結果
問題 | No.868 ハイパー部分和問題 |
ユーザー | vwxyz |
提出日時 | 2024-04-15 11:07:43 |
言語 | PyPy3 (7.3.15) |
結果 |
TLE
|
実行時間 | - |
コード長 | 25,046 bytes |
コンパイル時間 | 737 ms |
コンパイル使用メモリ | 82,108 KB |
実行使用メモリ | 84,752 KB |
最終ジャッジ日時 | 2024-10-05 06:07:48 |
合計ジャッジ時間 | 11,420 ms |
ジャッジサーバーID (参考情報) |
judge5 / judge4 |
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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 | 178 ms
77,096 KB |
testcase_01 | AC | 189 ms
76,948 KB |
testcase_02 | AC | 273 ms
77,336 KB |
testcase_03 | AC | 130 ms
76,744 KB |
testcase_04 | AC | 62 ms
72,640 KB |
testcase_05 | AC | 61 ms
73,828 KB |
testcase_06 | AC | 61 ms
73,548 KB |
testcase_07 | AC | 62 ms
74,016 KB |
testcase_08 | AC | 60 ms
73,444 KB |
testcase_09 | AC | 61 ms
72,904 KB |
testcase_10 | AC | 61 ms
73,656 KB |
testcase_11 | AC | 61 ms
73,344 KB |
testcase_12 | AC | 60 ms
73,040 KB |
testcase_13 | AC | 61 ms
74,648 KB |
testcase_14 | TLE | - |
testcase_15 | -- | - |
testcase_16 | -- | - |
testcase_17 | -- | - |
testcase_18 | -- | - |
testcase_19 | -- | - |
testcase_20 | -- | - |
testcase_21 | -- | - |
testcase_22 | -- | - |
testcase_23 | -- | - |
testcase_24 | -- | - |
testcase_25 | -- | - |
testcase_26 | -- | - |
testcase_27 | -- | - |
testcase_28 | -- | - |
testcase_29 | -- | - |
testcase_30 | -- | - |
testcase_31 | -- | - |
testcase_32 | -- | - |
testcase_33 | -- | - |
testcase_34 | -- | - |
testcase_35 | -- | - |
testcase_36 | -- | - |
testcase_37 | -- | - |
testcase_38 | -- | - |
testcase_39 | -- | - |
ソースコード
import random class Polynomial: def __init__(self,polynomial,max_degree=-1,eps=0,mod=0): self.max_degree=max_degree if self.max_degree!=-1 and len(polynomial)>self.max_degree+1: self.polynomial=polynomial[:self.max_degree+1] else: self.polynomial=polynomial self.mod=mod self.eps=eps def __eq__(self,other): if type(other)!=Polynomial: return False if len(self.polynomial)!=len(other.polynomial): return False for i in range(len(self.polynomial)): if self.eps<abs(self.polynomial[i]-other.polynomial[i]): return False return True def __ne__(self,other): if type(other)!=Polynomial: return True if len(self.polynomial)!=len(other.polynomial): return True for i in range(len(self.polynomial)): if self.eps<abs(self.polynomial[i]-other.polynomial[i]): return True return False def __add__(self,other): if type(other)==Polynomial: summ=[0]*max(len(self.polynomial),len(other.polynomial)) for i in range(len(self.polynomial)): summ[i]+=self.polynomial[i] for i in range(len(other.polynomial)): summ[i]+=other.polynomial[i] if self.mod: for i in range(len(summ)): summ[i]%=self.mod else: summ=[x for x in self.polynomial] if self.polynomial else [0] summ[0]+=other if self.mod: summ[0]%=self.mod while summ and abs(summ[-1])<=self.eps: summ.pop() summ=Polynomial(summ,max_degree=self.max_degree,eps=self.eps,mod=self.mod) return summ def __sub__(self,other): if type(other)==Polynomial: diff=[0]*max(len(self.polynomial),len(other.polynomial)) for i in range(len(self.polynomial)): diff[i]+=self.polynomial[i] for i in