多项式全家桶
Include
多项式乘法(* *=)
多项式求逆(~ Inv)
多项式除法(/)
多项式取模(%)
多项式对数函数(Ln)
多项式指数函数(Exp)
多项式正弦函数(Cos)
多项式余弦函数(Sin)
upda:2019.4.28:
对于任意模数NTT全部适用。
位于:namespace FastFourierTransform
开启方法:
1.取消注释 using namespace FastFourierTransform;
2.把//dele start here/* 到// delete end here */ 删除或者注释掉。
或者,直接把'/*'敲回车打下去即可。
后面的乘法和求逆都直接调用FastFourierTransform中内置的了。
#include<bits/stdc++.h> #define reg register int #define il inline #define fi first #define se second #define mk(a,b) make_pair(a,b) #define numb (ch^'0') using namespace std; typedef long long ll; template<class T>il void rd(T &x){ char ch;x=0;bool fl=false; while(!isdigit(ch=getchar()))(ch=='-')&&(fl=true); for(x=numb;isdigit(ch=getchar());x=x*10+numb); (fl==true)&&(x=-x); } template<class T>il void output(T x){if(x/10)output(x/10);putchar(x%10+'0');} template<class T>il void ot(T x){if(x<0) putchar('-'),x=-x;output(x);putchar(' ');} template<class T>il void prt(T a[],int st,int nd){for(reg i=st;i<=nd;++i) ot(a[i]);putchar('\n');} //--------------------------------------------------------------------------------------------------------------------// namespace Miracle{ const int mod; const int G=3; const int GI=332748118; const int I=86583718; const int iv2=499122177; const double Pi=acos(-1); il int qm(int x,int y){int ret=1;while(y){if(y&1) ret=(ll)ret*x%mod;x=(ll)x*x%mod;y>>=1;}return ret;} il int ad(int x,int y){return x+y>=mod?x+y-mod:x+y;} il int sub(int x,int y){return ad(x,mod-y);} il int mul(int x,int y){return (ll)x*y%mod;} namespace Polynomial{ struct Poly{ vector<int>f; Poly(){f.clear();} il int &operator[](const int &x){return f[x];} il const int &operator[](const int &x) const {return f[x];} il void resize(const int &n){f.resize(n);} il int size() const {return f.size();} il void cpy(Poly &b){f.resize(b.size());for(reg i=0;i<(int)f.size();++i)f[i]=b[i];} il void rev(){reverse(f.begin(),f.end());} il void clear(){f.clear();} il void read(const int &n){f.resize(n);for(reg i=0;i<n;++i)rd(f[i]);} il void out() const {for(reg i=0;i<(int)f.size();++i)ot(f[i]);putchar('\n');} }R; il int init(const int &n){int m;for(m=1;m<n;m<<=1);return m;} template<class T>il void rev(T &f){ int lp=f.size(); if(R.size()!=f.size()) { R.resize(f.size()); for(reg i=0;i<lp;++i){ R[i]=(R[i>>1]>>1)|((i&1)?lp>>1:0); } } for(reg i=0;i<lp;++i){ if(i<R[i]) swap(f[i],f[R[i]]); } } } using namespace Polynomial; //--------------------------------------------------------------------------------------------------------------------// il void operator +=(Poly &f,const Poly &g){for(reg i=0;i<f.size();++i) f[i]=ad(f[i],g[i]);} il void operator +=(Poly &f,const int &c){f[0]=ad(f[0],c);} il Poly operator +(Poly f,const Poly &g){for(reg i=0;i<f.size();++i) f[i]=ad(f[i],g[i]);return f;} il Poly operator +(Poly f,const int &c){f[0]=ad(f[0],c);return f;} il void operator -=(Poly &f,const Poly &g){for(reg