結果

問題 No.2075 GCD Subsequence
ユーザー gew1fw
提出日時 2025-06-12 13:39:07
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 2,600 ms / 4,000 ms
コード長 1,805 bytes
コンパイル時間 219 ms
コンパイル使用メモリ 82,360 KB
実行使用メモリ 136,400 KB
最終ジャッジ日時 2025-06-12 13:44:33
合計ジャッジ時間 33,977 ms
ジャッジサーバーID
(参考情報)
judge3 / judge1
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 * 3
other AC * 28
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 #

MOD = 998244353

def main():
    import sys
    input = sys.stdin.read().split()
    idx = 0
    N = int(input[idx])
    idx += 1
    A = list(map(int, input[idx:idx + N]))
    
    # Precompute smallest prime factors up to 1e6
    max_a = 10**6
    spf = list(range(max_a + 1))
    for i in range(2, int(max_a**0.5) + 1):
        if spf[i] == i:
            for j in range(i * i, max_a + 1, i):
                if spf[j] == j:
                    spf[j] = i
    
    def factorize(x):
        factors = set()
        if x == 1:
            return factors
        while x != 1:
            p = spf[x]
            factors.add(p)
            while x % p == 0:
                x //= p
        return factors
    
    cnt = dict()
    answer = 0
    for x in A:
        primes = factorize(x)
        if not primes:
            answer = (answer + 1) % MOD
            continue
        primes = list(primes)
        k = len(primes)
        sum_terms = 0
        subsets = []
        for mask in range(1, 1 << k):
            subset = []
            for i in range(k):
                if mask & (1 << i):
                    subset.append(primes[i])
            subsets.append(subset)
        for subset in subsets:
            m = len(subset)
            d = 1
            for p in subset:
                d *= p
            term = cnt.get(d, 0)
            if m % 2 == 1:
                sum_terms = (sum_terms + term) % MOD
            else:
                sum_terms = (sum_terms - term) % MOD
        new = (sum_terms + 1) % MOD
        answer = (answer + new) % MOD
        for subset in subsets:
            m = len(subset)
            d = 1
            for p in subset:
                d *= p
            cnt[d] = (cnt.get(d, 0) + new) % MOD
    print(answer % MOD)

if __name__ == '__main__':
    main()
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