結果

問題 No.1302 Random Tree Score
コンテスト
ユーザー zkou
提出日時 2021-03-16 22:48:44
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 2,706 ms / 3,000 ms
コード長 3,891 bytes
コンパイル時間 677 ms
コンパイル使用メモリ 82,432 KB
実行使用メモリ 239,696 KB
最終ジャッジ日時 2024-11-08 18:36:06
合計ジャッジ時間 22,186 ms
ジャッジサーバーID
（参考情報） 		judge5 / 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 * 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 # 

_fft_mod = 998244353
_fft_sum_e = (911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601,
              842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 867605899, 0, 0, 0, 0, 0, 0, 0, 0)
_fft_sum_ie = (86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960, 354738543,
               109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 103369235, 0, 0, 0, 0, 0, 0, 0, 0)


def _butterfly(a):
    n = len(a)
    h = (n - 1).bit_length()
    for ph in range(1, h + 1):
        w = 1 << (ph - 1)
        p = 1 << (h - ph)
        now = 1
        for s in range(w):
            offset = s << (h - ph + 1)
            for i in range(p):
                l = a[i + offset]
                r = a[i + offset + p] * now % _fft_mod
                a[i + offset] = (l + r) % _fft_mod
                a[i + offset + p] = (l - r) % _fft_mod
            now *= _fft_sum_e[(~s & -~s).bit_length() - 1]
            now %= _fft_mod


def _butterfly_inv(a):
    n = len(a)
    h = (n - 1).bit_length()
    for ph in range(h, 0, -1):
        w = 1 << (ph - 1)
        p = 1 << (h - ph)
        inow = 1
        for s in range(w):
            offset = s << (h - ph + 1)
            for i in range(p):
                l = a[i + offset]
                r = a[i + offset + p]
                a[i + offset] = (l + r) % _fft_mod
                a[i + offset + p] = (l - r) * inow % _fft_mod
            inow *= _fft_sum_ie[(~s & -~s).bit_length() - 1]
            inow %= _fft_mod


def _convolution_naive(a, b):
    n = len(a)
    m = len(b)
    ans = [0] * (n + m - 1)
    if n < m:
        for j in range(m):
            for i in range(n):
                ans[i + j] = (ans[i + j] + a[i] * b[j]) % _fft_mod
    else:
        for i in range(n):
            for j in range(m):
                ans[i + j] = (ans[i + j] + a[i] * b[j]) % _fft_mod
    return ans


def _convolution_fft(a, b):
    a = a.copy()
    b = b.copy()
    n = len(a)
    m = len(b)
    z = 1 << (n + m - 2).bit_length()
    a += [0] * (z - n)
    _butterfly(a)
    b += [0] * (z - m)
    _butterfly(b)
    for i in range(z):
        a[i] = a[i] * b[i] % _fft_mod
    _butterfly_inv(a)
    a = a[:n + m - 1]
    iz = pow(z, _fft_mod - 2, _fft_mod)
    for i in range(n + m - 1):
        a[i] = a[i] * iz % _fft_mod
    return a


def _convolution_square(a):
    a = a.copy()
    n = len(a)
    z = 1 << (2 * n - 2).bit_length()
    a += [0] * (z - n)
    _butterfly(a)
    for i in range(z):
        a[i] = a[i] * a[i] % _fft_mod
    _butterfly_inv(a)
    a = a[:2 * n - 1]
    iz = pow(z, _fft_mod - 2, _fft_mod)
    for i in range(2 * n - 1):
        a[i] = a[i] * iz % _fft_mod
    return a


def convolution(a, b):
    n = len(a)
    m = len(b)
    if n == 0 or m == 0:
        return []
    if min(n, m) <= 60:
        return _convolution_naive(a, b)
    if a is b:
        return _convolution_square(a)
    return _convolution_fft(a, b)


MOD = 998244353

def main():
    import sys
    input = sys.stdin.readline

    table_len = 10 ** 5 + 10

    fac = [1, 1]
    for i in range(2, table_len):
        fac.append(fac[-1] * i % MOD)

    finv = [0] * table_len
    finv[-1] = pow(fac[-1], MOD - 2, MOD)
    for i in range(table_len-1, 0, -1):
        finv[i - 1] = finv[i] * i % MOD
        
    N = int(input())
    f = [(i + 1) * finv[i] % MOD for i in range(N)]
    ans = [0] * N
    ans[0] = 1
    first = True
    for d in (format(N, 'b')):
        if first:
            first = False
        else:
            ans = convolution(ans, ans)[:N]
        if d == '1':
            ans = convolution(ans, f)[:N]
        
    print(ans[N - 2] * fac[N - 2] % MOD * pow(N, MOD - N + 1, MOD) % MOD)

main()
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