range(len(other.polynomial)): diff[i]-=other.polynomial[i] if self.mod: for i in range(len(diff)): diff[i]%=self.mod else: diff=[x for x in self.polynomial] if self.polynomial else [0] diff[0]-=other if self.mod: diff[0]%=self.mod while diff and abs(diff[-1])<=self.eps: diff.pop() diff=Polynomial(diff,max_degree=self.max_degree,eps=self.eps,mod=self.mod) return diff def __mul__(self,other): if type(other)==Polynomial: if self.max_degree==-1: prod=[0]*(len(self.polynomial)+len(other.polynomial)-1) for i in range(len(self.polynomial)): for j in range(len(other.polynomial)): prod[i+j]+=self.polynomial[i]*other.polynomial[j] else: prod=[0]*min(len(self.polynomial)+len(other.polynomial)-1,self.max_degree+1) for i in range(len(self.polynomial)): for j in range(min(len(other.polynomial),self.max_degree+1-i)): prod[i+j]+=self.polynomial[i]*other.polynomial[j] if self.mod: for i in range(len(prod)): prod[i]%=self.mod else: if self.mod: prod=[x*other%self.mod for x in self.polynomial] else: prod=[x*other for x in self.polynomial] while prod and abs(prod[-1])<=self.eps: prod.pop() prod=Polynomial(prod,max_degree=self.max_degree,eps=self.eps,mod=self.mod) return prod def __matmul__(self,other): assert type(other)==Polynomial if self.mod: prod=NTT(self.polynomial,other.polynomial) else: prod=FFT(self.polynomial,other.polynomial) if self.max_degree!=-1 and len(prod)>self.max_degree+1: prod=prod[:self.max_degree+1] while prod and abs(prod[-1])<=self.eps: prod.pop() prod=Polynomial(prod,max_degree=self.max_degree,eps=self.eps,mod=self.mod) return prod def __pow__(self,other): if other==0: prod=Polynomial([1],max_degree=self.max_degree,eps=self.eps,mod=self.mod) elif other==1: prod=Polynomial([x for x in self.polynomial],max_degree=self.max_degree,eps=self.eps,mod=self.mod) else: prod=[1] doub=self.polynomial if self.mod: convolve=NTT convolve_Pow=NTT_Pow else: convolve=FFT convolve_Pow=FFT_Pow while other>=2: if other&1: prod=convolve(prod,doub) if self.max_degree!=-1: prod=prod[:self.max_degree+1] doub=convolve_Pow(doub,2) if self.max_degree!=-1: doub=doub[:self.max_degree+1] other>>=1 prod=convolve(prod,doub) if self.max_degree!=-1: prod=prod[:self.max_degree+1] prod=Polynomial(prod,max_degree=self.max_degree,eps=self.eps,mod=self.mod) return prod def __truediv__(self,other): if type(other)==Polynomial: assert other.polynomial for n in range(len(other.polynomial)): if self.eps<abs(other.polynomial[n]): break assert len(self.polynomial)>n for i in range(n): assert abs(self.polynomial[i])<=self.eps self_polynomial=self.polynomial[n:] other_polynomial=other.polynomial[n:] if self.mod: inve=MOD(self.mod).Pow(other_polynomial[0],-1) else: inve=1/other_polynomial[0] quot=[] for i in range(len(self_polynomial)-len(other_polynomial)+1): if self.mod: quot.append(self_polynomial[i]*inve%self.mod) else: quot.append(self_polynomial[i]*inve) for j in range(len(other_polynomial)): self_polynomial[i+j]-=other_polynomial[j]*quot[-1] if self.mod: self_polynomial[i+j]%=self.mod for i in range(max(0,len(self_polynomial)-len(other_polynomial)+1),len(self_polynomial)): if self.eps<abs(self_polynomial[i]): assert self.max_degree!