test/yosupo-judge/system_of_linear_equations/main.test.cpp

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• Last update: 2021-04-23 23:44:44+09:00
• Problem: https://judge.yosupo.jp/problem/system_of_linear_equations
• Link: View error logs on GitHub Actions

Depends on

• Input vector (Mylib/IO/input_vector.cpp)
• join function (Mylib/IO/join.cpp)
• Simultaneous linear equations (Mylib/LinearAlgebra/simultaneous_linear_equations.cpp)
• Modint (Mylib/Number/Mint/mint.cpp)

Code

#define PROBLEM "https://judge.yosupo.jp/problem/system_of_linear_equations"

#include <vector>
#include "Mylib/IO/input_vector.cpp"
#include "Mylib/IO/join.cpp"
#include "Mylib/LinearAlgebra/simultaneous_linear_equations.cpp"
#include "Mylib/Number/Mint/mint.cpp"

namespace hl = haar_lib;

using mint = hl::modint<998244353>;

int main() {
  std::cin.tie(0);
  std::ios::sync_with_stdio(false);

  int N, M;
  std::cin >> N >> M;

  auto A = hl::input_vector<mint>(N, M);
  auto B = hl::input_vector<mint>(N);

  auto res = hl::simulaneous_linear_equations(A, B);

  if (not res) {
    std::cout << -1 << "\n";
  } else {
    std::cout << (*res).dim << "\n";

    std::cout << hl::join((*res).solution.begin(), (*res).solution.end()) << "\n";

    for (auto &b : (*res).basis) {
      std::cout << hl::join(b.begin(), b.end()) << "\n";
    }
  }

  return 0;
}

#line 1 "test/yosupo-judge/system_of_linear_equations/main.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/system_of_linear_equations"

#include <vector>
#line 2 "Mylib/IO/input_vector.cpp"
#include <iostream>
#line 4 "Mylib/IO/input_vector.cpp"

namespace haar_lib {
  template <typename T>
  std::vector<T> input_vector(int N) {
    std::vector<T> ret(N);
    for (int i = 0; i < N; ++i) std::cin >> ret[i];
    return ret;
  }

  template <typename T>
  std::vector<std::vector<T>> input_vector(int N, int M) {
    std::vector<std::vector<T>> ret(N);
    for (int i = 0; i < N; ++i) ret[i] = input_vector<T>(M);
    return ret;
  }
}  // namespace haar_lib
#line 3 "Mylib/IO/join.cpp"
#include <sstream>
#include <string>

namespace haar_lib {
  template <typename Iter>
  std::string join(Iter first, Iter last, std::string delim = " ") {
    std::stringstream s;

    for (auto it = first; it != last; ++it) {
      if (it != first) s << delim;
      s << *it;
    }

    return s.str();
  }
}  // namespace haar_lib
#line 2 "Mylib/LinearAlgebra/simultaneous_linear_equations.cpp"
#include <optional>
#include <utility>
#line 5 "Mylib/LinearAlgebra/simultaneous_linear_equations.cpp"

namespace haar_lib {
  namespace simulaneous_linear_equations_impl {
    template <typename T>
    struct result {
      int rank, dim;
      std::vector<T> solution;
      std::vector<std::vector<T>> basis;
    };
  }  // namespace simulaneous_linear_equations_impl

  template <typename T>
  auto simulaneous_linear_equations(std::vector<std::vector<T>> a, std::vector<T> b) {
    using result = simulaneous_linear_equations_impl::result<T>;
    std::optional<result> ret;
    const int n = a.size();
    const int m = a[0].size();

    int rank = 0;

    for (int j = 0; j < m; ++j) {
      int pivot = -1;

      for (int i = rank; i < n; ++i) {
        if (a[i][j] != 0) {
          pivot = i;
          break;
        }
      }

      if (pivot == -1) continue;

      std::swap(a[pivot], a[rank]);
      std::swap(b[pivot], b[rank]);

      auto d = a[rank][j];
      for (int k = 0; k < m; ++k) a[rank][k] /= d;
      b[rank] /= d;

      for (int i = 0; i < n; ++i) {
        if (i == rank or a[i][j] == 0) continue;
        auto d = a[i][j];
        for (int k = 0; k < m; ++k) a[i][k] -= a[rank][k] * d;
        b[i] -= b[rank] * d;
      }

      ++rank;
    }

    for (int i = rank; i < n; ++i) {
      if (b[i] != 0) {
        return ret;
      }
    }

    const int dim = m - rank;

    std::vector<std::vector<T>> basis(dim, std::vector<T>(m));
    std::vector<int> index;

