FFT&NTT模板

Posted 2021-03-22 yiqiatiya

博主菜鸡，只会背模板，根本解释不来嘤嘤嘤~

FFT：

#include<bits/stdc++.h>
#define IL inline
#define LF double
using namespace std;
const int N=5e6+5;
const LF Pi=acos(-1.0);
struct com{
    LF x,y;
    com(LF xx=0,LF yy=0){x=xx,y=yy;}
    com operator+(const com &a) const{return com(a.x+x,a.y+y);}
    com operator-(const com &a) const{return com(x-a.x,y-a.y);}
    com operator*(const com &a) const{return com(x*a.x-y*a.y,a.x*y+a.y*x);}
}a[N],b[N];
IL int in(){
    char c;int f=1;
    while((c=getchar())<‘0‘||c>‘9‘)
      if(c==‘-‘) f=-1;
    int x=c-‘0‘;
    while((c=getchar())>=‘0‘&&c<=‘9‘)
      x=x*10+c-‘0‘;
    return x*f;
}
int n,m,r[N],Max=1,cnt;
void FFT(com *a,int op){
    for(int i=0;i<Max;++i) if(i<r[i]) swap(a[i],a[r[i]]);
    for(int i=1;i<Max;i<<=1){
        com Wn=com(cos(Pi/i),op*sin(Pi/i));
        for(int k=i<<1,j=0;j<Max;j+=k){
            com w=com(1,0);
            for(int l=0;l<i;++l,w=w*Wn){
                com x=a[j+l],y=w*a[j+i+l];
                a[j+l]=x+y,a[j+i+l]=x-y;
            }
        }
    }
}
int main()
{
    n=in(),m=in();
    while(Max<=n+m) Max<<=1,++cnt;
    for(int i=0;i<Max;++i) r[i]=(r[i>>1]>>1)|((i&1)<<cnt-1);
    for(int i=0;i<=n;++i) a[i].x=in();
    for(int i=0;i<=m;++i) b[i].x=in();
    FFT(a,1),FFT(b,1);
    for(int i=0;i<=Max;++i) a[i]=a[i]*b[i];
    FFT(a,-1);
    for(int i=0;i<=n+m;++i) printf("%d ",(int)(a[i].x/Max+0.5));
    return 0; 
}

 

NTT：

#include<bits/stdc++.h>
#define IL inline
#define LL long long
using namespace std;
const LL P=998244353,G=3,Gi=332748118,N=4e6+3;
LL n,m,a[N],b[N];
int r[N],Max=1,cnt;
IL int in(){
    char c;int f=1;
    while((c=getchar())<‘0‘||c>‘9‘)
      if(c==‘-‘) f=-1;
    int x=c-‘0‘;
    while((c=getchar())>=‘0‘&&c<=‘9‘)
      x=x*10+c-‘0‘;
    return x*f;
}
IL LL ksm(LL a,LL b){
    LL c=1;
    while(b){
        if(b&1) c=c*a%P;a=a*a%P;
        b>>=1;
    }
    return c;
}
void NTT(LL *a,int op){
    for(int i=0;i<Max;++i) if(i<r[i]) swap(a[i],a[r[i]]);
    for(int i=1;i<Max;i<<=1){
        LL wn=ksm(~op?G:Gi,(P-1)/(i<<1));
        for(int j=0;j<Max;j+=(i<<1)){
            LL w=1;
            for(int k=0;k<i;++k,w=wn*w%P){
                LL x=a[j+k],y=w*a[j+i+k]%P;
                a[j+k]=(x+y)%P,a[j+i+k]=(x-y+P)%P;
            }
        }
    }
}
int main()
{
    n=in(),m=in();
    for(int i=0;i<=n;++i) a[i]=(in()+P)%P;
    for(int i=0;i<=m;++i) b[i]=(in()+P)%P;
    while(Max<=n+m) Max<<=1,++cnt;
    for(int i=0;i<Max;++i) r[i]=(r[i>>1]>>1)|((i&1)<<cnt-1);
    NTT(a,1),NTT(b,1);
    for(int i=0;i<Max;++i) a[i]=a[i]*b[i]%P;NTT(a,-1);
    LL inv=ksm(Max,P-2);
    for(int i=0;i<=n+m;++i) printf("%lld ",(a[i]*inv)%P);
    return 0;
}