結果
問題 | No.931 Multiplicative Convolution |
ユーザー |
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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 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 14 |
ソースコード
import sysreadline=sys.stdin.readlineimport mathmod=998244353def NTT(polynomial1,polynomial2):prim_root=3prim_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-1x=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+jt=s+adft[s],dft[t]=(dft[s]+dft[t]*U[j])%mod,(dft[s]-dft[t]*U[j])%modx=pow((mod+1)//2,n)for i in range(1<<n):dft[i]*=xdft[i]%=modelse:for bit in range(n,0,-1):a=1<<bit-1x=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+jt=s+adft[s],dft[t]=(dft[s]+dft[t])%mod,U[j]*(dft[s]-dft[t])%modreturn dftn=(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 nttdef Extended_Euclid(n,m):stack=[]while m:stack.append((n,m))n,m=m,n%mif n>=0:x,y=1,0else:x,y=-1,0for i in range(len(stack)-1,-1,-1):n,m=stack[i]x,y=y,x-(n//m)*yreturn x,yclass MOD:def __init__(self,p,e=1):self.p=pself.e=eself.mod=self.p**self.edef Pow(self,a,n):a%=self.modif n>=0:return pow(a,n,self.mod)else:assert math.gcd(a,self.mod)==1x=Extended_Euclid(a,self.mod)[0]return pow(x,-n,self.mod)def Build_Fact(self,N):assert N>=0self.factorial=[1]self.cnt=[0]*(N+1)for i in range(1,N+1):ii=iself.cnt[i]=self.cnt[i-1]while ii%self.p==0:ii//=self.pself.cnt[i]+=1self.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+1while ii%self.p==0:ii//=self.pself.factorial_inve[i]=(self.factorial_inve[i+1]*ii)%self.moddef Fact(self,N):return self.factorial[N]*pow(self.p,self.cnt[N],self.mod)%self.moddef Fact_Inve(self,N):if self.cnt[N]:return Nonereturn self.factorial_inve[N]def Comb(self,N,K,divisible_count=False):if K<0 or K>N:return 0retu=self.factorial[N]*self.factorial_inve[K]*self.factorial_inve[N-K]%self.modcnt=self.cnt[N]-self.cnt[N-K]-self.cnt[K]if divisible_count:return retu,cntelse:retu*=pow(self.p,cnt,self.mod)retu%=self.modreturn retudef Primitive_Root(p):if p==2:return 1if p==167772161:return 3if p==469762049:return 3if p==754974721:return 11if p==998244353:return 3if p==10**9+7:return 5divisors=[2]pp=(p-1)//2while pp%2==0:pp//=2for d in range(3,pp+1,2):if d**2>pp:breakif pp%d==0:divisors.append(d)while pp%d==0:pp//=dif pp>1:divisors.append(pp)primitive_root=2while True:for d in divisors:if pow(primitive_root,(p-1)//d,p)==1:breakelse:return primitive_rootprimitive_root+=1P=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=1for i in range(P-1):polyA[i]=A[x-1]polyB[i]=B[x-1]x*=rx%=Ppoly=NTT(polyA,polyB)ans_lst=[0]*(P-1)x=1for i in range(2*P-3):ans_lst[x-1]+=poly[i]ans_lst[x-1]%=modx*=rx%=Pprint(*ans_lst)