FFT多项式乘法模板

Posted 2020-08-29 Saurus

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(-1);
const int maxn =  111111;
typedef complex<double> Complex;
void DFT(Complex *a, int n, int t)
{
    if(n == 1) return;
    complex <double> a0[n>>1], a1[n>>1];
    for(int i = 0; i < n; i += 2) a0[i>>1] = a[i], a1[i>>1] = a[i+1];
    DFT(a0, n>>1, t); DFT(a1, n>>1, t);
    complex <double> wn(cos(2*pi/n), t*sin(2*pi/n)), w(1, 0);
    for(int i = 0; i < (n>>1); i++, w *= wn) a[i] = a0[i] + w*a1[i], a[i+(n>>1)] = 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 = 0; i <= n1; i++) cin>>x, a[i] = Complex(x, 0);
    for(int i = 0; i <= n2; i++) cin>>x, b[i] = Complex(x, 0);
    nn = 1; while(nn <= n1+n2) nn <<= 1;
    DFT(a, nn, 1); DFT(b, nn, 1);
    for(int i = 0; i <= nn; i++) a[i] = a[i]*b[i];
    DFT(a, nn, -1);
    for(int i = 0; i <= n1+n2; i++) c[i] = (a[i].real()/nn+0.5);
    for(int i = 0; i < n1+n2; i++) if(c[i] > 10) c[i+1] += c[i]/10, c[i] %= 10;
    for(int i = n1+n2; i >= 0; i--) cout<<c[i];
    return 0;
}