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@ -2,7 +2,7 @@
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#include <algorithm>
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#include <cmath>
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#include <complex>
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#include <vector>
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#include <valarray>
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using std::cin;
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using std::cout;
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@ -10,27 +10,22 @@ const char endl = '\n';
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const double PI = std::acos(-1);
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void FFT(std::vector<std::complex<double>>& a) {
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void fast_fourier_transform(std::valarray<std::complex<double>>& a) {
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if (a.size() == 1) return;
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int m = a.size() >> 1;
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std::vector<std::complex<double>> a0, a1;
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std::valarray<std::complex<double>>
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even = a[std::slice(0, m, 2)],
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odd = a[std::slice(1, m, 2)];
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fast_fourier_transform(even);
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fast_fourier_transform(odd);
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for (int i = 0; i < m; i++) {
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a0.emplace_back(a[i << 1]);
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a1.emplace_back(a[i << 1 | 1]);
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}
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FFT(a0), FFT(a1);
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std::complex<double>
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w0{std::cos(PI / m), std::sin(PI / m)},
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w1{1.0, 0.0};
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for (int i = 0; i < m; i++) {
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a[i] = a0[i] + w1 * a1[i];
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a[i + m] = a0[i] - w1 * a1[i];
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w1 *= w0;
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auto t = std::polar(1.0, -2 * PI * i / a.size()) * odd[i];
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a[i] = even[i] + t;
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a[i + m] = even[i] - t;
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}
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}
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@ -43,7 +38,7 @@ int main() {
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cin >> n >> m;
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int k = 1 << (std::__lg(n + m) + 1);
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std::vector<std::complex<double>> f(k), g(k);
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std::valarray<std::complex<double>> f(k), g(k);
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for (int i = 0; i <= n; i++) {
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cin >> f[i];
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@ -53,14 +48,15 @@ int main() {
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cin >> g[i];
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}
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FFT(f), FFT(g);
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fast_fourier_transform(f);
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fast_fourier_transform(g);
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for (int i = 0; i < k; i++) {
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f[i] *= g[i];
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}
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FFT(f);
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std::reverse(f.begin() + 1, f.end());
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fast_fourier_transform(f);
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std::reverse(std::begin(f) + 1, std::end(f));
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for (int i = 0; i <= n + m; i++) {
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cout << static_cast<int>(std::round(f[i].real() / k)) << ' ';
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