i=0;i<f.size();++i) f[i]=sub(f[i],g[i]);} il void operator -=(Poly &f,const int &c){f[0]=sub(f[0],c);} il Poly operator -(Poly f,const Poly &g){for(reg i=0;i<f.size();++i) f[i]=sub(f[i],g[i]);return f;} il Poly operator -(Poly f,const int &c){f[0]=sub(f[0],c);return f;} il Poly operator -(Poly f){for(reg i=0;i<f.size();++i) f[i]=mod-f[i];return f;} //--------------------------------------------------------------------------------------------------------------------// namespace FastFourierTransform{ struct cplx{ double x,y; cplx(){x=0.0;y=0.0;} cplx(double xx,double yy){x=xx;y=yy;} cplx friend operator !(cplx a){return cplx(a.x,-a.y);} cplx friend operator +(cplx a,cplx b){return cplx(a.x+b.x,a.y+b.y);} cplx friend operator -(cplx a,cplx b){return cplx(a.x-b.x,a.y-b.y);} cplx friend operator *(cplx a,cplx b){return cplx(a.x*b.x-a.y*b.y,a.x*b.y+a.y*b.x);} }; struct Cps{ vector<cplx>f; Cps(){f.clear();} il cplx &operator[](const int &x){return f[x];} il const cplx &operator[](const int &x) const {return f[x];} il void resize(const int &n){f.resize(n);} il int size() const {return f.size();} il void cpy(Cps &b){f.resize(b.size());for(reg i=0;i<(int)f.size();++i)f[i]=b[i];} il void rev(){reverse(f.begin(),f.end());} il void clear(){f.clear();} il void out(){ for(reg i=0;i<(int)f.size();++i){ cout<<"("<<f[i].x<<","<<f[i].y<<") "; }cout<<endl; } }W; il void FFT(Cps &f,int c){ int n=f.size();rev(f); for(reg p=2;p<=n;p<<=1){ int len=p/2; for(reg l=0;l<n;l+=p){ for(reg k=l;k<l+len;++k){ cplx tmp=f[k+len]*(c>0?W[n/p*(k-l)]:!W[n/p*(k-l)]); f[k+len]=f[k]-tmp; f[k]=f[k]+tmp; } } } if(c==-1){ for(reg i=0;i<n;++i){ f[i].x/=n;f[i].y/=n; } } } il void prework(int n){ if(W.size()!=n){ W.resize(n); for(reg i=0;i<n;++i){ W[i]=cplx(cos(2*Pi/n*i),sin(2*Pi/n*i)); } } } il Poly MTT(const Poly &F,const Poly &G,const int &P){ int n=F.size(),m=G.size(); Cps a,b,c,d; int len=init(n+m-1); a.resize(len);b.resize(len); c.resize(len);d.resize(len); for(reg i=0;i<n;++i){ a[i].x=F[i]>>15;a[i].y=F[i]&32767; } for(reg i=0;i<m;++i){ b[i].x=G[i]>>15;b[i].y=G[i]&32767; } prework(len); FFT(a,1);FFT(b,1); cplx ka,kb,ba,bb; cplx aaa=cplx(0.5,0),bbb=cplx(0,-0.5),o=cplx(0,1); for(reg i=0;i<len;++i){ int j=(len-i)%len; ka=(a[i]+!a[j])*aaa;ba=(a[i]-!a[j])*bbb; kb=(b[i]+!b[j])*aaa;bb=(b[i]-!b[j])*bbb; c[i]=ka*kb+ba*kb*o; d[i]=bb*ka+bb*ba*o; } FFT(c,-1);FFT(d,-1); Poly ret; ret.resize(n+m-1); for(reg i=0;i<n+m-1;++i){ ll A=(ll)(c[i].x+0.5)%P,B=(ll)(c[i].y+0.5)%P; ll C=(ll)(d[i].x+0.5)%P,D=(ll)(d[i].y+0.5)%P; ret[i]=((((A<<30)%P)+((B+C)<<15)%P)%P+D)%P; } return ret; } il void operator *=(Poly &f,Poly g){ f=MTT(f,g,mod); } il void operator *=(Poly &f,const int &c){for(reg i=0;i<f.size();++i) f[i]=mul(f[i],c);} il Poly operator *(Poly f,const Poly &g){f*=g;return f;} il Poly operator *(Poly f,const int &c){for(reg i=0;i<f.size();++i) f[i]=mul(f[i],c);return