結果

問題 No.931 Multiplicative Convolution
ユーザー vwxyz
提出日時 2021-10-04 23:45:13
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 497 ms / 2,000 ms
コード長 4,482 bytes
コンパイル時間 216 ms
コンパイル使用メモリ 82,408 KB
実行使用メモリ 159,808 KB
最終ジャッジ日時 2024-07-23 00:47:13
合計ジャッジ時間 6,080 ms
ジャッジサーバーID
(参考情報)
judge4 / judge3
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
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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

import sys
readline=sys.stdin.readline
import math
mod=998244353
def NTT(polynomial1,polynomial2):
prim_root=3
prim_root_inve=MOD(mod).Pow(3,-1)
def DFT(polynomial,n,inverse=False):
dft=polynomial+[0]*((1<<n)-len(polynomial))
if inverse:
for bit in range(1,n+1):
a=1<<bit-1
x=pow(prim_root,mod-1>>bit,mod)
U=[1]
for _ in range(a):
U.append(U[-1]*x%mod)
for i in range(1<<n-bit):
for j in range(a):
s=i*2*a+j
t=s+a
dft[s],dft[t]=(dft[s]+dft[t]*U[j])%mod,(dft[s]-dft[t]*U[j])%mod
x=pow((mod+1)//2,n)
for i in range(1<<n):
dft[i]*=x
dft[i]%=mod
else:
for bit in range(n,0,-1):
a=1<<bit-1
x=pow(prim_root_inve,mod-1>>bit,mod)
U=[1]
for _ in range(a):
U.append(U[-1]*x%mod)
for i in range(1<<n-bit):
for j in range(a):
s=i*2*a+j
t=s+a
dft[s],dft[t]=(dft[s]+dft[t])%mod,U[j]*(dft[s]-dft[t])%mod
return dft
n=(len(polynomial1)+len(polynomial2)-2).bit_length()
ntt=[x*y%mod for x,y in zip(DFT(polynomial1,n),DFT(polynomial2,n))]
ntt=DFT(ntt,n,inverse=True)[:len(polynomial1)+len(polynomial2)-1]
return ntt
def Extended_Euclid(n,m):
stack=[]
while m:
stack.append((n,m))
n,m=m,n%m
if n>=0:
x,y=1,0
else:
x,y=-1,0
for i in range(len(stack)-1,-1,-1):
n,m=stack[i]
x,y=y,x-(n//m)*y
return x,y
class MOD:
def __init__(self,p,e=1):
self.p=p
self.e=e
self.mod=self.p**self.e
def Pow(self,a,n):
a%=self.mod
if n>=0:
return pow(a,n,self.mod)
else:
assert math.gcd(a,self.mod)==1
x=Extended_Euclid(a,self.mod)[0]
return pow(x,-n,self.mod)
def Build_Fact(self,N):
assert N>=0
self.factorial=[1]
self.cnt=[0]*(N+1)
for i in range(1,N+1):
ii=i
self.cnt[i]=self.cnt[i-1]
while ii%self.p==0:
ii//=self.p
self.cnt[i]+=1
self.factorial.append((self.factorial[-1]*ii)%self.mod)
self.factorial_inve=[None]*(N+1)
self.factorial_inve[-1]=self.Pow(self.factorial[-1],-1)
for i in range(N-1,-1,-1):
ii=i+1
while ii%self.p==0:
ii//=self.p
self.factorial_inve[i]=(self.factorial_inve[i+1]*ii)%self.mod
def Fact(self,N):
return self.factorial[N]*pow(self.p,self.cnt[N],self.mod)%self.mod
def Fact_Inve(self,N):
if self.cnt[N]:
return None
return self.factorial_inve[N]
def Comb(self,N,K,divisible_count=False):
if K<0 or K>N:
return 0
retu=self.factorial[N]*self.factorial_inve[K]*self.factorial_inve[N-K]%self.mod
cnt=self.cnt[N]-self.cnt[N-K]-self.cnt[K]
if divisible_count:
return retu,cnt
else:
retu*=pow(self.p,cnt,self.mod)
retu%=self.mod
return retu
def Primitive_Root(p):
if p==2:
return 1
if p==167772161:
return 3
if p==469762049:
return 3
if p==754974721:
return 11
if p==998244353:
return 3
if p==10**9+7:
return 5
divisors=[2]
pp=(p-1)//2
while pp%2==0:
pp//=2
for d in range(3,pp+1,2):
if d**2>pp:
break
if pp%d==0:
divisors.append(d)
while pp%d==0:
pp//=d
if pp>1:
divisors.append(pp)
primitive_root=2
while True:
for d in divisors:
if pow(primitive_root,(p-1)//d,p)==1:
break
else:
return primitive_root
primitive_root+=1
P=int(readline())
A=list(map(int,readline().split()))
B=list(map(int,readline().split()))
polyA=[None]*(P-1)
polyB=[None]*(P-1)
r=Primitive_Root(P)
x=1
for i in range(P-1):
polyA[i]=A[x-1]
polyB[i]=B[x-1]
x*=r
x%=P
poly=NTT(polyA,polyB)
ans_lst=[0]*(P-1)
x=1
for i in range(2*P-3):
ans_lst[x-1]+=poly[i]
ans_lst[x-1]%=mod
x*=r
x%=P
print(*ans_lst)
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