linalg/spmat_det.hpp

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• Last update: 2023-05-20 12:35:33+09:00
• Include: #include "linalg/spmat_det.hpp"

Depends on

• linalg/spmat_min_poly.hpp
• random/base.hpp
• seq/find_linear_rec.hpp

Verified with

• test/library_checker/matrix/sparse_matrix_det.test.cpp

Code

#include "linalg/spmat_min_poly.hpp"

template <typename T>
T spmat_det(int N, vc<tuple<int, int, T>> dat) {
  vc<T> c(N);
  FOR(i, N) c[i] = RNG(1, T::get_mod());
  T r = 1;
  FOR(i, N) r *= c[i];
  for (auto&& [i, j, x]: dat) x *= c[i];
  vc<T> f = spmat_min_poly(N, dat);
  T det = (len(f) == N + 1 ? f[0] : T(0));
  if (N & 1) det *= -1;
  det /= r;
  return det;
}

#line 2 "seq/find_linear_rec.hpp"

template <typename mint>
vector<mint> find_linear_rec(vector<mint>& A) {
  int N = len(A);
  vc<mint> B = {1}, C = {1};
  int l = 0, m = 1;
  mint p = 1;
  FOR(i, N) {
    mint d = A[i];
    FOR3(j, 1, l + 1) { d += C[j] * A[i - j]; }
    if (d == 0) {
      ++m;
      continue;
    }
    auto tmp = C;
    mint q = d / p;
    if (len(C) < len(B) + m) C.insert(C.end(), len(B) + m - len(C), 0);
    FOR(j, len(B)) C[j + m] -= q * B[j];
    if (l + l <= i) {
      B = tmp;
      l = i + 1 - l, m = 1;
      p = d;
    } else {
      ++m;
    }
  }
  return C;
}
#line 2 "random/base.hpp"

u64 RNG_64() {
  static uint64_t x_
      = uint64_t(chrono::duration_cast<chrono::nanoseconds>(
                     chrono::high_resolution_clock::now().time_since_epoch())
                     .count())
        * 10150724397891781847ULL;
  x_ ^= x_ << 7;
  return x_ ^= x_ >> 9;
}

u64 RNG(u64 lim) { return RNG_64() % lim; }

ll RNG(ll l, ll r) { return l + RNG_64() % (r - l); }
#line 3 "linalg/spmat_min_poly.hpp"

template <typename mint>
vc<mint> spmat_min_poly(int N, vc<tuple<int, int, mint>> dat) {
  vc<mint> S(N + N + 10);
  vc<mint> c(N);
  vc<mint> v(N);
  FOR(i, N) c[i] = RNG(0, mint::get_mod());
  FOR(i, N) v[i] = RNG(0, mint::get_mod());
  FOR(k, N + N + 10) {
    FOR(i, N) S[k] += c[i] * v[i];
    vc<mint> w(N);
    for (auto&& [i, j, x]: dat) w[j] += x * v[i];
    swap(v, w);
  }
  vc<mint> f = find_linear_rec(S);
  reverse(all(f));
  return f;
}
#line 2 "linalg/spmat_det.hpp"

template <typename T>
T spmat_det(int N, vc<tuple<int, int, T>> dat) {
  vc<T> c(N);
  FOR(i, N) c[i] = RNG(1, T::get_mod());
  T r = 1;
  FOR(i, N) r *= c[i];
  for (auto&& [i, j, x]: dat) x *= c[i];
  vc<T> f = spmat_min_poly(N, dat);
  T det = (len(f) == N + 1 ? f[0] : T(0));
  if (N & 1) det *= -1;
  det /= r;
  return det;
}

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