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Convolution_(FFT).cpp
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Convolution_(FFT).cpp
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double PI = acos(-1);
vector<complex<double>> fft(vector<complex<double>> A, bool inv){
int N = A.size();
complex<double> r = polar((double) 1, (2 * PI) / (N));
if (inv){
r = pow(r, -1);
}
vector<complex<double>> B(N);
for (int i = N / 2; i > 0; i /= 2){
complex<double> z = pow(r, i);
complex<double> z2 = 1;
for (int j = 0; j < N; j += i * 2){
for (int k = 0; k < i; k++){
A[i + j + k] *= z2;
B[j / 2 + k] = A[j + k] + A[i + j + k];
B[N / 2 + j / 2 + k] = A[j + k] - A[i + j + k];
}
z2 *= z;
}
swap(A, B);
}
if (inv){
for (int i = 0; i < N; i++){
A[i] /= N;
}
}
return A;
}
vector<double> convolution(vector<double> A, vector<double> B){
int deg = A.size() + B.size() - 1;
int N = 1;
while (N < deg){
N *= 2;
}
vector<complex<double>> A2(N, 0);
for (int i = 0; i < A.size(); i++){
A2[i] = A[i];
}
vector<complex<double>> B2(N, 0);
for (int i = 0; i < B.size(); i++){
B2[i] = B[i];
}
A2 = fft(A2, false);
B2 = fft(B2, false);
vector<complex<double>> C2(N);
for (int i = 0; i < N; i++){
C2[i] = A2[i] * B2[i];
}
C2 = fft(C2, true);
vector<double> C(deg);
for (int i = 0; i < deg; i++){
C[i] = C2[i].real();
}
return C;
}