結果

問題 No.1611 Minimum Multiple with Double Divisors
ユーザー lam6er
提出日時 2025-04-16 01:13:59
言語 PyPy3
(7.3.15)
結果
WA  
実行時間 -
コード長 2,762 bytes
コンパイル時間 386 ms
コンパイル使用メモリ 82,088 KB
実行使用メモリ 106,364 KB
最終ジャッジ日時 2025-04-16 01:15:48
合計ジャッジ時間 24,254 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge1
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ファイルパターン 結果
sample AC * 2
other AC * 9 WA * 20 TLE * 8
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
import random
from math import gcd
from collections import defaultdict

def input():
    return sys.stdin.read()

def is_prime(n):
    if n < 2:
        return False
    for p in [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37]:
        if n % p == 0:
            return n == p
    d = n - 1
    s = 0
    while d % 2 == 0:
        d //= 2
        s += 1
    for a in [2, 325, 9375, 28178, 450775, 9780504, 1795265022]:
        if a >= n:
            continue
        x = pow(a, d, n)
        if x == 1 or x == n - 1:
            continue
        for _ in range(s - 1):
            x = pow(x, 2, n)
            if x == n - 1:
                break
        else:
            return False
    return True

def pollards_rho(n):
    if n % 2 == 0:
        return 2
    if n % 3 == 0:
        return 3
    if n % 5 == 0:
        return 5
    while True:
        c = random.randint(1, n-1)
        f = lambda x: (pow(x, 2, n) + c) % n
        x, y, d = 2, 2, 1
        while d == 1:
            x = f(x)
            y = f(f(y))
            d = gcd(abs(x - y), n)
        if d != n:
            return d

def factor(n):
    factors = []
    def _factor(n):
        if n == 1:
            return
        if is_prime(n):
            factors.append(n)
            return
        d = pollards_rho(n)
        _factor(d)
        _factor(n // d)
    _factor(n)
    return sorted(factors)

def get_prime_exponents(factors):
    counts = defaultdict(int)
    for p in factors:
        counts[p] += 1
    return counts

def find_s(primes_set):
    for p in [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]:
        if p not in primes_set:
            return p
    candidate = 101
    while True:
        if candidate > 10**6:
            break
        if is_prime(candidate) and candidate not in primes_set:
            return candidate
        candidate += 2
    candidate = 2
    while True:
        if candidate not in primes_set:
            if is_prime(candidate):
                return candidate
        candidate += 1

def solve():
    data = input().split()
    T = int(data[0])
    cases = list(map(int, data[1:T+1]))
    for X in cases:
        if X == 1:
            print(2)
            continue
        factors = factor(X)
        prime_exponents = get_prime_exponents(factors)
        primes_set = set(prime_exponents.keys())
        s = find_s(primes_set)
        Y_a = X * s
        min_power = None
        for p in prime_exponents:
            exponent = prime_exponents[p]
            current = p ** (exponent + 1)
            if min_power is None or current < min_power:
                min_power = current
        Y_b = X * min_power
        print(min(Y_a, Y_b))

if __name__ == "__main__":
    solve()
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