Berlekamp Massey (math/fps/berlekamp-massey.hpp)

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• Last update: 2024-05-01 23:44:47+09:00
• Include: #include "math/fps/berlekamp-massey.hpp"

Verified with

• test/verify/yosupo-find-linear-recurrence.test.cpp
• test/verify/yosupo-sparse-matrix-det.test.cpp

Code

/**
 * @brief Berlekamp Massey
 */
template <template <typename> class FPS, typename Mint>
FPS<Mint> berlekamp_massey(const FPS<Mint> &s) {
  const int N = (int)s.size();
  FPS<Mint> b = {Mint(-1)}, c = {Mint(-1)};
  Mint y = Mint(1);
  for (int ed = 1; ed <= N; ed++) {
    int l = int(c.size()), m = int(b.size());
    Mint x = 0;
    for (int i = 0; i < l; i++) x += c[i] * s[ed - l + i];
    b.emplace_back(0);
    m++;
    if (x == Mint(0)) continue;
    Mint freq = x / y;
    if (l < m) {
      auto tmp = c;
      c.insert(begin(c), m - l, Mint(0));
      for (int i = 0; i < m; i++) c[m - 1 - i] -= freq * b[m - 1 - i];
      b = tmp;
      y = x;
    } else {
      for (int i = 0; i < m; i++) c[l - 1 - i] -= freq * b[m - 1 - i];
    }
  }
  return c;
}

#line 1 "math/fps/berlekamp-massey.hpp"
/**
 * @brief Berlekamp Massey
 */
template <template <typename> class FPS, typename Mint>
FPS<Mint> berlekamp_massey(const FPS<Mint> &s) {
  const int N = (int)s.size();
  FPS<Mint> b = {Mint(-1)}, c = {Mint(-1)};
  Mint y = Mint(1);
  for (int ed = 1; ed <= N; ed++) {
    int l = int(c.size()), m = int(b.size());
    Mint x = 0;
    for (int i = 0; i < l; i++) x += c[i] * s[ed - l + i];
    b.emplace_back(0);
    m++;
    if (x == Mint(0)) continue;
    Mint freq = x / y;
    if (l < m) {
      auto tmp = c;
      c.insert(begin(c), m - l, Mint(0));
      for (int i = 0; i < m; i++) c[m - 1 - i] -= freq * b[m - 1 - i];
      b = tmp;
      y = x;
    } else {
      for (int i = 0; i < m; i++) c[l - 1 - i] -= freq * b[m - 1 - i];
    }
  }
  return c;
}

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