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)

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• Last update: 2022-09-11 00:53:50+09:00
• Include: #include "math/fft/subset-zeta-moebius-transform.hpp"

Required by

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

Verified with

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

Code

/**
 * @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 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];
      }
    }
  }
}

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