1. 程式人生 > >2019.01.01洛谷 P4725/P4726 多項式對數/指數函式(牛頓迭代)

2019.01.01洛谷 P4725/P4726 多項式對數/指數函式(牛頓迭代)

4725傳送門
4726傳送門
解析
程式碼:

#include<bits/stdc++.h>
#define ri register int
using namespace std;
inline int read(){
	int ans=0;
	char ch=getchar();
	while(!isdigit(ch))ch=getchar();
	while(isdigit(ch))ans=(ans<<3)+(ans<<1)+(ch^48),ch=getchar();
	return ans;
}
typedef long long ll;
const int mod=998244353; int n,lim,tim; vector<int>A,B,pos,Inv; inline int add(const int&a,const int&b){return a+b>=mod?a+b-mod:a+b;} inline int dec(const int&a,const int&b){return a>=b?a-b:a-b+mod;} inline int mul(const int&a,const int&b){return (ll)a*b%mod;} inline
int ksm(int a,int p){int ret=1;for(;p;p>>=1,a=mul(a,a))if(p&1)ret=mul(ret,a);return ret;} inline void ntt(vector<int>&a,int type){ for(ri i=0;i<lim;++i)if(i<pos[i])swap(a[i],a[pos[i]]); for(ri mid=1,wn,mult=(mod-1)/2,typ=type==1?3:(mod+1)/3;mid<lim;mid<<=1,mult>>=
1){ wn=ksm(typ,mult); for(ri j=0,len=mid<<1;j<lim;j+=len)for(ri w=1,a0,a1,k=0;k<mid;++k,w=mul(w,wn)){ a0=a[j+k],a1=mul(w,a[j+k+mid]); a[j+k]=add(a0,a1),a[j+k+mid]=dec(a0,a1); } } if(type==-1)for(ri i=0,inv=ksm(lim,mod-2);i<lim;++i)a[i]=mul(a[i],inv); } inline void init(int up){ lim=1,tim=0; while(lim<=up)lim<<=1,++tim; pos.resize(lim-1),pos[0]=0; for(ri i=0;i<lim;++i)pos[i]=(pos[i>>1]>>1)|((i&1)<<(tim-1)); } struct poly{ vector<int>a; inline int deg()const{return a.size()-1;} poly(int k,int x=0){a.resize(k+1),a[k]=x;} inline int&operator[](const int&k){return a[k];} inline const int&operator[](const int&k)const{return a[k];} inline poly extend(const int&k){poly ret=*this;return ret.a.resize(k+1),ret;} friend inline poly operator+(const poly&a,const poly&b){ poly ret(max(a.deg(),b.deg())); for(ri i=0;i<=a.deg();++i)ret[i]=add(ret[i],a[i]); for(ri i=0;i<=b.deg();++i)ret[i]=add(ret[i],b[i]); return ret; } friend inline poly operator-(const poly&a,const poly&b){ poly ret(max(a.deg(),b.deg())); for(ri i=0;i<=a.deg();++i)ret[i]=add(ret[i],a[i]); for(ri i=0;i<=b.deg();++i)ret[i]=dec(ret[i],b[i]); return ret; } friend inline poly operator*(const int&a,const poly&b){ poly ret(b.deg()); for(ri i=0;i<=b.deg();++i)ret[i]=mul(a,b[i]); return ret; } friend inline poly operator*(const poly&a,const poly&b){ int n=a.deg(),m=b.deg(); init(n+m),A.resize(lim),B.resize(lim); poly ret(lim-1); for(ri i=0;i<=n;++i)A[i]=a[i]; for(ri i=0;i<=m;++i)B[i]=b[i]; for(ri i=n+1;i<lim;++i)A[i]=0; for(ri i=m+1;i<lim;++i)B[i]=0; ntt(A,1),ntt(B,1); for(ri i=0;i<lim;++i)A[i]=mul(A[i],B[i]); return ntt(A,-1),ret.a=A,ret; } inline poly poly_inv(poly a,const int&k){ a=a.extend(k); if(k==1)return poly(0,ksm(a[0],mod-2)); poly f0=poly_inv(a,(k+1)>>1); return (2*f0-((f0*f0.extend(k))*a).extend(k)).extend(k); } inline poly poly_direv(poly a){ poly ret(a.deg()-1); for(ri i=0;i<=ret.deg();++i)ret[i]=mul(a[i+1],i+1); return ret; } inline poly poly_inter(poly a){ poly ret(a.deg()+1); for(ri i=1;i<=ret.deg();++i)ret[i]=mul(Inv[i],a[i-1]); return ret; } inline poly poly_ln(poly a,int len){ poly ret=a.poly_direv(a); return ret=ret*a.poly_inv(a,len),ret.poly_inter(ret); } inline poly poly_exp(poly a,const int&k){ a=a.extend(k); if(k==1)return poly(0,1); poly f0=poly_exp(a,(k+1)>>1).extend(k); poly delt=a-poly_ln(f0,k); ++delt[0]; return (f0*delt).extend(k); } }; int main(){ n=read()-1; poly ans(n); for(ri i=0;i<=n;++i)ans[i]=read(); int len=1; while(len<=n*2)len<<=1; Inv.resize(len),Inv[1]=1; for(ri i=2;i<len;++i)Inv[i]=mul(Inv[mod%i],mod-mod/i); ans=ans.poly_exp(ans,len); for(ri i=0;i<=n;++i)cout<<ans[i]<<' '; return 0; }