結果

問題 No.308 素数は通れません
コンテスト
ユーザー qwewe
提出日時 2025-05-14 12:48:58
言語 PyPy3
(7.3.15)
結果
WA  
実行時間 -
コード長 3,430 bytes
コンパイル時間 301 ms
コンパイル使用メモリ 82,632 KB
実行使用メモリ 85,396 KB
最終ジャッジ日時 2025-05-14 12:50:14
合計ジャッジ時間 7,285 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge5
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ファイルパターン 結果
other AC * 12 WA * 47 TLE * 2 -- * 46
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
import math

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 = math.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 divisors(n):
    if n == 0:
        return []
    factors = factor(n)
    from collections import defaultdict
    cnt = defaultdict(int)
    for p in factors:
        cnt[p] += 1
    divs = [1]
    for p, exp in cnt.items():
        temp = []
        for d in divs:
            current = d
            for e in range(1, exp + 1):
                current *= p
                temp.append(current)
        divs += temp
    divs = list(set(divs))
    divs.sort()
    return divs

def solve():
    N = int(sys.stdin.readline())
    if N == 1:
        print(1)
        return

    candidate = N - 1

    def check_divisors():
        if N - 1 == 0:
            return []
        divs = divisors(N - 1)
        valid = []
        for w in divs:
            if w == 0:
                continue
            if w >= N:
                continue
            k = (N - 1) // w
            ok = True
            for i in range(1, k + 1):
                num = i * w + 1
                if num == 1:
                    continue
                if is_prime(num):
                    ok = False
                    break
            if ok and w > 0:
                valid.append(w)
        return valid

    valid_divs = check_divisors()
    if valid_divs:
        min_div = min(valid_divs)
    else:
        min_div = float('inf')

    start = (N + 1) // 2
    found = None
    for W in range(start, N):
        if W <= 0:
            continue
        if not is_prime(W + 1):
            h = (N - 1) // W + 1
            row_start = (h - 1) * W + 1
            row_length = N - row_start + 1
            if row_length == 1:
                found = W
                break
            if row_length == 2:
                if not is_prime(row_start + 1):
                    found = W
                    break
            else:
                pass
    if found is not None and found < min_div and found < candidate:
        print(found)
        return

    if min_div != float('inf') and min_div < candidate:
        print(min_div)
        return

    if candidate < min_div:
        print(candidate)
    else:
        print(min_div)

solve()
0