結果

問題 No.931 Multiplicative Convolution
ユーザー neterukun
提出日時 2021-09-22 04:53:42
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 261 ms / 2,000 ms
コード長 2,334 bytes
コンパイル時間 146 ms
コンパイル使用メモリ 82,160 KB
実行使用メモリ 114,036 KB
最終ジャッジ日時 2024-07-04 15:08:21
合計ジャッジ時間 4,651 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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ファイルパターン 結果
sample AC * 3
other AC * 14
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 #
プレゼンテーションモードにする

def primitive_root(p):
    if p == 2:
        return 1
    x = p - 1
    factors = [2]
    while x % 2 == 0:
         x //= 2
    for k in range(3, int(p ** 0.5) + 1, 2):
        if x % k == 0:
            factors.append(k)
            while x % k == 0:
                x //= k
    if x != 1:
        factors.append(x)
    g = 2
    while True:
        ok = True
        for val in factors:
            if pow(g, (p - 1) // val, p) == 1:
                ok = False
                break
        if ok:
            return g
        g += 1
MOD = 998244353
ROOT = 5
def _ntt(a, h):
    roots = [pow(ROOT, (MOD - 1) >> i, MOD) for i in range(h + 1)]
    for i in range(h):
        m = 1 << (h - i - 1)
        for j in range(1 << i):
            w = 1
            j *= 2 * m
            for k in range(m):
                a[j + k], a[j + k + m] = \
                    (a[j + k] + a[j + k + m]) % MOD, \
                    (a[j + k] - a[j + k + m]) * w % MOD
                w *= roots[h - i]
                w %= MOD
def _intt(a, h):
    roots = [pow(ROOT, (MOD - 1) >> i, MOD) for i in range(h + 1)]
    iroots = [pow(r, MOD - 2, MOD) for r in roots]
    for i in range(h):
        m = 1 << i
        for j in range(1 << (h - i - 1)):
            w = 1
            j *= 2 * m
            for k in range(m):
                a[j + k], a[j + k + m] = \
                    (a[j + k] + a[j + k + m] * w) % MOD, \
                    (a[j + k] - a[j + k + m] * w) % MOD
                w *= iroots[i + 1]
                w %= MOD
    inv = pow(1 << h, MOD - 2, MOD)
    for i in range(1 << h):
        a[i] *= inv
        a[i] %= MOD
def ntt_convolve(a, b):
    len_ab = len(a) + len(b)
    n = 1 << (len(a) + len(b) - 1).bit_length()
    h = n.bit_length() - 1
    a = list(a) + [0] * (n - len(a))
    b = list(b) + [0] * (n - len(b))
    _ntt(a, h), _ntt(b, h)
    a = [va * vb % MOD for va, vb in zip(a, b)]
    _intt(a, h)
    return a[:len_ab - 1]
  
  
p = int(input())
a = [0] + list(map(int, input().split()))
b = [0] + list(map(int, input().split()))
rt = primitive_root(p)
aa = [0] * p
bb = [0] * p
v = 1
for i in range(p - 1):
    aa[i] = a[v]
    bb[i] = b[v]
    v = v * rt % p
cc = ntt_convolve(aa, bb)
c = [0] * p
v = 1
for i in range(len(cc)):
    c[v] += cc[i]
    c[v] %= MOD
    v = v * rt % p
print(*c[1:])
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