=-1 self_polynomial=self_polynomial[-len(other_polynomial)+1:]+[0]*(len(other_polynomial)-1-len(self_polynomial)) while len(quot)<=self.max_degree: self_polynomial.append(0) if self.mod: quot.append(self_polynomial[0]*inve%self.mod) self_polynomial=[(self_polynomial[i]-other_polynomial[i]*quot[-1])%self.mod for i in range(1,len(self_polynomial))] else: quot.append(self_polynomial[0]*inve) self_polynomial=[(self_polynomial[i]-other_polynomial[i]*quot[-1]) for i in range(1,len(self_polynomial))] break quot=Polynomial(quot,max_degree=self.max_degree,eps=self.eps,mod=self.mod) else: assert self.eps<abs(other) if self.mod: inve=MOD(self.mod).Pow(other,-1) quot=Polynomial([x*inve%self.mod for x in self.polynomial],max_degree=self.max_degree,eps=self.eps,mod=self.mod) else: quot=Polynomial([x/other for x in self.polynomial],max_degree=self.max_degree,eps=self.eps,mod=self.mod) return quot def __floordiv__(self,other): assert type(other)==Polynomial quot=[0]*(len(self.polynomial)-len(other.polynomial)+1) rema=[x for x in self.polynomial] if self.mod: inve=MOD(self.mod).Pow(other.polynomial[-1],-1) for i in range(len(self.polynomial)-len(other.polynomial),-1,-1): quot[i]=rema[i+len(other.polynomial)-1]*inve%self.mod for j in range(len(other.polynomial)): rema[i+j]-=quot[i]*other.polynomial[j] rema[i+j]%=self.mod else: inve=1/other.polynomial[-1] for i in range(len(self.polynomial)-len(other.polynomial),-1,-1): quot[i]=rema[i+len(other.polynomial)-1]*inve for j in range(len(other.polynomial)): rema[i+j]-=quot[i]*other.polynomial[j] quot=Polynomial(quot,max_degree=self.max_degree,eps=self.eps,mod=self.mod) return quot def __mod__(self,other): assert type(other)==Polynomial quot=[0]*(len(self.polynomial)-len(other.polynomial)+1) rema=[x for x in self.polynomial] if self.mod: inve=MOD(self.mod).Pow(other.polynomial[-1],-1) for i in range(len(self.polynomial)-len(other.polynomial),-1,-1): quot[i]=rema[i+len(other.polynomial)-1]*inve%self.mod for j in range(len(other.polynomial)): rema[i+j]-=quot[i]*other.polynomial[j] rema[i+j]%=self.mod else: inve=1/other.polynomial[-1] for i in range(len(self.polynomial)-len(other.polynomial),-1,-1): quot[i]=rema[i+len(other.polynomial)-1]*inve for j in range(len(other.polynomial)): rema[i+j]-=quot[i]*other.polynomial[j] while rema and abs(rema[-1])<=self.eps: rema.pop() rema=Polynomial(rema,max_degree=self.max_degree,eps=self.eps,mod=self.mod) return rema def __divmod__(self,other): assert type(other)==Polynomial quot=[0]*(len(self.polynomial)-len(other.polynomial)+1) rema=[x for x in self.polynomial] if self.mod: inve=MOD(self.mod).Pow(other.polynomial[-1],-1) for i in range(len(self.polynomial)-len(other.polynomial),-1,-1): quot[i]=rema[i+len(other.polynomial)-1]*inve%self.mod for j in range(len(other.polynomial)): rema[i+j]-=quot[i]*other.polynomial[j] rema[i+j]%=self.mod else: inve=1/other.polynomial[-1] for i in range(len(self.polynomial)-len(other.polynomial),-1,-1): quot[i]=rema[i+len(other.polynomial)-1]*inve