Bitwise畳み込みOR
(library/polynomial/fft/convolution_bitwise_or.hpp)

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• Last update: 2026-01-20 20:11:22+09:00
• Include: #include "library/polynomial/fft/convolution_bitwise_or.hpp"

Bitwise畳み込みOR

できること

$h_k = \sum_{i OR j=k}　f_i \cdot g_j$

• Bitwise畳み込み OR を計算する

計算量

$O(NlogN)$

使い方

auto c = convolution_bitwise_or(a, b);

Depends on

• 下位集合のゼータ・メビウス変換 (library/polynomial/fft/subset_zeta_moebius_transform.hpp)

Verified with

• Bitwise畳み込みORのテスト (tests/polynomial.fft.convolution_bitwise_or.test.cpp)

Code

#pragma once
#include "library/polynomial/fft/subset_zeta_moebius_transform.hpp"
template <typename T>
vector<T> convolution_bitwise_or(vector<T> f, vector<T> g) {
    const int n = (int)f.size();
    assert(f.size() == g.size());
    assert((n & (n - 1)) == 0);
    subset_zeta_transform(f);
    subset_zeta_transform(g);
    for (int i = 0; i < n; i++) f[i] *= g[i];
    subset_moebius_transform(f);
    return f;
}

#line 2 "library/polynomial/fft/subset_zeta_moebius_transform.hpp"
template <typename T> void subset_zeta_transform(vector<T> &f) {
    const int n = (int)f.size();
    assert((n & (n - 1)) == 0ll);
    for (int i = 1; i < n; i <<= 1) {
        for (int j = 0; j < n; j += i << 1) {
            for (int k = 0; k < i; k++) {
                f[j + k + i] += f[j + k];
            }
        }
    }
}
template <typename T> void subset_moebius_transform(vector<T> &f) {
    const int n = (int)f.size();
    assert((n & (n - 1)) == 0ll);
    for (int i = 1; i < n; i <<= 1) {
        for (int j = 0; j < n; j += i << 1) {
            for (int k = 0; k < i; k++) {
                f[j + k + i] -= f[j + k];
            }
        }
    }
}
#line 3 "library/polynomial/fft/convolution_bitwise_or.hpp"
template <typename T>
vector<T> convolution_bitwise_or(vector<T> f, vector<T> g) {
    const int n = (int)f.size();
    assert(f.size() == g.size());
    assert((n & (n - 1)) == 0);
    subset_zeta_transform(f);
    subset_zeta_transform(g);
    for (int i = 0; i < n; i++) f[i] *= g[i];
    subset_moebius_transform(f);
    return f;
}

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