#1015607 (PyPy3) No.2917 二重木

提出ソース

結果

問題	No.2917 二重木
ユーザー	PNJ
提出日時	2024-10-05 01:40:22
言語	PyPy3 (7.3.15)
結果	AC
実行時間	2,910 ms / 3,000 ms
コード長	7,163 bytes
コンパイル時間	274 ms
コンパイル使用メモリ	82,244 KB
実行使用メモリ	84,916 KB
最終ジャッジ日時	2024-10-05 01:40:50
合計ジャッジ時間	27,732 ms
ジャッジサーバーID （参考情報）	judge1 / judge2

このコードへのチャレンジ
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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	41 ms 54,652 KB
testcase_01	AC	41 ms 54,992 KB
testcase_02	AC	41 ms 54,596 KB
testcase_03	AC	41 ms 55,480 KB
testcase_04	AC	41 ms 54,684 KB
testcase_05	AC	42 ms 54,648 KB
testcase_06	AC	41 ms 55,508 KB
testcase_07	AC	42 ms 55,640 KB
testcase_08	AC	42 ms 54,900 KB
testcase_09	AC	42 ms 54,616 KB
testcase_10	AC	44 ms 56,052 KB
testcase_11	AC	44 ms 55,828 KB
testcase_12	AC	43 ms 55,612 KB
testcase_13	AC	45 ms 59,512 KB
testcase_14	AC	45 ms 61,532 KB
testcase_15	AC	41 ms 54,040 KB
testcase_16	AC	41 ms 53,732 KB
testcase_17	AC	42 ms 54,620 KB
testcase_18	AC	42 ms 54,500 KB
testcase_19	AC	42 ms 54,900 KB
testcase_20	AC	164 ms 77,308 KB
testcase_21	AC	344 ms 78,824 KB
testcase_22	AC	689 ms 79,616 KB
testcase_23	AC	42 ms 55,816 KB
testcase_24	AC	1,168 ms 80,700 KB
testcase_25	AC	1,350 ms 81,868 KB
testcase_26	AC	1,688 ms 82,136 KB
testcase_27	AC	42 ms 55,220 KB
testcase_28	AC	2,492 ms 84,036 KB
testcase_29	AC	2,890 ms 84,568 KB
testcase_30	AC	2,910 ms 84,796 KB
testcase_31	AC	2,860 ms 84,420 KB
testcase_32	AC	2,884 ms 84,676 KB
testcase_33	AC	2,905 ms 84,648 KB
testcase_34	AC	2,890 ms 84,916 KB

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ソースコード

raw source code

N,P = map(int,input().split())

if N == P:
  print((N % 2) ^ 1)
  exit()

mod,Mod,MOD = 1045430273,1051721729,1053818881

n = N

fact = [1 for i in range(n + 1)]
for i in range(1,n + 1):
  fact[i] = fact[i - 1] * i % P

fact_inv = [1 for i in range(n + 1)]
fact_inv[-1] = pow(fact[-1],P - 2,P)
for i in range(n,0,-1):
  fact_inv[i - 1] = fact_inv[i] * i % P

def binom(n,r):
  res = fact[n] * (fact_inv[n - r] * fact_inv[r] % P) % P
  return res

NTT_friend = [120586241,167772161,469762049,754974721,880803841,924844033,943718401,998244353,1045430273,1051721729,1053818881]
NTT_dict = {}
for i in range(len(NTT_friend)):
  NTT_dict[NTT_friend[i]] = i
NTT_info = [[20,74066978],[25,17],[26,30],[24,362],[23,211],[21,44009197],[22,663003469],[23,31],[20,363],[20,330],[20,2789]]

def popcount(n):
  c=(n&0x5555555555555555)+((n>>1)&0x5555555555555555)
  c=(c&0x3333333333333333)+((c>>2)&0x3333333333333333)
  c=(c&0x0f0f0f0f0f0f0f0f)+((c>>4)&0x0f0f0f0f0f0f0f0f)
  c=(c&0x00ff00ff00ff00ff)+((c>>8)&0x00ff00ff00ff00ff)
  c=(c&0x0000ffff0000ffff)+((c>>16)&0x0000ffff0000ffff)
  c=(c&0x00000000ffffffff)+((c>>32)&0x00000000ffffffff)
  return c

def topbit(n):
  h = n.bit_length()
  h -= 1
  return h

def prepared_fft(mod = 998244353):
  rank2 = NTT_info[NTT_dict[mod]][0]
  root,iroot = [0] * 30,[0] * 30
  rate2,irate2= [0] * 30,[0] * 30
  rate3,irate3= [0] * 30,[0] * 30

  root[rank2] = NTT_info[NTT_dict[mod]][1]
  iroot[rank2] = pow(root[rank2],mod - 2,mod)
  for i in range(rank2-1,-1,-1):
    root[i] = root[i+1] * root[i+1] % mod
    iroot[i] = iroot[i+1] * iroot[i+1] % mod

  prod,iprod = 1,1
  for i in range(rank2-1):
    rate2[i] = root[i + 2] * prod % mod
    irate2[i] = iroot[i + 2] * iprod % mod
    prod = prod * iroot[i + 2] % mod
    iprod = iprod * root[i + 2] % mod
  
