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#108. 多项式乘法

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https://loj.ac/s/1646459
This commit is contained in:
Baoshuo Ren 2022-11-30 15:26:26 +08:00
parent 21425c532f
commit c5b2052e3d
Signed by: baoshuo
GPG Key ID: 00CB9680AB29F51A
1 changed files with 27 additions and 10 deletions
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37
LibreOJ/108/108.cpp
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@ -13,19 +13,36 @@ const double PI = std::acos(-1);
void fast_fourier_transform(std::valarray<std::complex<double>>& a) {
if (a.size() == 1) return;
int m = a.size() >> 1;
// assert(a.size() == 1 << std::__lg(a.size()));
int k = std::__lg(a.size());
std::valarray<std::complex<double>>
even = a[std::slice(0, m, 2)],
odd = a[std::slice(1, m, 2)];
for (int i = 0; i < a.size(); i++) {
int t = 0;
fast_fourier_transform(even);
fast_fourier_transform(odd);
for (int j = 0; j < k; j++) {
if (i & (1 << j)) {
t |= 1 << (k - j - 1);
}
}
for (int i = 0; i < m; i++) {
auto t = std::polar(1.0, -2 * PI * i / a.size()) * odd[i];
a[i] = even[i] + t;
a[i + m] = even[i] - t;
if (i < t) std::swap(a[i], a[t]);
}
for (int len = 2; len <= a.size(); len <<= 1) {
std::complex<double> wlen(std::cos(2 * PI / len), std::sin(2 * PI / len));
for (int i = 0; i < a.size(); i += len) {
std::complex<double> w(1);
for (int j = 0; j < len / 2; j++) {
std::complex<double> 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;
}
}
}
}