test/verify/yosupo-matrix-det.test.cpp

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• Last update: 2024-04-24 02:34:04+09:00
• Problem: https://judge.yosupo.jp/problem/matrix_det

Depends on

• math/combinatorics/montgomery-mod-int.hpp
• math/matrix/matrix.hpp
• template/template.hpp

Code

// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/matrix_det

#include "../../template/template.hpp"

#include "../../math/combinatorics/montgomery-mod-int.hpp"

#include "../../math/matrix/matrix.hpp"

using mint = modint998244353;

int main() {
  int N;
  cin >> N;
  Matrix< mint > mat(N);
  for(int i = 0; i < N; i++) cin >> mat[i];
  cout << mat.determinant() << endl;
}

#line 1 "test/verify/yosupo-matrix-det.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/matrix_det

#line 1 "template/template.hpp"
#include<bits/stdc++.h>

using namespace std;

using int64 = long long;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template< typename T1, typename T2 >
ostream &operator<<(ostream &os, const pair< T1, T2 >& p) {
  os << p.first << " " << p.second;
  return os;
}

template< typename T1, typename T2 >
istream &operator>>(istream &is, pair< T1, T2 > &p) {
  is >> p.first >> p.second;
  return is;
}

template< typename T >
ostream &operator<<(ostream &os, const vector< T > &v) {
  for(int i = 0; i < (int) v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template< typename T >
istream &operator>>(istream &is, vector< T > &v) {
  for(T &in : v) is >> in;
  return is;
}

template< typename T1, typename T2 >
inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }

template< typename T1, typename T2 >
inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); }

template< typename T = int64 >
vector< T > make_v(size_t a) {
  return vector< T >(a);
}

template< typename T, typename... Ts >
auto make_v(size_t a, Ts... ts) {
  return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...));
}

template< typename T, typename V >
typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) {
  t = v;
}

template< typename T, typename V >
typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) {
  for(auto &e : t) fill_v(e, v);
}

template< typename F >
struct FixPoint : F {
  explicit FixPoint(F &&f) : F(forward< F >(f)) {}

  template< typename... Args >
  decltype(auto) operator()(Args &&... args) const {
    return F::operator()(*this, forward< Args >(args)...);
  }
};
 
template< typename F >
inline decltype(auto) MFP(F &&f) {
  return FixPoint< F >{forward< F >(f)};
}
#line 4 "test/verify/yosupo-matrix-det.test.cpp"

#line 2 "math/combinatorics/montgomery-mod-int.hpp"

template< uint32_t mod_, bool fast = false >
struct MontgomeryModInt {
private:
  using mint = MontgomeryModInt;
  using i32 = int32_t;
  using i64 = int64_t;
  using u32 = uint32_t;
  using u64 = uint64_t;

  static constexpr u32 get_r() {
    u32 ret = mod_;
    for (i32 i = 0; i < 4; i++) ret *= 2 - mod_ * ret;
    return ret;
  }

  static constexpr u32 r = get_r();

  static constexpr u32 n2 = -u64(mod_) % mod_;

  static_assert(r * mod_ == 1, "invalid, r * mod != 1");
  static_assert(mod_ < (1 << 30), "invalid, mod >= 2 ^ 30");
  static_assert((mod_ & 1) == 1, "invalid, mod % 2 == 0");

  u32 x;

public:
  MontgomeryModInt(): x{} {}

  MontgomeryModInt(const i64 &a)
      : x(reduce(u64(fast ? a : (a % mod() + mod())) * n2)) {}

  static constexpr u32 reduce(const u64 &b) {
    return u32(b >> 32) + mod() - u32((u64(u32(b) * r) * mod()) >> 32);
  }

  mint &operator+=(const mint &p) {
    if (i32(x += p.x - 2 * mod()) < 0) x += 2 * mod();
    return *this;
  }

  mint &operator-=(const mint &p) {
    if (i32(x -= p.x) < 0) x += 2 * mod();
    return *this;
  }

  mint &operator*=(const mint &p) {
    x = reduce(u64(x) * p.x);
    return *this;
  }

