Bitwise AND Convolution
(lib/convolution/bitwise_and_convolution.hpp)

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• Last update: 2024-11-13 13:43:26+09:00
• Include: #include "lib/convolution/bitwise_and_convolution.hpp"

Depends on

• Set Zeta/Mobius Transform (lib/convolution/set_zeta_mobius_transform.hpp)

Verified with

• test/library_checker/convolution/bitwise_and_convolution.test.cpp

Code

#pragma once

/**
 * @brief Bitwise AND Convolution
 */

#include <vector>
#include <cassert>

#include "../convolution/set_zeta_mobius_transform.hpp"

template <typename T>
std::vector<T> bitwise_and_convolution(std::vector<T> f, std::vector<T> g){
    const int n = (int) f.size();
    assert(f.size() == g.size());
    assert((n & (n - 1)) == 0);
    superset_zeta_transform(f);
    superset_zeta_transform(g);
    for(int i = 0; i < n; ++i){
        f[i] *= g[i];
    }
    superset_mobius_transform(f);
    return f;
}

#line 2 "lib/convolution/bitwise_and_convolution.hpp"

/**
 * @brief Bitwise AND Convolution
 */

#include <vector>
#include <cassert>

#line 2 "lib/convolution/set_zeta_mobius_transform.hpp"

/**
 * @brief Set Zeta/Mobius Transform
 */

#line 9 "lib/convolution/set_zeta_mobius_transform.hpp"

template <typename T>
void superset_zeta_transform(std::vector<T> &f){
    const int n = f.size();
    assert((n & (n - 1)) == 0);
    for(int i = 1; i < n; i <<= 1){
        for(int j = 0; j < n; ++j){
            if((j & i) == 0){
                f[j] += f[j | i];
            }
        }
    }
}

template <typename T>
void superset_mobius_transform(std::vector<T> &f){
    const int n = f.size();
    assert((n & (n - 1)) == 0);
    for(int i = 1; i < n; i <<= 1){
        for(int j = 0; j < n; ++j){
            if((j & i) == 0){
                f[j] -= f[j | i];
            }
        }
    }
}

template <typename T>
void subset_zeta_transform(std::vector<T> &f){
    const int n = f.size();
    assert((n & (n - 1)) == 0);
    for(int i = 1; i < n; i <<= 1){
        for(int j = 0; j < n; ++j){
            if((j & i) == 0){
                f[j | i] += f[j];
            }
        }
    }
}

template <typename T>
void subset_mobius_transform(std::vector<T> &f){
    const int n = f.size();
    assert((n & (n - 1)) == 0);
    for(int i = 1; i < n; i <<= 1){
        for(int j = 0; j < n; ++j){
            if((j & i) == 0){
                f[j | i] -= f[j];
            }
        }
    }
}
#line 11 "lib/convolution/bitwise_and_convolution.hpp"

template <typename T>
std::vector<T> bitwise_and_convolution(std::vector<T> f, std::vector<T> g){
    const int n = (int) f.size();
    assert(f.size() == g.size());
    assert((n & (n - 1)) == 0);
    superset_zeta_transform(f);
    superset_zeta_transform(g);
    for(int i = 0; i < n; ++i){
        f[i] *= g[i];
    }
    superset_mobius_transform(f);
    return f;
}

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