linalg/blackbox/det.hpp

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Last update: 2024-01-21 23:24:39+09:00
Include: #include "linalg/blackbox/det.hpp"

Depends on

Required by

graph/count/BEST.hpp

Verified with

Code

#include "linalg/blackbox/min_poly.hpp"


template <typename mint, typename F>
mint blackbox_det(int N, F apply) {
  vc<mint> c(N);
  FOR(i, N) c[i] = RNG(1, mint::get_mod());
  mint r = 1;
  FOR(i, N) r *= c[i];
  auto g = [&](vc<mint> v) -> vc<mint> {
    FOR(i, N) v[i] *= c[i];
    return apply(v);
  };
  auto f = blackbox_min_poly<mint>(N, g);
  mint det = (len(f) == N + 1 ? f[0] : mint(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/blackbox/min_poly.hpp"

// 行列 A をかけることを表す線形変換 f を渡す

// auto f = [&](vc<mint> v) -> vc<mint> {};

template <typename mint, typename F>
vc<mint> blackbox_min_poly(int N, F f) {
  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];
    v = f(v);
  }
  S = find_linear_rec(S);
  reverse(all(S));
  return S;
}
#line 2 "linalg/blackbox/det.hpp"

template <typename mint, typename F>
mint blackbox_det(int N, F apply) {
  vc<mint> c(N);
  FOR(i, N) c[i] = RNG(1, mint::get_mod());
  mint r = 1;
  FOR(i, N) r *= c[i];
  auto g = [&](vc<mint> v) -> vc<mint> {
    FOR(i, N) v[i] *= c[i];
    return apply(v);
  };
  auto f = blackbox_min_poly<mint>(N, g);
  mint det = (len(f) == N + 1 ? f[0] : mint(0));
  if (N & 1) det *= -1;
  det /= r;
  return det;
}