結果

問題 No.1302 Random Tree Score
ユーザー zkou
提出日時 2020-11-27 23:04:01
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 2,966 ms / 3,000 ms
コード長 3,995 bytes
コンパイル時間 428 ms
コンパイル使用メモリ 82,272 KB
実行使用メモリ 259,708 KB
最終ジャッジ日時 2024-07-26 19:20:30
合計ジャッジ時間 23,323 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge1
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ファイルパターン 結果
sample AC * 3
other AC * 14
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ソースコード

diff #
プレゼンテーションモードにする

# TODO 高速化
# FIXME 非破壊的にする 
# 変数をグローバル変数におけないので998244353に特化させる。
# 衝突しにくそうな名前で...
_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, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0]
def butterfly_998244353(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
                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_998244353(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_square_998244353(a):
    n = len(a)
    if n == 0:
        return []
    if n <= 60:
        ans = [0] * (n * 2 - 1)
        for i in range(n):
            for j in range(n):
                ans[i + j] += a[i] * a[j]
                ans[i + j] %= _fft_mod
        return ans
    z = 1 << (n * 2 - 2).bit_length()
    a += [0] * (z - n)
    butterfly_998244353(a)
    c = [x * x % _fft_mod for x in a]
    butterfly_inv_998244353(c)
    c = c[:n * 2 - 1]
    iz = pow(z, _fft_mod - 2, _fft_mod)
    for i in range(n * 2 - 1):
        c[i] *= iz
        c[i] %= _fft_mod
    return c
def convolution_998244353(a, b):
    if a is b:
        return convolution_square_998244353(a)
    n = len(a)
    m = len(b)
    if n == 0 or m == 0:
        return []
    if min(n, m) <= 60:
        if n < m:  # 逆の方が速いかも？(オーバーヘッドの関係)
            n, m = m, n
            a, b = b, a
        ans = [0] * (n + m - 1)
        for i in range(n):
            for j in range(m):
                ans[i + j] += a[i] * b[j]
                ans[i + j] %= _fft_mod
        return ans
    z = 1 << (n + m - 2).bit_length()
    a += [0] * (z - n)
    b += [0] * (z - m)
    butterfly_998244353(a)
    butterfly_998244353(b)
    c = [x * y % _fft_mod for x, y in zip(a, b)]
    butterfly_inv_998244353(c)
    c = c[:n + m - 1]
    iz = pow(z, _fft_mod - 2, _fft_mod)
    for i in range(n + m - 1):
        c[i] *= iz
        c[i] %= _fft_mod
    return c
import sys
input = sys.stdin.readline
MOD = 998244353
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
for d in (format(N, 'b')):
    ans = convolution_square_998244353(ans)[:N]
    # print(len(ans))
    # ans = ans[:N]
    if d == '1':
        ans = convolution_998244353(ans, f.copy())[:N]
    
print(ans[N - 2] * fac[N - 2] % MOD * pow(N, MOD - N + 1, MOD) % MOD)
# print(ans)
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