【模板】vector 封装模意义下的多项式操作

就是放一个自己用的版子，没有讲解。

用vector主要是因为好写且好调。

能在考场上用数组指针码出多项式的所有操作的“神仙”还是留给别人当吧

反正我没见过谁真的为了跑的比vector快，去码了6,7K的操作，我见过的最长的是11K的多项式操作。

写那么优秀有什么屁用呢？反正你考场上也写不完，其次所有用数组写的可读性比vector低一个档次，不好调试啊。而且开了O2可能还没有vector快。。。

#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define re register
#define gc get_char
#define cs const

namespace IO{
	inline char get_char(){
		static cs int Rlen=1<<20|1;
		static char buf[Rlen],*p1,*p2;
		return (p1==p2)&&(p2=(p1=buf)+fread(buf,1,Rlen,stdin),p1==p2)?EOF:*p1++;
	}
	
	inline int getint(){
		re char c;
		while(!isdigit(c=gc()));re int num=c^48;
		while(isdigit(c=gc()))num=(num+(num<<2)<<1)+(c^48);
		return num;
	}
}
using namespace IO;

cs int mod=998244353,N=410000,inv2=mod+1>>1;
inline int add(int a,int b){return a+b>=mod?a+b-mod:a+b;}
inline int dec(int a,int b){return a<b?a-b+mod:a-b;}
inline int mul(int a,int b){return (ll)a*b%mod;}
inline int quickpow(int a,int b,int res=1){
	while(b){
		if(b&1)res=mul(res,a);
		a=mul(a,a);
		b>>=1;
	}
	return res;
}

typedef vector<int> Poly;

inline void print(cs Poly &a,char c=' ',ostream &out=cout){
	for(int re i=0;i<a.size();++i)out<<a[i]<<c;
}

int r[N],inv[N];
inline void NTT(Poly &A,int len,int typ){
	for(int re i=0;i<len;++i)if(i<r[i])swap(A[i],A[r[i]]);
	for(int re i=1;i<len;i<<=1){
		int wn=quickpow(typ==-1?(mod+1)/3:3,(mod-1)/i/2);
		for(int re j=0;j<len;j+=i<<1)
		for(int re k=0,x,y,w=1;k<i;++k,w=mul(w,wn)){
			x=A[j+k],y=mul(w,A[j+k+i]);
			A[j+k]=add(x,y);
			A[j+k+i]=dec(x,y);
		}
	}
	if(typ==-1)for(int re i=0;i<len;++i)A[i]=mul(A[i],inv[len]);
}
inline void init_rev(int len){
	for(int re i=0;i<len;++i)r[i]=r[i>>1]>>1|((i&1)*(len>>1));
}

inline Poly operator+(cs Poly &a,cs Poly &b){
	Poly c=a;c.resize(max(a.size(),b.size()));
	for(int re i=0;i<b.size();++i)c[i]=add(c[i],b[i]);
	return c;
}

inline Poly operator-(cs Poly &a,cs Poly &b){
	Poly c=a;c.resize(max(a.size(),b.size()));
	for(int re i=0;i<b.size();++i)c[i]=dec(c[i],b[i]);
	return c;
}

inline Poly operator*(Poly a,Poly b){
	int n=a.size(),m=b.size(),l=1;
	while(l<n+m-1)l<<=1;
	init_rev(l);
	a.resize(l),NTT(a,l,1);
	b.resize(l),NTT(b,l,1);
	for(int re i=0;i<l;++i)a[i]=mul(a[i],b[i]);
	NTT(a,l,-1);
	a.resize(n+m-1);
	return a;
}

inline Poly operator*(Poly a,int b){
	for(int re i=0;i<a.size();++i)a[i]=mul(a[i],b);
	return a;
}

inline Poly Deriv(Poly a){
	for(int re i=0;i+1<a.size();++i)a[i]=mul(a[i+1],i+1);
	a.pop_back();
	return a;
}

