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