FFT多项式乘法模板

有时间来补算法原理orz

#include <iostream>
#include <cstdio>
#include <cmath>
#include <complex>
using namespace std;
const double pi = acos(-);
const int maxn =  ;
typedef complex<double> Complex;
void DFT(Complex *a, int n, int t)
{
    if(n == ) return;
    Complex a0[n>>], a1[n>>];
    for(int i = ; i < n; i += ) a0[i>>] = a[i], a1[i>>] = a[i+];
    DFT(a0, n>>, t); DFT(a1, n>>, t);
    Complex wn(cos(*pi/n), t*sin(*pi/n)), w(, );
    for(int i = ; i < (n>>); i++, w *= wn) a[i] = a0[i] + w*a1[i], a[i+(n>>)] = a0[i] - w*a1[i];
}
Complex a[maxn], b[maxn];
int n1, n2, nn, x, c[maxn];
int main()
{
    freopen("a.txt", "r", stdin);
    cin>>n1>>n2;
    for(int i = ; i <= n1; i++) cin>>x, a[i] = Complex(x, );
    for(int i = ; i <= n2; i++) cin>>x, b[i] = Complex(x, );
    nn = ; while(nn <= n1+n2) nn <<= ;
    DFT(a, nn, ); DFT(b, nn, );
    for(int i = ; i <= nn; i++) a[i] = a[i]*b[i];
    DFT(a, nn, -);
    for(int i = ; i <= n1+n2; i++) c[i] = (a[i].real()/nn+0.5);
    for(int i = ; i < n1+n2; i++) if(c[i] > ) c[i+] += c[i]/, c[i] %= ;
    for(int i = n1+n2; i >= ; i--) cout<<c[i];
    return ;
}