  prod,iprod = 1,1
  for i in range(rank2-2):
    rate3[i] = root[i + 3] * prod % mod
    irate3[i] = iroot[i + 3] * iprod % mod
    prod = prod * iroot[i + 3] % mod
    iprod = iprod * root[i + 3] % mod
  
  return root,iroot,rate2,irate2,rate3,irate3

root,iroot,rate2,irate2,rate3,irate3 = prepared_fft()

def ntt(a,mod = 998244353):
  root,iroot,rate2,irate2,rate3,irate3 = prepared_fft(mod)
  n = len(a)
  h = topbit(n)
  assert (n == 1 << h)
  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 % mod
          a[i + offset] = (l + r) % mod
          a[i + offset + p] = (l - r) % mod
        rot = rot * rate2[topbit(~s & -~s)] % mod
      le += 1
    else:
      p = 1 << (h - le - 2)
      rot,imag = 1,root[2]
      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 = rot * rate3[topbit(~s & -~s)] % mod
      le += 2

def intt(a,mod = 998244353):
  root,iroot,rate2,irate2,rate3,irate3 = prepared_fft(mod)
  n = len(a)
  h = topbit(n)
  assert (n == 1 << h)
  coef = pow(n,mod - 2,mod)
  for i in range(n):
    a[i] = a[i] * coef % mod
  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 = irot * irate2[topbit(~s & -~s)] % mod
      le -= 1
    else:
      p = 1 << (h - le)
      irot,iimag = 1,iroot[2]
      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[topbit(~s & -~s)]
        irot %= mod
      le -= 2

def convolute_naive(a,b,mod = 998244353):
  res = [0] * (len(a) + len(b) - 1)
  for i in range(len(a)):
    for j in range(len(b)):
      res[i+j] = (res[i+j] + a[i] * b[j] % mod) % mod
  return res

def convolute(a,b,mod = 998244353):
  s = a[:]
  t = b[:]
  n = len(s)
  m = len(t)
  if min(n,m) <= 60:
    return convolute_naive(s,t,mod)
  le = 1
  while le < n + m - 1:
    le *= 2
  s += [0] * (le - n)
  t += [0] * (le - m)
  ntt(s,mod)
  ntt(t,mod)
  for i in range(le):
    s[i] = s[i] * t[i] % mod
  intt(s,mod)
  s = s[:n + m - 1]
  return s

def mod_inv(a,mod):
  if mod == 1:
    return 0
  a %= mod
  b,s,t = mod,1,0
  while True:
    if a == 1:
      return s
    t -= (b // a) * s
    b %= a
    if b == 1:
      return t + mod
    s -= (a // b) * t
    a %= b

def gcd_inv(a,mod):
  a %= mod
  b,s,t = mod,1,0
  while True:
    if a == 0:
      return (b,t + mod)
    t -= (b // a) * s
    b %= a
    if b == 0:
      return (a,s)
    s -= (a // b) * t
    a %= b

# (0,0)のとき存在しない.
def garner(Rem,Mod):
  assert (len(Rem) == len(Mod))

  r,m = 0,1
  for i in range(len(Rem)):
    assert (Mod[i])
    Rem[i] %= Mod[i]
    m1,r1 = Mod[i],Rem[i]
    if m < m1:
      m,m1,r,r1 = m1,m,r1,r
    if m % m1 == 0:
      if r % m1 != r1:
        return (0,0)

    g,im = gcd_inv(m,m1)
    y = abs(r1 - r)
    if y % g:
      return (0,0)
    u1 = m1 // g
    y = y // g % u1
    if (r > r1 and y != 0):
      y = u1 - y
    x = y * im % u1
    r += x * m
    m *= u1
  return r

# Modの中身が互いに素じゃないとダメ
def Garner(Rem,Mod,mod):
  assert (len(Rem) == len(Mod))

  for i in range(len(Mod)):
    if Mod[i] == mod:
      return Rem[i]

  Rem.append(0)
  Mod.append(mod)
  n = len(Mod)
  coffs = [1] * n
  constants = [0] * n
  for i in range(n - 1):
    v = (Rem[i] - constants[i]) * mod_inv(coffs[i],Mod[i]) % Mod[i]
    for j in range(i + 1,n):
      constants[j] = (constants[j] + coffs[j] * v) % Mod[j]
      coffs[j] = (coffs[j] * Mod[i]) % Mod[j]
  return constants[-1]

f = [1]
for i in range(1,N):
  c = pow(i + 1,i - 1,P) * fact_inv[i] % P
  f.append(c)

ans = 0
g = [0] * N
g[0] = 1
for n in range(1,N + 1):
  res = fact_inv[n] * pow(n,n - 2,P) % P
  h = convolute(f,g,mod)
  hh = convolute(f,g,Mod)
  hhh = convolute(f,g,MOD)
  for i in range(N + 1 - n):
    g[i] = Garner([h[i],hh[i],hhh[i]],[mod,Mod,MOD],P) % P
  res = res * g.pop() % P
  f.pop()
  ans = (ans + res) % P
print(ans * fact[N] % P)

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結果

テストケース

ソースコード