Include
多项式乘法
多项式求逆
多项式除法
多项式取模
多项式对数函数
多项式指数函数
多项式正弦函数
多项式余弦函数
#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=998244353; const int G=3; const int GI=332748118; const int I=86583718; const int iv2=499122177; 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;} 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;} il void rev(Poly &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]]); } } 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;} 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 ~(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()); } //i^2=998244352 i=86583718 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(){ int n,t;rd(n);rd(t); Poly f;f.read(n); if(t==0) (Sin(f)).out(); else (Cos(f)).out(); return 0; } } signed main(){ Miracle::main(); return 0; } /* Author: *Miracle* Date: 2019/4/8 18:57:00 */
持(yi)续(ding)更(bu)新(gu)~
原文地址:https://www.cnblogs.com/Miracevin/p/10674814.html
时间: 2024-11-08 16:58:58