for j in range(len(other.polynomial)): rema[i+j]-=quot[i]*other.polynomial[j] while rema and abs(rema[-1])<=self.eps: rema.pop() quot=Polynomial(quot,max_degree=self.max_degree,eps=self.eps,mod=self.mod) rema=Polynomial(rema,max_degree=self.max_degree,eps=self.eps,mod=self.mod) return quot,rema def __neg__(self): if self.mod: nega=Polynomial([(-x)%self.mod for x in self.polynomial],max_degree=self.max_degree,eps=self.eps,mod=self.mod) else: nega=Polynomial([-x for x in self.polynomial],max_degree=self.max_degree,eps=self.eps,mod=self.mod) return nega def __pos__(self): posi=Polynomial([x for x in self.polynomial],max_degree=self.max_degree,eps=self.eps,mod=self.mod) return posi def __bool__(self): return self.polynomial def __getitem__(self,n): if type(n)==int: if n<=len(self.polynomial)-1: return self.polynomial[n] else: return 0 else: return Polynomial(polynomial=self.polynomial[n],max_degree=self.max_degree,eps=self.eps,mod=self.mod) def __setitem__(self,n,a): if self.mod: a%=self.mod if self.max_degree==-1 or n<=self.max_degree: if n<=len(self.polynomial)-1: self.polynomial[n]=a elif self.eps<abs(a): self.polynomial+=[0]*(n-len(self.polynomial))+[a] def __iter__(self): for x in self.polynomial: yield x def __call__(self,x): retu=0 pow_x=1 for i in range(len(self.polynomial)): retu+=pow_x*self.polynomial[i] pow_x*=x if self.mod: retu%=self.mod pow_x%=self.mod return retu def __str__(self): return "["+", ".join(map(str,self.polynomial))+"]" def __len__(self): return len(self.polynomial) def Differentiate(self): if self.mod: differential=[x*i%self.mod for i,x in enumerate(self.polynomial[1:],1)] else: differential=[x*i for i,x in enumerate(self.polynomial[1:],1)] return Polynomial(differential,max_degree=self.max_degree,eps=self.eps,mod=self.mod) def Integrate(self): if self.mod: MD=MOD(self.mod) MD.Build_Inverse(len(self.polynomial)) integral=[0]+[x*MD.Inverse(i+1)%self.mod for i,x in enumerate(self.polynomial)] else: integral=[0]+[x/(i+1) for i,x in enumerate(self.polynomial)] while integral and abs(integral[-1])<=self.eps: integral.pop() return Polynomial(integral,max_degree=self.max_degree,eps=self.eps,mod=self.mod) def Inverse(self): assert self.polynomial and self.eps<self.polynomial[0] assert self.max_degree!=-1 if self.mod: quot=[MOD(self.mod).Pow(self.polynomial[0],-1)] if self.mod==998244353: prim_root=3 prim_root_inve=332748118 else: prim_root=Primitive_Root(self.mod) prim_root_inve=MOD(self.mod).Pow(prim_root,-1) def DFT(polynomial,n,inverse=False): polynomial=polynomial+[0]*((1<<n)-len(polynomial)) if inverse: for bit in range(1,n+1): a=1<<bit-1 x=pow(prim_root,self.mod-1>>bit,self.mod) U=[1] for _ in range(a): U.append(U[-1]*x%self.mod) for i in range(1<<n-bit): for j in range(a): s=i*2*a+j t=s+a polynomial[s],polynomial[t]=(polynomial[s]+polynomial[t]*U[j])%self.mod,(polynomial[s]-polynomial[t]*U[j])%self.mod x=pow((self.mod+1)//2,n,self.mod) for i in range(1<<n): polynomial[i]*=x polynomial[i]%=self.mod else: for bit in range(n,0,-1): a=1<<bit-1 