FFT - YessineJallouli/Competitive-Programming GitHub Wiki

#include <bits/stdc++.h>
#define ll long long
using namespace std;
using cx = complex<double>;

constexpr auto pi = M_PI;
// use C[i].real() to get real part

void inplace_fft2(vector<cx> &a, bool inv=false) {
    int n = a.size();
    for (int i = 1, j = 0; i < n; i++) {
        int bit = n >> 1;
        for (; j & bit; bit >>= 1)
            j ^= bit;
        j ^= bit;
        if (i < j)
            swap(a[i], a[j]);
    }
    for (int len = 2; len <= n; len <<= 1) {
        double ang = 2 * pi / len * (inv ? -1 : 1);
        cx wlen = polar(1., ang);
        for (int i = 0; i < n; i += len) {
            cx w(1);
            for (int j = 0; j < len / 2; j++) {
                cx u = a[i + j], v = a[i + j + len / 2] * w;
                a[i + j] = u + v;
                a[i + j + len / 2] = u - v;
                w *= wlen;
            }
        }
    }
    if (inv)
        for (auto &z: a)
            z /= n;
}

vector<cx> multiply(vector<cx> a, vector<cx> b) {
    int r = a.size() + b.size()-1;
    int n = 1;
    while (n < r)
        n*= 2;

    a.resize(n);
    b.resize(n);
    inplace_fft2(a, false); 
    inplace_fft2(b, false); // true for cross correlation
    for (int i = 0; i < n; i++)
        a[i]*= b[i];
    inplace_fft2(a, true);
    a.resize(r);
    return a;
}