結果

問題 No.917 Make One With GCD
コンテスト
ユーザー lam6er
提出日時 2025-03-20 20:45:37
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 88 ms / 2,000 ms
コード長 2,397 bytes
コンパイル時間 462 ms
コンパイル使用メモリ 82,172 KB
実行使用メモリ 77,380 KB
最終ジャッジ日時 2025-03-20 20:45:41
合計ジャッジ時間 3,374 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge2
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 * 4
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 # 

def factorize(n):
    factors = {}
    while n % 2 == 0:
        factors[2] = factors.get(2, 0) + 1
        n = n // 2
    i = 3
    while i * i <= n:
        while n % i == 0:
            factors[i] = factors.get(i, 0) + 1
            n = n // i
        i += 2
    if n > 2:
        factors[n] = 1
    return factors

def generate_divisors_with_mu(factors):
    primes = list(factors.keys())
    divisors = [(1, {}, False)]  # (value, exponents dict, has_squared)
    result = []

    for p in primes:
        max_e = factors[p]
        temp = []
        for d in divisors:
            current_value, current_exponents, current_has_squared = d
            # Append e=0 (same as current divisor)
            temp.append((current_value, current_exponents.copy(), current_has_squared))
            for e in range(1, max_e + 1):
                new_value = current_value * (p ** e)
                new_exponents = current_exponents.copy()
                new_exponents[p] = e
                new_has_squared = current_has_squared or (e >= 2)
                temp.append((new_value, new_exponents, new_has_squared))
        divisors = temp

    for d in divisors:
        value, exponents, has_squared = d
        if has_squared:
            mu = 0
        else:
            k = len(exponents)
            mu = (-1) ** k
        result.append((value, mu))
    
    # Remove duplicate divisors, keeping the first occurrence (mu should be consistent)
    unique = {}
    for val, mu in result:
        if val not in unique:
            unique[val] = mu
    return list(unique.items())

def main():
    import sys
    input = sys.stdin.read().split()
    N = int(input[0])
    A = list(map(int, input[1:N+1]))
    
    D = {}
    for a in A:
        if a == 0:
            continue  # handle zero if needed, but problem says 1 <= A_i
        factors = factorize(a)
        if not factors and a == 1:
            factors = {}  # 1's factors are none
        div_mu = generate_divisors_with_mu(factors)
        for d, mu in div_mu:
            if d not in D:
                D[d] = mu
    
    sum_total = 0
    for d, mu in D.items():
        count = 0
        for x in A:
            if d == 0:
                continue
            if x % d == 0:
                count += 1
        if count > 0:
            sum_total += mu * ((1 << count) - 1)
    print(sum_total)

if __name__ == '__main__':
    main()
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