library/fft.cpp at master · yongwhan/library · GitHub

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#include<bits/stdc++.h>
using namespace std;

typedef long long ll;

using cd = complex<double>;
const double PI = acos(-1);

void fft(vector<cd> & a, bool invert) {
  int n = a.size();
  if (n == 1)
    return;

  vector<cd> a0(n / 2), a1(n / 2);
  for (int i = 0; 2 * i < n; i++) {
    a0[i] = a[2*i];
    a1[i] = a[2*i+1];
  }
  fft(a0, invert);
  fft(a1, invert);

  double ang = 2 * PI / n * (invert ? -1 : 1);
  cd w(1), wn(cos(ang), sin(ang));
  for (int i = 0; 2 * i < n; i++) {
    a[i] = a0[i] + w * a1[i];
    a[i + n/2] = a0[i] - w * a1[i];
    if (invert) {
      a[i] /= 2;
      a[i + n/2] /= 2;
    }
    w *= wn;
  }
}

vector<int> multiply(vector<int> const& a, vector<int> const& b) {
  vector<cd> fa(a.begin(), a.end()), fb(b.begin(), b.end());
  int n = 1;
  while (n < a.size() + b.size())
    n <<= 1;
  fa.resize(n);
  fb.resize(n);

  fft(fa, false);
  fft(fb, false);
  for (int i = 0; i < n; i++)
    fa[i] *= fb[i];
  fft(fa, true);

  vector<int> result(n);
  for (int i = 0; i < n; i++)
    result[i] = round(fa[i].real());
  return result;
}

int main() {
  return 0;
}