x=pow(prim_root_inve,self.mod-1>>bit,self.mod) U=[1] for _ in range(a): U.append(U[-1]*x%self.mod) for i in range(1<<n-bit): for j in range(a): s=i*2*a+j t=s+a polynomial[s],polynomial[t]=(polynomial[s]+polynomial[t])%self.mod,U[j]*(polynomial[s]-polynomial[t])%self.mod return polynomial else: quot=[1/self.polynomial[0]] def DFT(polynomial,n,inverse=False): N=len(polynomial) if inverse: primitive_root=[math.cos(-i*2*math.pi/(1<<n))+math.sin(-i*2*math.pi/(1<<n))*1j for i in range(1<<n)] else: primitive_root=[math.cos(i*2*math.pi/(1<<n))+math.sin(i*2*math.pi/(1<<n))*1j for i in range(1<<n)] polynomial=polynomial+[0]*((1<<n)-N) if inverse: for bit in range(1,n+1): a=1<<bit-1 for i in range(1<<n-bit): for j in range(a): s=i*2*a+j t=s+a polynomial[s],polynomial[t]=polynomial[s]+polynomial[t]*primitive_root[j<<n-bit],polynomial[s]-polynomial[t]*primitive_root[j<<n-bit] for i in range(1<<n): polynomial[i]=round((polynomial[i]/(1<<n)).real) else: for bit in range(n,0,-1): a=1<<bit-1 for i in range(1<<n-bit): for j in range(a): s=i*2*a+j t=s+a polynomial[s],polynomial[t]=polynomial[s]+polynomial[t],primitive_root[j<<n-bit]*(polynomial[s]-polynomial[t]) return polynomial for n in range(self.max_degree.bit_length()): prev=quot DFT_prev=DFT(prev,n+1) if self.mod: quot=[x*y%self.mod for x,y in zip(DFT_prev,DFT(self.polynomial[:1<<n+1],n+1))] else: quot=[x*y for x,y in zip(DFT_prev,DFT(self.polynomial[:1<<n+1],n+1))] quot=DFT([0]*(1<<n)+DFT(quot,n+1,inverse=True)[1<<n:],n+1) if self.mod: quot=[(-x*y)%self.mod for x,y in zip(DFT_prev,quot)] else: quot=[-x*y for x,y in zip(DFT_prev,quot)] quot=prev+DFT(quot,n+1,inverse=True)[1<<n:] quot=quot[:self.max_degree+1] quot=Polynomial(quot,max_degree=self.max_degree,eps=self.eps,mod=self.mod) return quot def Log(self): assert self.max_degree!=-1 assert self.polynomial and abs(self.polynomial[0]-1)<=self.eps log=self.inverse() if self.mod: log=Polynomial(NTT(self.differentiate().polynomial,log.polynomial),max_degree=self.max_degree,eps=self.eps,mod=self.mod) else: log=Polynomial(FFT(self.differentiate().polynomial,log.polynomial),max_degree=self.max_degree,eps=self.eps,mod=self.mod) log=log.integrate() return log def Newton(self,n0,f,differentiated_f=None): newton=[n0] while len(newton)<self.max_degree+1: prev=newton if differentiated_f==None: newton=f(prev,self.polynomial) else: newton=f(prev) for i in range(min(len(self.polynomial),len(newton))): newton[i]-=self.polynomial[i] newton[i]%=self.mod if self.mod: newton=NTT(newton,Polynomial(differentiated_f(prev),max_degree=len(newton)-1,eps=self.eps,mod=self.mod).inverse().polynomial)[:len(newton)] else: newton=FFT(newton,Polynomial(differentiated_f(prev),max_degree=len(newton)-1,eps=self.eps,mod=self.mod).inverse().polynomial)[:len(newton)] for i in range(len(newton)): newton[i]=-newton[i] newton[i]%=self.mod for i in range(len(prev)): newton[i]+=prev[i] newton[i]%=self.mod newton=newton[:self.max_degree+1] while newton and newton[-1]<=self.eps: newton.pop() return Polynomial(newton,max_degree=self.max_degree,eps=self.eps,mod=self.mod) def