Bitwise Or Convolution (Bitwise-OR畳み込み)
(math/fft/bitwise-or-convolution.hpp)

• View this file on GitHub
• Last update: 2022-09-11 00:53:50+09:00
• Include: #include "math/fft/bitwise-or-convolution.hpp"

Depends on

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

Verified with

• test/verify/yosupo-bitwise-and-convolution-2.test.cpp

Code

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

/**
 * @brief Bitwise Or Convolution (Bitwise-OR畳み込み)
 */
template< typename T >
vector< T > bitwise_or_convolution(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 1 "math/fft/subset-zeta-moebius-transform.hpp"
/**
 * @brief Subset Zeta/Moebius Transform (下位集合のゼータ/メビウス変換)
 */
template< typename T >
void subset_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 + i] += f[j + k];
      }
    }
  }
}

template< typename T >
void subset_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 + i] -= f[j + k];
      }
    }
  }
}
#line 2 "math/fft/bitwise-or-convolution.hpp"

/**
 * @brief Bitwise Or Convolution (Bitwise-OR畳み込み)
 */
template< typename T >
vector< T > bitwise_or_convolution(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;
}

Back to top page