  mint &operator/=(const mint &p) {
    *this *= p.inv();
    return *this;
  }

  mint operator-() const { return mint() - *this; }

  mint operator+(const mint &p) const { return mint(*this) += p; }

  mint operator-(const mint &p) const { return mint(*this) -= p; }

  mint operator*(const mint &p) const { return mint(*this) *= p; }

  mint operator/(const mint &p) const { return mint(*this) /= p; }

  bool operator==(const mint &p) const {
    return (x >= mod() ? x - mod() : x) == (p.x >= mod() ? p.x - mod() : p.x);
  }

  bool operator!=(const mint &p) const {
    return (x >= mod() ? x - mod() : x) != (p.x >= mod() ? p.x - mod() : p.x);
  }

  u32 val() const {
    u32 ret = reduce(x);
    return ret >= mod() ? ret - mod() : ret;
  }

  mint pow(u64 n) const {
    mint ret(1), mul(*this);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  mint inv() const {
    return pow(mod() - 2);
  }

  friend ostream &operator<<(ostream &os, const mint &p) {
    return os << p.val();
  }

  friend istream &operator>>(istream &is, mint &a) {
    i64 t;
    is >> t;
    a = mint(t);
    return is;
  }

  static constexpr u32 mod() { return mod_; }
};

template< uint32_t mod >
using modint = MontgomeryModInt< mod >;
using modint998244353 = modint< 998244353 >;
using modint1000000007 = modint< 1000000007 >;
#line 6 "test/verify/yosupo-matrix-det.test.cpp"

#line 1 "math/matrix/matrix.hpp"
template< class T >
struct Matrix {
  vector< vector< T > > A;

  Matrix() {}

  Matrix(size_t n, size_t m) : A(n, vector< T >(m, 0)) {}

  Matrix(size_t n) : A(n, vector< T >(n, 0)) {};

  size_t size() const {
     if(A.empty()) return 0;
     assert(A.size() == A[0].size());
     return A.size();
  }

  size_t height() const {
    return (A.size());
  }

  size_t width() const {
    return (A[0].size());
  }

  inline const vector< T > &operator[](int k) const {
    return (A.at(k));
  }

  inline vector< T > &operator[](int k) {
    return (A.at(k));
  }

  static Matrix I(size_t n) {
    Matrix mat(n);
    for(int i = 0; i < n; i++) mat[i][i] = 1;
    return (mat);
  }

  Matrix &operator+=(const Matrix &B) {
    size_t n = height(), m = width();
    assert(n == B.height() && m == B.width());
    for(int i = 0; i < n; i++)
      for(int j = 0; j < m; j++)
        (*this)[i][j] += B[i][j];
    return (*this);
  }

  Matrix &operator-=(const Matrix &B) {
    size_t n = height(), m = width();
    assert(n == B.height() && m == B.width());
    for(int i = 0; i < n; i++)
      for(int j = 0; j < m; j++)
        (*this)[i][j] -= B[i][j];
    return (*this);
  }

  Matrix &operator*=(const Matrix &B) {
    size_t n = height(), m = B.width(), p = width();
    assert(p == B.height());
    vector< vector< T > > C(n, vector< T >(m, 0));
    for(int i = 0; i < n; i++)
      for(int j = 0; j < m; j++)
        for(int k = 0; k < p; k++)
          C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]);
    A.swap(C);
    return (*this);
  }

  Matrix &operator^=(long long k) {
    Matrix B = Matrix::I(height());
    while(k > 0) {
      if(k & 1) B *= *this;
      *this *= *this;
      k >>= 1LL;
    }
    A.swap(B.A);
    return (*this);
  }

  Matrix operator+(const Matrix &B) const {
    return (Matrix(*this) += B);
  }

  Matrix operator-(const Matrix &B) const {
    return (Matrix(*this) -= B);
  }

  Matrix operator*(const Matrix &B) const {
    return (Matrix(*this) *= B);
  }

  Matrix operator^(const long long k) const {
    return (Matrix(*this) ^= k);
  }

  friend ostream &operator<<(ostream &os, Matrix &p) {
    size_t n = p.height(), m = p.width();
    for(int i = 0; i < n; i++) {
      os << "[";
      for(int j = 0; j < m; j++) {
        os << p[i][j] << (j + 1 == m ? "]\n" : ",");
      }
    }
    return (os);
  }


