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Add number/fft.cc 

Signed-off-by: subcrip <contact@subc.rip>
This commit is contained in:
subcrip 2024-09-02 19:00:05 +08:00
parent 01abf5fdb8
commit c42d033dcc
1 changed files with 48 additions and 0 deletions
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void fft(vector<complex<ld>>& y, bool idft) {
int n = y.size();
vector<int> rev(n);
for (int i = 0; i < n; ++i) {
rev[i] = rev[i >> 1] >> 1;
if (i & 1) {
rev[i] |= n >> 1;
}
}
for (int i = 0; i < n; ++i) {
if (i < rev[i]) {
swap(y[i], y[rev[i]]);
}
}
for (int h = 2; h <= n; h <<= 1) {
complex<ld> wn(cos(2 * M_PI / h), sin(2 * M_PI / h));
for (int j = 0; j < n; j += h) {
complex<ld> w(1);
for (int k = j; k < j + h / 2; ++k) {
complex<ld> u = y[k], t = w * y[k + h / 2];
y[k] = u + t;
y[k + h / 2] = u - t;
w *= wn;
}
}
}
if (idft) {
reverse(y.begin() + 1, y.end());
for (int i = 0; i < n; ++i) {
y[i] /= n;
}
}
}
vector<int> multiply(const vector<int>& a, const vector<int>& b) {
vector<complex<ld>> A(a.begin(), a.end()), B(b.begin(), b.end());
int n = 1;
while (n < a.size() + b.size()) n <<= 1;
A.resize(n), B.resize(n);
fft(A, false), fft(B, false);
for (int i = 0; i < n; ++i) {
A[i] *= B[i];
}
fft(A, true);
vector<int> res(n);
transform(A.begin(), A.end(), res.begin(), expr(int(round(x.real())), auto&& x));
return res;
}