inline Poly Integ(Poly a){
	a.push_back(0);
	for(int re i=a.size()-1;i;--i)a[i]=mul(a[i-1],inv[i]);
	a[0]=0;
	return a;
}

inline Poly Inv(cs Poly &a,int lim){
	Poly c,b(1,quickpow(a[0],mod-2));
	for(int re l=4;(l>>2)<lim;l<<=1){
		init_rev(l);
		c=a,c.resize(l>>1);
		c.resize(l),NTT(c,l,1);
		b.resize(l),NTT(b,l,1);
		for(int re i=0;i<l;++i)b[i]=mul(b[i],dec(2,mul(c[i],b[i])));
		NTT(b,l,-1);
		b.resize(l>>1);
	}
	b.resize(lim);
	return b;
}
inline Poly Inv(cs Poly &a){return Inv(a,a.size());}

inline Poly Ln(Poly a,int lim){
	a=Integ(Deriv(a)*Inv(a,lim));
	a.resize(lim);
	return a;
}
inline Poly Ln(cs Poly &a){return Ln(a,a.size());}

inline Poly Exp(cs Poly &a,int lim){
	Poly c,b(1,1);int n=a.size();
	for(int re i=2;(i>>1)<lim;i<<=1){
		c=Ln(b,i);
		for(int re j=0;j<i;++j)c[j]=dec(j<n?a[j]:0,c[j]);
		c[0]=add(c[0],1);
		b=b*c;
		b.resize(i);
	}
	b.resize(lim);
	return b;
}
inline Poly Exp(cs Poly &a){return Exp(a,a.size());}

cs int w4=quickpow(3,(mod-1)/4);
inline Poly Cos(cs Poly &a,int lim){
	Poly c=a;c.resize(lim);
	c=(Exp(c*w4)+Exp(c*(mod-w4)))*inv2;
	return c;
}
inline Poly Cos(cs Poly &a){return Cos(a,a.size());}

inline Poly Sin(cs Poly &a,int lim){
	Poly c=a;c.resize(lim);
	c=(Exp(c*w4)-Exp(c*(mod-w4)))*mul(inv2,quickpow(w4,mod-2));
	return c;
}
inline Poly Sin(cs Poly &a){return Sin(a,a.size());}

inline Poly Sqrt(cs Poly &a,int lim){
	Poly c,d,b(1,1);
	for(int re l=4;(l>>2)<lim;l<<=1){
		init_rev(l);
		c=a,c.resize(l>>1);
		d=Inv(b,l>>1);
		c.resize(l),NTT(c,l,1);
		d.resize(l),NTT(d,l,1);
		for(int re j=0;j<l;++j)c[j]=mul(c[j],d[j]);
		NTT(c,l,-1);
		b.resize(l>>1);
		for(int re j=0;j<(l>>1);++j)b[j]=mul(add(c[j],b[j]),inv2);
	}
	b.resize(lim);
	return b;
}
inline Poly Sqrt(cs Poly &a){return Sqrt(a,a.size());}

inline Poly Ksm(Poly a,int k,int lim){
	a=Exp(Ln(a)*k);
	a.resize(lim);
	return a;
}
inline Poly Ksm(cs Poly &a,int k){return Ksm(a,k,a.size());}

inline Poly operator/(Poly a,Poly b){
	int re len=1,deg=a.size()-b.size()+1;
	reverse(a.begin(),a.end());
	reverse(b.begin(),b.end());
	while(len<=deg)len<<=1;
	b=Inv(b,len);b.resize(deg);
	a=a*b;a.resize(deg);
	reverse(a.begin(),a.end());
	return a;
}

inline Poly operator%(cs Poly &a,cs Poly &b){
	Poly c=a-(a/b)*b;
	c.resize(b.size()-1);
	return c;
}

inline void init_inv(){
	inv[0]=inv[1]=1;
	for(int re i=2;i<N;++i)inv[i]=mul(inv[mod%i],mod-mod/i);
}

signed main(){
	init_inv();
	
	return 0;
}

【模板】vector 封装模意义下的多项式操作

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