Sqrt(self): if self.polynomial: for cnt0 in range(len(self.polynomial)): if self.polynomial[cnt0]: break if cnt0%2: sqrt=None else: if self.mod: n0=Tonelli_Shanks(self.polynomial[cnt0],self.mod) else: if self.polynomial[cnt0]>=self.eps: n0=self.polynomial[cnt0]**.5 if n0==None: sqrt=None else: def f(prev): if self.mod: return NTT_Pow(prev,2)+[0] else: return FFT_Pow(prev,2)+[0] def differentiated_f(prev): retu=[0]*(2*len(prev)-1) for i in range(len(prev)): retu[i]+=2*prev[i] if self.mod: retu[i]%self.mod return retu sqrt=[0]*(cnt0//2)+Polynomial(self.polynomial[cnt0:],max_degree=self.max_degree-cnt0//2,mod=self.mod).Newton(n0,f,differentiated_f).polynomial sqrt=Polynomial(sqrt,max_degree=self.max_degree,eps=self.eps,mod=self.mod) else: sqrt=Polynomial([],max_degree=self.max_degree,eps=self.eps,mod=self.mod) return sqrt def Exp(self): assert not self.polynomial or abs(self.polynomial[0])<=self.eps def f(prev,poly): newton=Polynomial(prev,max_degree=2*len(prev)-1,eps=self.eps,mod=self.mod).log().polynomial newton+=[0]*(2*len(prev)-len(newton)) for i in range(min(len(poly),len(newton))): newton[i]-=poly[i] if self.mod: for i in range(len(newton)): newton[i]%=self.mod if self.mod: return NTT(prev,newton)[:2*len(prev)] else: return FFT(prev,newton)[:2*len(prev)] return Polynomial(self.polynomial,max_degree=self.max_degree,mod=self.mod).Newton(1,f) def Degree(self): return len(self.polynomial)-1 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=None): self.p=p self.e=e if self.e==None: self.mod=self.p else: 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] if self.e==None: for i in range(1,N+1): self.factorial.append(self.factorial[-1]*i%self.mod) else: self.cnt=[0]*(N+1) for i in range(1,N+1): self.cnt[i]=self.cnt[i-1] ii=i 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 Build_Inverse(self,N): self.inverse=[None]*(N+1) assert self.p>N self.inverse[1]=1 for n in range(2,N+1): if n%self.p==0: continue a,b=divmod(self.mod,n) self.inverse[n]=(-a*self.inverse[b])%self.mod def Inverse(self,n): return self.inverse[n] def Fact(self,N): if N<0: return 0 retu=self.factorial[N] if self.e!=None and self.cnt[N]: retu*=pow(self.p,self.cnt[N],self.mod)%self.mod retu%=self.mod return retu def Fact_Inve(self,N): if self.e!=None and 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.mod*self.factorial_inve[N-K]%self.mod if self.e!=None: 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 N,K=map(int,input().split()) A=list(map(int,input().split())) mod=(1<<61)-1 rand=[random.randint(1<<40,1<<50) for i in range(N)] P=Polynomial(polynomial=[1],max_degree=K,mod=mod) for a in A: poly=[0]*(a+1) poly[0]+=1 poly[a]+=1 P*=Polynomial(polynomial=poly,max_degree=K,mod=mod) Q=int(input()) for q in range(Q): x,v=map(int,input().split()) x-=1 poly=[0]*(A[x]+1) poly[0]+=1 poly[A[x]]+=1 P/=Polynomial(polynomial=poly,max_degree=K,mod=mod) A[x]=v poly=[0]*(A[x]+1) poly[0]+=1 poly[A[x]]+=1 P*=Polynomial(polynomial=poly,max_degree=K,mod=mod) if P[K]: ans=1 else: ans=0 print(ans)