f;} il Poly Inv(const Poly &f,int n){ if(n==1){ Poly g;g.resize(1);g[0]=qm(f[0],mod-2);return g; } Poly h=Inv(f,(n+1)>>1); Poly tmp=h,t; t.resize(n); for(reg i=0;i<n;++i) t[i]=f[i]; tmp=tmp*tmp*t; h.resize(tmp.size()); Poly g=h*2-tmp; g.resize(n); return g; } } // using namespace FastFourierTransform; //--------------------------------------------------------------------------------------------------------------------// // dele start here/* il void NTT(Poly &f,int c){ int n=f.size();rev(f); for(reg p=2;p<=n;p<<=1){ int gen=(c==1)?qm(G,(mod-1)/p):qm(GI,(mod-1)/p); for(reg l=0;l<n;l+=p){ int buf=1; for(reg k=l;k<l+p/2;++k){ int tmp=mul(f[k+p/2],buf); f[k+p/2]=sub(f[k],tmp); f[k]=ad(f[k],tmp); buf=mul(buf,gen); } } } if(c==-1){ int iv=qm(n,mod-2);for(reg i=0;i<n;++i) f[i]=mul(f[i],iv); } } il Poly Inv(const Poly &f,int n){ if(n==1){ Poly g;g.resize(1);g[0]=qm(f[0],mod-2);return g; } Poly g=Inv(f,(n+1)>>1),t; int m=init(n*2); t.resize(m); for(reg i=0;i<n;++i)t[i]=f[i]; g.resize(m); NTT(g,1);NTT(t,1); for(reg i=0;i<m;++i)g[i]=mul(sub(2,mul(g[i],t[i])),g[i]); NTT(g,-1);g.resize(n); return g; } il void operator *=(Poly &f,Poly g){ int st=f.size()+g.size()-1; int len=init(f.size()+g.size()-1);f.resize(len);g.resize(len); NTT(f,1);NTT(g,1);for(reg i=0;i<len;++i) f[i]=mul(f[i],g[i]); NTT(f,-1); f.resize(st); } il void operator *=(Poly &f,const int &c){for(reg i=0;i<f.size();++i) f[i]=mul(f[i],c);} il Poly operator *(Poly f,const Poly &g){f*=g;return f;} il Poly operator *(Poly f,const int &c){for(reg i=0;i<f.size();++i) f[i]=mul(f[i],c);return f;} // delete end here*/ il Poly operator ~(const Poly &f){return Inv(f,f.size());} il Poly operator /(Poly f,Poly g){int len=f.size()-g.size()+1;f.rev();g.rev();g.resize(len);f=f*(~g);f.resize(len);f.rev();return f;} il Poly operator %(Poly f,Poly g){Poly s=f/g;f=f-g*s;f.resize(g.size()-1);return f;} //--------------------------------------------------------------------------------------------------------------------// il Poly Inter(Poly f){int st=f.size();f.resize(st+1);for(reg i=st;i>=1;--i){f[i]=mul(f[i-1],qm(i,mod-2));}f[0]=0;return f;} il Poly Diff(Poly f){int st=f.size();for(reg i=0;i<st-1;++i) f[i]=mul(f[i+1],(i+1));f.resize(st-1);return f;} il Poly Ln(const Poly &f){Poly g=Diff(f),h=(~f);g=g*h;g.resize(f.size()-1);return Inter(g);} il Poly Exp(const Poly &f,int n){ if(n==1){ Poly g;g.resize(1);g[0]=1; return g; } Poly g=Exp(f,(n+1)>>1); g.resize(n); g=g*(((Ln(g)*(mod-1))+1)+f); g.resize(n); return g; } il Poly Exp(const Poly &f){ return Exp(f,f.size()); } il Poly Cos(const Poly &f){ Poly g=Exp(f*I);return (g+(~g))*iv2; } il Poly Sin(const Poly &f){ Poly g=Exp(f*I);return (g-(~g))*qm(ad(I,I),mod-2); } int main(){ return 0; } } signed main(){ Miracle::main(); return 0; } /* Author: *Miracle* Date: 2019/4/8 18:57:00 */
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