• 【洛谷 P4721】【模板】—分治FFT(CDQ分治+NTT)


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    模板

    #include<bits/stdc++.h>
    using namespace std;
    const int RLEN=1<<20|1;
    inline char gc(){
        static char ibuf[RLEN],*ib,*ob;
        (ob==ib)&&(ob=(ib=ibuf)+fread(ibuf,1,RLEN,stdin));
        return (ob==ib)?EOF:*ib++;
    }
    #define gc getchar
    inline int read(){
        char ch=gc();
        int res=0,f=1;
        while(!isdigit(ch))f^=ch=='-',ch=gc();
        while(isdigit(ch))res=(res+(res<<2)<<1)+(ch^48),ch=gc();
        return f?res:-res;
    }
    #define ll long long
    #define re register
    #define pii pair<int,int>
    #define fi first
    #define se second
    #define pb push_back
    #define cs const
    #define bg begin
    #define poly vector<int>  
    cs int mod=998244353,G=3;
    inline int add(int a,int b){return (a+=b)>=mod?a-mod:a;}
    inline void Add(int &a,int b){(a+=b)>=mod?a-=mod:0;}
    inline int dec(int a,int b){return (a-=b)<0?a+mod:a;}
    inline void Dec(int &a,int b){(a-=b)<0?a+=mod:0;}
    inline int mul(int a,int b){return 1ll*a*b%mod;}
    inline void Mul(int &a,int b){a=1ll*a*b%mod;}
    inline int ksm(int a,int b,int res=1){for(;b;b>>=1,Mul(a,a))(b&1)&&(Mul(res,a),1);return res;}
    inline int Inv(int x){return ksm(x,mod-2);}
    template<class tp>inline void chemx(tp &a,tp b){a<b?a=b:0;}
    template<class tp>inline void chemn(tp &a,tp b){a>b?a=b:0;}
    cs int C=19;
    poly w[C+1];
    inline void init_w(){
    	for(int i=1;i<=C;i++)w[i].resize(1<<(i-1));
    	int wn=ksm(G,(mod-1)/(1<<C));
    	w[C][0]=1;
    	for(int i=1;i<(1<<(C-1));i++)w[C][i]=mul(w[C][i-1],wn);
    	for(int i=C-1;i;i--)
    	for(int j=0;j<(1<<(i-1));j++)w[i][j]=w[i+1][j<<1];
    }
    int rev[(1<<C)|5],inv[(1<<C)|5];
    inline void init_inv(){
    	inv[0]=inv[1]=1;
    	for(int i=2;i<=(1<<C);i++)inv[i]=mul(mod-mod/i,inv[mod%i]);
    }
    inline void init_rev(int lim){
    	for(int i=0;i<lim;i++)rev[i]=(rev[i>>1]>>1)|((i&1)*(lim>>1));
    }
    inline void ntt(poly &f,int lim,int kd){
    	for(int i=0;i<lim;i++)if(i>rev[i])swap(f[i],f[rev[i]]);
    	for(int mid=1,l=1,a0,a1;mid<lim;mid<<=1,l++)
    	for(int i=0;i<lim;i+=(mid<<1))
    	for(int j=0;j<mid;j++)
    	a0=f[i+j],a1=mul(f[i+j+mid],w[l][j]),f[i+j]=add(a0,a1),f[i+j+mid]=dec(a0,a1);
    	if(kd==-1){
    		reverse(f.bg()+1,f.bg()+lim);
    		for(int i=0;i<lim;i++)Mul(f[i],inv[lim]);
    	}
    }
    inline poly operator *(poly a,poly b){
    	int deg=a.size()+b.size()-1,lim=1;
    	if(deg<=32){
    		poly c(deg,0);
    		for(int i=0;i<a.size();i++)
    		for(int j=0;j<b.size();j++)
    		Add(c[i+j],mul(a[i],b[j]));
    		return c;
    	}
    	while(lim<deg)lim<<=1;
    	init_rev(lim);
    	a.resize(lim),ntt(a,lim,1);
    	b.resize(lim),ntt(b,lim,1);
    	for(int i=0;i<lim;i++)Mul(a[i],b[i]);
    	ntt(a,lim,-1),a.resize(deg);
    	return a;
    }
    cs int N=100005;
    int f[N],g[N],n;
    void cdq(int l,int r){
    	if(l==r)return;
    	int mid=(l+r)>>1;
    	cdq(l,mid);
    	poly a,b;
    	for(int i=l;i<=mid;i++)
    	a.pb(f[i]);
    	for(int i=l;i<=r;i++)b.pb(g[i-l+1]);
    	a=a*b;
    	for(int i=mid+1;i<=r;i++)
    	Add(f[i],a[i-l-1]);
    	cdq(mid+1,r);
    }
    int main(){
    	init_w(),init_inv();
    	n=read();
    	for(int i=1;i<n;i++)g[i]=read();
    	f[0]=1;
    	cdq(0,n-1);
    	for(int i=0;i<n;i++)cout<<f[i]<<" ";
    }
    
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  • 原文地址:https://www.cnblogs.com/stargazer-cyk/p/12328416.html
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