[学习笔记]快速傅里叶变换 FFT

屯板子

#include<iostream>#include<cstring>#include<cstdio>#include<algorithm>#include<cmath>#define N 2621450#define pi P_Pusing namespace std;const double pi=acos(-1);struct E{    double x,y;    E(double _x=0.0,double _y=0.0) { x=_x,y=_y; }    inline E operator=(const E &w)    { this->x=w.x,this->y=w.y;return *this; }    inline E operator+(const E &w)    { return E(x+w.x,y+w.y); }    inline E operator-(const E &w)    { return E(x-w.x,y-w.y); }    inline E operator*(const E &w)    { return E(x*w.x-y*w.y,x*w.y+y*w.x); }    inline E operator*=(const E &w)    { return (*this)=(*this)*w; }}a[N],b[N];int r[N];inline int FFT(E *a,int n,int sgn){    for(int i=0;i<n;i++)        if(i<r[i]) swap(a[i],a[r[i]]);    for(int i=1;i<n;i<<=1)    {        E wn(cos(pi/i),sgn*sin(pi/i));        for(int p=i<<1,j=0;j<n;j+=p)        {            E w(1.0,0.0);            for(int k=0;k<i;k++,w*=wn)            {                E x=a[j+k],y=w*a[j+k+i];                a[j+k]=x+y,a[j+k+i]=x-y;            }        }    }    return 0;}#define gc getchar()inline int inn(){   int x;while((x=gc)<'0'||x>'9');return x^'0';  }#undef gcint main(){    int n,m,L;scanf("%d%d",&n,&m);    for(int i=0;i<=n;i++) a[i]=E(inn(),0.0);    for(int i=0;i<=m;i++) b[i]=E(inn(),0.0);    for(m+=n,n=1,L=0;n<=m;n<<=1,L++);    for(int i=0;i<n;i++)        r[i]=((r[i>>1]>>1)|((i&1)<<(L-1)));    FFT(a,n,1),FFT(b,n,1);    for(int i=0;i<=n;i++) a[i]*=b[i];    FFT(a,n,-1);    for(int i=0;i<=m;i++)        printf("%d ",(int)(a[i].x/n+0.5));    return !printf("\n");}