結果

問題 No.1195 数え上げを愛したい（文字列編）
コンテスト
ユーザー ああいい
提出日時 2022-03-07 19:22:19
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 554 ms / 3,000 ms
コード長 5,465 bytes
コンパイル時間 297 ms
コンパイル使用メモリ 82,364 KB
実行使用メモリ 132,092 KB
最終ジャッジ日時 2024-07-22 14:25:48
合計ジャッジ時間 10,626 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge2
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ファイルパターン 結果
other AC * 26
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 # 

P = 998244353

def get_root(m):
    if m == 2:return 1
    if m == 998244353:return 3
    if m == 469762049:return 3
    if m == 754974721:return 11
    if m == 167772161:return 3
    divs = [0] * 20
    divs[0] = 2
    cnt = 1
    x = (m-1) // 2
    while x % 2 == 0:
        x //= 2
    i = 3
    while i * i <= x:
        if x % i == 0:
            divs[cnt] = i
            cnt += 1
            while x % i == 0:
                x //= i
        i += 2
    if x > 1:
        divs[cnt] = x
        cnt += 1
    g = 2
    while True:
        ok = True
        for i in range(cnt):
            if pow(g,(m-1)//divs[i],m) == 1:
                ok = False
                break
        if ok:return g
        g += 1


MOD = 998244353
IMAG = 911660635
IIMAG = 86583718
rate2 = (0, 911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601, 842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 867605899, 0)
irate2 = (0, 86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960, 354738543, 109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 103369235, 0)
rate3 = (0, 372528824, 337190230, 454590761, 816400692, 578227951, 180142363, 83780245, 6597683, 70046822, 623238099, 183021267, 402682409, 631680428, 344509872, 689220186, 365017329, 774342554, 729444058, 102986190, 128751033, 395565204, 0)
irate3 = (0, 509520358, 929031873, 170256584, 839780419, 282974284, 395914482, 444904435, 72135471, 638914820, 66769500, 771127074, 985925487, 262319669, 262341272, 625870173, 768022760, 859816005, 914661783, 430819711, 272774365, 530924681, 0)
 
def butterfly_base4(a):
  n = len(a)
  h = (n - 1).bit_length()
  le = 0
  while le < h:
    if h - le == 1:
      p = 1 << (h - le - 1)
      rot = 1
      for s in range(1 << le):
        offset = s << (h - le)
        for i in range(p):
          l = a[i + offset]
          r = a[i + offset + p] * rot
          a[i + offset] = (l + r) % MOD
          a[i + offset + p] = (l - r) % MOD
        rot *= rate2[(~s & -~s).bit_length()]
        rot %= MOD
      le += 1
    else:
      p = 1 << (h - le - 2)
      rot = 1
      for s in range(1 << le):
        rot2 = rot * rot % MOD
        rot3 = rot2 * rot % MOD
        offset = s << (h - le)
        for i in range(p):
          a0 = a[i + offset]
          a1 = a[i + offset + p] * rot
          a2 = a[i + offset + p * 2] * rot2
          a3 = a[i + offset + p * 3] * rot3
          a1na3imag = (a1 - a3) % MOD * IMAG
          a[i + offset] = (a0 + a2 + a1 + a3) % MOD
          a[i + offset + p] = (a0 + a2 - a1 - a3) % MOD
          a[i + offset + p * 2] = (a0 - a2 + a1na3imag) % MOD
          a[i + offset + p * 3] = (a0 - a2 - a1na3imag) % MOD
        rot *= rate3[(~s & -~s).bit_length()]
        rot %= MOD
      le += 2
 
def butterfly_inv_base4(a):
  n = len(a)
  h = (n - 1).bit_length()
  le = h
  while le:
    if le == 1:
      p = 1 << (h - le)
      irot = 1
      for s in range(1 << (le - 1)):
        offset = s << (h - le + 1)
        for i in range(p):
          l = a[i + offset]
          r = a[i + offset + p]
          a[i + offset] = (l + r) % MOD
          a[i + offset + p] = (l - r) * irot % MOD
        irot *= irate2[(~s & -~s).bit_length()]
        irot %= MOD
      le -= 1
    else:
      p = 1 << (h - le)
      irot = 1
      for s in range(1 << (le - 2)):
        irot2 = irot * irot % MOD
        irot3 = irot2 * irot % MOD
        offset = s << (h - le + 2)
        for i in range(p):
          a0 = a[i + offset]
          a1 = a[i + offset + p]
          a2 = a[i + offset + p * 2]
          a3 = a[i + offset + p * 3]
          a2na3iimag = (a2 - a3) * IIMAG % MOD
          a[i + offset] = (a0 + a1 + a2 + a3) % MOD
          a[i + offset + p] = (a0 - a1 + a2na3iimag) * irot % MOD
          a[i + offset + p * 2] = (a0 + a1 - a2 - a3) * irot2 % MOD
          a[i + offset + p * 3] = (a0 - a1 - a2na3iimag) * irot3 % MOD
        irot *= irate3[(~s & -~s).bit_length()]
        irot %= MOD
      le -= 2
 
def convolution(s,t):
  n = len(s)
  m = len(t)
  if min(n, m) <= 40:
    a = [0] * (n + m - 1)
    for i in range(n):
      if i % 8 == 0:        
        for j in range(m):
          a[i + j] += s[i] * t[j]
          a[i + j] %= MOD
      else:
        for j in range(m):
          a[i + j] += s[i] * t[j]
    return a

  z = 1 << (n + m - 2).bit_length()
  a = s + [0] * (z - n)
  b = t + [0] * (z - m)
  butterfly_base4(a)
  butterfly_base4(b)
  for i in range(z):
    a[i] *= b[i]
    a[i] %= MOD
  butterfly_inv_base4(a)
  a = a[:n + m - 1]
  iz = pow(z, MOD - 2, MOD)
  return [v * iz for v in a]

S = input()
dat = [0] * 26
for s in S:
    c = ord(s) - ord('a')
    dat[c] += 1
C = 3 * 10 ** 5 + 2
fact = [1] * C
fact_inv = [1] * C
for i in range(2,C):
    fact[i] = fact[i-1] * i % P
fact_inv[-1] = pow(fact[-1],P-2,P)
for i in range(C-2,0,-1):
    fact_inv[i] = fact_inv[i+1] * (i + 1) % P
dat.sort()
import heapq
q = []
for i in range(26):
    if dat[i] == 0:
        continue
    n = dat[i]
    b = fact_inv[:n+1]
    heapq.heappush(q,(len(b),b))
while len(q) >= 2:
    n,a = heapq.heappop(q)
    m,b = heapq.heappop(q)
    c = convolution(a,b)
    heapq.heappush(q,(len(c),c))
n,a = heapq.heappop(q)
ans = 0
for i in range(n):
    ans = (ans + a[i] * fact[i]) % P
print((ans-1)%P)
0