Bitwise And Convolution (Bitwise-AND畳み込み) (math/fft/bitwise-and-convolution.hpp)

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• Last update: 2024-04-24 02:34:04+09:00
• Include: #include "math/fft/bitwise-and-convolution.hpp"

Depends on

• Superset Zeta/Moebius Transform (上位集合のゼータ/メビウス変換) (math/fft/superset-zeta-moebius-transform.hpp)

Verified with

• test/verify/yosupo-bitwise-and-convolution.test.cpp

Code

#include "superset-zeta-moebius-transform.hpp"

/**
 * @brief Bitwise And Convolution (Bitwise-AND畳み込み)
 */
template< typename T >
vector< T > bitwise_and_convolution(vector< T > f, 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_moebius_transform(f);
  return f;
}

#line 1 "math/fft/superset-zeta-moebius-transform.hpp"
/**
 * @brief Superset Zeta/Moebius Transform (上位集合のゼータ/メビウス変換)
 */
template< typename T >
void superset_zeta_transform(vector< T > &f) {
  const int n = (int) f.size();
  assert((n & (n - 1)) == 0);
  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] += f[j + k + i];
      }
    }
  }
}

template< typename T >
void superset_moebius_transform(vector< T > &f) {
  const int n = (int) f.size();
  assert((n & (n - 1)) == 0);
  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] -= f[j + k + i];
      }
    }
  }
}
#line 2 "math/fft/bitwise-and-convolution.hpp"

/**
 * @brief Bitwise And Convolution (Bitwise-AND畳み込み)
 */
template< typename T >
vector< T > bitwise_and_convolution(vector< T > f, 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_moebius_transform(f);
  return f;
}

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