結果

問題 No.1302 Random Tree Score
ユーザー sasa8uyauya
提出日時 2024-09-19 21:08:09
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 2,282 ms / 3,000 ms
コード長 1,836 bytes
コンパイル時間 196 ms
コンパイル使用メモリ 82,048 KB
実行使用メモリ 250,908 KB
最終ジャッジ日時 2024-09-19 21:08:54
合計ジャッジ時間 39,756 ms
ジャッジサーバーID
(参考情報)
judge4 / 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 #
プレゼンテーションモードにする

mod = 998244353
R = 3
Rinv = 332748118
W = [pow(R, (mod-1)>>i, mod) for i in range(24)]
Winv = [pow(Rinv, (mod-1)>>i, mod) for i in range(24)]
def fft(k, f):
for l in range(k, 0, -1):
d = 1<<l-1
U = [1]
for i in range(d):
U.append(U[-1]*W[l]%mod)
for i in range(1<<k-l):
for j in range(d):
s = i*2*d+j
f[s], f[s+d] = (f[s]+f[s+d])%mod, U[j]*(f[s]-f[s+d])%mod
def fftinv(k, f):
for l in range(1, k+1):
d = 1<<l-1
for i in range(1<<k-l):
u = 1
for j in range(i*2*d, (i*2+1)*d):
f[j+d] *= u
f[j], f[j+d] = (f[j]+f[j+d])%mod, (f[j]-f[j+d])%mod
u *= Winv[l]
u %= mod
def convolution(a, b):
le = len(a)+len(b)-1
k = le.bit_length()
n = 1<<k
a = a+[0]*(n-len(a))
b = b+[0]*(n-len(b))
fft(k, a)
fft(k, b)
for i in range(n):
a[i] *= b[i]
a[i] %= mod
fftinv(k, a)
ninv = pow(n, mod-2, mod)
for i in range(le):
a[i] *= ninv
a[i] %= mod
return a[:le]
def FPSinv(H):
I=[pow(H[0],M-2,M)]
l=1
while l<len(H):
I+=[0]*l
nI=convolution(H[:l*2],convolution(I,I)[:l*2])[:l*2]
for i in range(l*2):
nI[i]=(2*I[i]-nI[i])%M
I=nI
l*=2
return I[:len(H)]
def FPSlog(H):
H1=[H[i]*i%M for i in range(1,len(H))]+[0]
H2=FPSinv(H)
I=convolution(H1,H2)
I=[0]+[I[i]*fb[i+1]*fa[i]%M for i in range(len(H)-1)]
return I
def FPSexp(H):
I=[1]
l=1
while l<len(H):
I+=[0]*l
I2=FPSlog(I)[:l*2]
I3=H[:l*2]
I3[0]+=1
for i in range(l*2):
I3[i]-=I2[i]
nI=convolution(I,I3)[:l*2]
I=nI
l*=2
return I[:len(H)]
n=int(input())
L=1<<17
M=998244353
fa=[1,1]
fb=[1,1]
for i in range(2,L+1):
fa+=[fa[-1]*i%M]
fb+=[fb[-1]*(M//i)*fb[M%i]*fa[M%i-1]*(-1)%M]
q1=[(i+1)*fb[i]%M for i in range(L)]
q2=FPSlog(q1)
for i in range(L):
q2[i]*=n
q2[i]%=M
q3=FPSexp(q2)
a=q3[n-2]
print(a*fa[n-2]*pow(pow(n,n-2,M),M-2,M)%M)
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