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// s.size() muss eine Zweierpotenz sein!
vector<cplx> fft(const vector<cplx> &a, bool inverse = 0) {
int logn = 1, n = a.size();
vector<cplx> A(n);
while ((1 << logn) < n) logn++;
for (int i = 0; i < n; i++) {
int j = 0;
for (int k = 0; k < logn; k++) j = (j << 1) | ((i >> k) & 1);
A[j] = a[i];
}
for (int s = 2; s <= n; s <<= 1) {
double angle = 2 * PI / s * (inverse ? -1 : 1);
cplx ws(cos(angle), sin(angle));
for (int j = 0; j < n; j+= s) {
cplx w = 1;
for (int k = 0; k < s / 2; k++) {
cplx u = A[j + k], t = A[j + s / 2 + k];
A[j + k] = u + w * t;
A[j + s / 2 + k] = u - w * t;
if (inverse) A[j + k] /= 2, A[j + s / 2 + k] /= 2;
w *= ws;
}
}
}
return A;
}
// Polynome: a_0, a_1, ... & b_0, b_1, ...
vector<cplx> a = {0,0,0,0,1,2,3,4}, b = {0,0,0,0,2,3,0,1};
a = fft(a); b = fft(b);
for (int i = 0; i < (int)a.size(); i++) a[i] *= b[i];
a = fft(a,1); // a = a * b
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