    {
      int k = 0;
      for (int i = 0; i < rank; ++i) {
        for (int j = k; j < m; ++j) {
          if (a[i][j] == 1) {
            k = j + 1;
            break;
          }

          index.push_back(j);
        }
      }

      for (int j = k; j < m; ++j) index.push_back(j);
    }

    for (int i = 0, k = 0; i < rank; ++i) {
      for (int j = k; j < m; ++j) {
        if (a[i][j] == 1) {
          for (int l = 0; l < dim; ++l) basis[l][j] = -a[i][index[l]];
          k = j + 1;
          break;
        }
      }
    }

    for (int i = 0; i < dim; ++i) basis[i][index[i]] = 1;

    std::vector<T> solution(m);
    for (int i = 0; i < rank; ++i) solution[i] = b[i];

    ret = result({rank, dim, solution, basis});

    return ret;
  }
}  // namespace haar_lib
#line 4 "Mylib/Number/Mint/mint.cpp"

namespace haar_lib {
  template <int32_t M>
  class modint {
    uint32_t val_;

  public:
    constexpr static auto mod() { return M; }

    constexpr modint() : val_(0) {}
    constexpr modint(int64_t n) {
      if (n >= M)
        val_ = n % M;
      else if (n < 0)
        val_ = n % M + M;
      else
        val_ = n;
    }

    constexpr auto &operator=(const modint &a) {
      val_ = a.val_;
      return *this;
    }
    constexpr auto &operator+=(const modint &a) {
      if (val_ + a.val_ >= M)
        val_ = (uint64_t) val_ + a.val_ - M;
      else
        val_ += a.val_;
      return *this;
    }
    constexpr auto &operator-=(const modint &a) {
      if (val_ < a.val_) val_ += M;
      val_ -= a.val_;
      return *this;
    }
    constexpr auto &operator*=(const modint &a) {
      val_ = (uint64_t) val_ * a.val_ % M;
      return *this;
    }
    constexpr auto &operator/=(const modint &a) {
      val_ = (uint64_t) val_ * a.inv().val_ % M;
      return *this;
    }

    constexpr auto operator+(const modint &a) const { return modint(*this) += a; }
    constexpr auto operator-(const modint &a) const { return modint(*this) -= a; }
    constexpr auto operator*(const modint &a) const { return modint(*this) *= a; }
    constexpr auto operator/(const modint &a) const { return modint(*this) /= a; }

    constexpr bool operator==(const modint &a) const { return val_ == a.val_; }
    constexpr bool operator!=(const modint &a) const { return val_ != a.val_; }

    constexpr auto &operator++() {
      *this += 1;
      return *this;
    }
    constexpr auto &operator--() {
      *this -= 1;
      return *this;
    }

    constexpr auto operator++(int) {
      auto t = *this;
      *this += 1;
      return t;
    }
    constexpr auto operator--(int) {
      auto t = *this;
      *this -= 1;
      return t;
    }

    constexpr static modint pow(int64_t n, int64_t p) {
      if (p < 0) return pow(n, -p).inv();

      int64_t ret = 1, e = n % M;
      for (; p; (e *= e) %= M, p >>= 1)
        if (p & 1) (ret *= e) %= M;
      return ret;
    }

    constexpr static modint inv(int64_t a) {
      int64_t b = M, u = 1, v = 0;

      while (b) {
        int64_t t = a / b;
        a -= t * b;
        std::swap(a, b);
        u -= t * v;
        std::swap(u, v);
      }

      u %= M;
      if (u < 0) u += M;

      return u;
    }

    constexpr static auto frac(int64_t a, int64_t b) { return modint(a) / modint(b); }

    constexpr auto pow(int64_t p) const { return pow(val_, p); }
    constexpr auto inv() const { return inv(val_); }

    friend constexpr auto operator-(const modint &a) { return modint(M - a.val_); }

    friend constexpr auto operator+(int64_t a, const modint &b) { return modint(a) + b; }
    friend constexpr auto operator-(int64_t a, const modint &b) { return modint(a) - b; }
    friend constexpr auto operator*(int64_t a, const modint &b) { return modint(a) * b; }
    friend constexpr auto operator/(int64_t a, const modint &b) { return modint(a) / b; }

    friend std::istream &operator>>(std::istream &s, modint &a) {
      s >> a.val_;
      return s;
    }
    friend std::ostream &operator<<(std::ostream &s, const modint &a) {
      s << a.val_;
      return s;
    }

    template <int N>
    static auto div() {
      static auto value = inv(N);
      return value;
    }

    explicit operator int32_t() const noexcept { return val_; }
    explicit operator int64_t() const noexcept { return val_; }
  };
}  // namespace haar_lib
#line 8 "test/yosupo-judge/system_of_linear_equations/main.test.cpp"

namespace hl = haar_lib;

using mint = hl::modint<998244353>;

int main() {
  std::cin.tie(0);
  std::ios::sync_with_stdio(false);

  int N, M;
  std::cin >> N >> M;

  auto A = hl::input_vector<mint>(N, M);
  auto B = hl::input_vector<mint>(N);

  auto res = hl::simulaneous_linear_equations(A, B);

  if (not res) {
    std::cout << -1 << "\n";
  } else {
    std::cout << (*res).dim << "\n";

    std::cout << hl::join((*res).solution.begin(), (*res).solution.end()) << "\n";

    for (auto &b : (*res).basis) {
      std::cout << hl::join(b.begin(), b.end()) << "\n";
    }
  }

  return 0;
}

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