt:
            prime_dict[i] = cnt
    if n != 1:
        prime_dict[n] = 1
    return prime_dict

# 約数列挙（単体）
def divisors(x):
    res = set()
    for i in range(1, int(x**0.5) + 2):
        if x % i == 0:
            res.add(i)
            res.add(x//i)
    return res


# https://github.com/tatyam-prime/SortedSet/blob/main/SortedSet.py
# https://github.com/tatyam-prime/SortedSet/blob/main/SortedMultiset.py
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 main():
    N = NI()
    A = NLI()

    D = [SortedMultiset() for _ in range(10001)]
    divs = []
    for i, a in enumerate(A):
        div = sorted(list(divisors(a)), reverse=True)
        divs.append(div)
        for d in div:
            D[d].add((a, i))

    divx = divs[0]
    for d in divx:
        D[d].discard((A[0], 0))

    ans = [A[0]] * N

    for i in range(N-1):
        div = divisors(ans[i])
        L = 10**10
        x = -1
        idx = -1
        for d in div:
            ms = D[d]
            if len(ms) == 0:
                continue
            a, ai = ms[0]
            l = ans[i] * a // d
            # print("#", d, a, ai, l)
            if l < L or (l == L and a < x):
                L = l
                x = a
                idx = ai
        divx = divs[idx]
        for d in divx:
            D[d].discard((x, idx))

        ans[i+1] = A[idx]
        # print(L, x, idx)

    print(*ans)


if __name__ == "__main__":
    main()
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