  T determinant() {
    Matrix B(*this);
    assert(width() == height());
    T ret = 1;
    for(int i = 0; i < width(); i++) {
      int idx = -1;
      for(int j = i; j < width(); j++) {
        if(B[j][i] != 0) idx = j;
      }
      if(idx == -1) return (0);
      if(i != idx) {
        ret *= -1;
        swap(B[i], B[idx]);
      }
      ret *= B[i][i];
      T vv = B[i][i];
      for(int j = 0; j < width(); j++) {
        B[i][j] /= vv;
      }
      for(int j = i + 1; j < width(); j++) {
        T a = B[j][i];
        for(int k = 0; k < width(); k++) {
          B[j][k] -= B[i][k] * a;
        }
      }
    }
    return (ret);
  }
};
#line 8 "test/verify/yosupo-matrix-det.test.cpp"

using mint = modint998244353;

int main() {
  int N;
  cin >> N;
  Matrix< mint > mat(N);
  for(int i = 0; i < N; i++) cin >> mat[i];
  cout << mat.determinant() << endl;
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	example_00	AC	6 ms	4 MB
g++	example_01	AC	6 ms	4 MB
g++	example_02	AC	6 ms	4 MB
g++	lowrank_max_random_00	AC	117 ms	5 MB
g++	lowrank_max_random_01	AC	104 ms	5 MB
g++	lowrank_max_random_02	AC	135 ms	5 MB
g++	lowrank_max_random_03	AC	103 ms	5 MB
g++	lowrank_max_random_04	AC	119 ms	5 MB
g++	max_random_00	AC	143 ms	5 MB
g++	max_random_01	AC	144 ms	5 MB
g++	max_random_02	AC	145 ms	5 MB
g++	max_random_03	AC	140 ms	5 MB
g++	max_random_04	AC	142 ms	5 MB
g++	perm_max_random_00	AC	136 ms	5 MB
g++	perm_max_random_01	AC	136 ms	5 MB
g++	perm_max_random_02	AC	137 ms	5 MB
g++	perm_max_random_03	AC	132 ms	5 MB
g++	perm_max_random_04	AC	136 ms	5 MB
g++	random_00	AC	16 ms	4 MB
g++	random_01	AC	19 ms	4 MB
g++	random_02	AC	8 ms	4 MB
g++	random_03	AC	18 ms	4 MB
g++	random_04	AC	6 ms	4 MB
g++	signed_overflow_00	AC	6 ms	4 MB
g++	unsigned_overflow_00	AC	6 ms	4 MB
clang++	example_00	AC	6 ms	4 MB
clang++	example_01	AC	6 ms	4 MB
clang++	example_02	AC	6 ms	4 MB
clang++	lowrank_max_random_00	AC	65 ms	5 MB
clang++	lowrank_max_random_01	AC	58 ms	5 MB
clang++	lowrank_max_random_02	AC	74 ms	5 MB
clang++	lowrank_max_random_03	AC	57 ms	5 MB
clang++	lowrank_max_random_04	AC	64 ms	5 MB
clang++	max_random_00	AC	81 ms	5 MB
clang++	max_random_01	AC	82 ms	5 MB
clang++	max_random_02	AC	82 ms	5 MB
clang++	max_random_03	AC	79 ms	5 MB
clang++	max_random_04	AC	80 ms	5 MB
clang++	perm_max_random_00	AC	73 ms	5 MB
clang++	perm_max_random_01	AC	74 ms	5 MB
clang++	perm_max_random_02	AC	74 ms	5 MB
clang++	perm_max_random_03	AC	72 ms	5 MB
clang++	perm_max_random_04	AC	73 ms	5 MB
clang++	random_00	AC	14 ms	4 MB
clang++	random_01	AC	15 ms	4 MB
clang++	random_02	AC	8 ms	4 MB
clang++	random_03	AC	15 ms	4 MB
clang++	random_04	AC	6 ms	4 MB
clang++	signed_overflow_00	AC	6 ms	4 MB
clang++	unsigned_overflow_00	AC	6 ms	4 MB

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