Fast Fourier Transform Templates

Template title

Read a long time, still do not understand $ fft $ principle orz, but okay, anyway, is a hard partition only, do not be afraid

Save a board, the future certainly will be used to.

I hope the next time I have to understand 233

#include <iostream>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <complex>
#include <math.h>
#define MAXN 3000010
#define cp complex<double>
using namespace std;
const double PI=acos(-1.0);
int n,m,rev[MAXN],lim=1,bit;
cp a[MAXN],b[MAXN];

int read(){
    int x=0,f=1;char c=getchar();
    while(c<'0'||c>'9') {if(c=='-')f=-1;c=getchar();}
    while(c>='0'&&c<='9') {x=x*10+c-'0';c=getchar();}
    return x*f;
}

void FFT(cp *a,int inv){
    for(int i=0;i<lim;i++)
        if(i<rev[i]) swap(a[i],a[rev[i]]);
    for(int mid=1;mid<lim;mid<<=1){
        cp wn(cos(PI/mid),inv*sin(PI/mid));
        for(int i=0;i<lim;i+=mid*2){
            cp w(1,0);
            for(int j=0;j<mid;j++,w*=wn){
                cp x=a[i+j],y=w*a[i+j+mid];
                a[i+j]=x+y,a[i+j+mid]=x-y;
            }
        }
    }
}

int main(){
    n=read();m=read();
    for(int i=0;i<=n;i++) a[i].real(read());
    for(int i=0;i<=m;i++) b[i].real(read());
    while(lim<=m+n) lim<<=1,bit++;
    for(int i=0;i<lim;i++) rev[i]=(rev[i>>1]>>1) | ((i&1)<<(bit-1));
    FFT(a,1);FFT(b,1);
    for(int i=0;i<=lim;i++) a[i]*=b[i];
    FFT(a,-1);
    for(int i=0;i<=n+m;i++) printf("%d ",(int)(a[i].real()/lim+0.5));
    return 0;
}