結果
| 問題 | No.2441 行列累乗 |
| ユーザー |
 a01sa01to
|
| 提出日時 | 2024-04-01 00:48:49 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 2 ms / 2,000 ms |
| コード長 | 11,237 bytes |
| コンパイル時間 | 2,563 ms |
| コンパイル使用メモリ | 248,652 KB |
| 実行使用メモリ | 5,248 KB |
| 最終ジャッジ日時 | 2024-09-30 21:32:32 |
| 合計ジャッジ時間 | 3,475 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 20 |
ソースコード
#line 1 "main.cpp"#include <bits/stdc++.h>using namespace std;#define rep(i, n) for (int i = 0; i < (n); ++i)using ll = long long;using ull = unsigned long long;#line 2 "library\\data_structure\\matrix.hpp"#line 4 "library\\data_structure\\matrix.hpp"using namespace std;#line 2 "library\\data_structure\\modint.hpp"#line 4 "library\\data_structure\\modint.hpp"#include <concepts>#line 7 "library\\data_structure\\modint.hpp"#include <type_traits>using namespace std;#line 2 "library\\math\\extgcd.hpp"#line 4 "library\\math\\extgcd.hpp"#include <optional>#line 7 "library\\math\\extgcd.hpp"using namespace std;namespace asalib {namespace math {// Returns a pair (x, y) such that ax + by = ctemplate<integral T>constexpr optional<pair<T, T>> extgcd(T a, T b, T c) {if (b == 0) {if (c % a != 0) return nullopt;return make_pair(c / a, 0);}auto res = extgcd(b, a % b, c);if (!res) return nullopt;auto [x, y] = *res;return make_pair(y, x - (a / b) * y);}} // namespace math} // namespace asalib#line 11 "library\\data_structure\\modint.hpp"namespace asalib {namespace ds {class modint_base {};template<typename T>concept is_modint = is_base_of_v<modint_base, T>;template<typename T>concept integral_or_modint = integral<T> || is_modint<T>;template<unsigned int mod, enable_if_t<(1 <= mod)>* = nullptr>class static_modint: private modint_base {using mint = static_modint;public:constexpr static_modint(): _val(0) {};template<integral T>constexpr static_modint(T x): _val(((long long) x % mod + mod) % mod) {};friend constexpr mint operator+(const mint& l, const mint& r) { return mint(l._val + r._val); }friend constexpr mint operator-(const mint& l, const mint& r) { return mint(l._val + mod - r._val); }friend constexpr mint operator*(const mint& l, const mint& r) { return mint((long long) l._val * r._val); }friend constexpr mint operator/(const mint& l, const mint& r) { return l * r.inv(); }constexpr mint operator+() const { return *this; }constexpr mint operator-() const { return 0 - *this; }constexpr mint& operator+=(const mint& other) { return *this = *this + other; }constexpr mint& operator-=(const mint& other) { return *this = *this - other; }constexpr mint& operator*=(const mint& other) { return *this = *this * other; }constexpr mint& operator/=(const mint& other) { return *this = *this / other; }constexpr mint& operator++() { return *this += 1; }constexpr mint& operator--() { return *this -= 1; }constexpr mint operator++(int) {mint res = *this;++*this;return res;}constexpr mint operator--(int) {mint res = *this;--*this;return res;}friend constexpr bool operator==(const mint& l, const mint& r) { return l._val == r._val; }friend constexpr bool operator!=(const mint& l, const mint& r) { return !(l == r); }friend constexpr bool operator<(const mint& l, const mint& r) { return l._val < r._val; }template<integral T>constexpr mint pow(T x) const {assert(x >= 0);mint res = 1, base = *this;while (x) {if (x & 1) res *= base;base *= base;x >>= 1;}return res;}constexpr mint inv() const {if (is_prime_mod()) return pow(mod - 2);if (gcd(_val, mod) != 1) throw invalid_argument("Modular inverse does not exist");return mint(math::extgcd<long long>(_val, mod, 1).value().first);}constexpr unsigned int val() const { return _val; }private:unsigned int _val;static constexpr bool is_prime_mod() {for (unsigned int i = 2; i * i <= mod; ++i) {if (mod % i == 0) return false;}return true;}};template<unsigned int id>class dynamic_modint: private modint_base {using mint = dynamic_modint;public:constexpr dynamic_modint(): _val(0) {}template<integral T>constexpr dynamic_modint(T x) {assert(_mod >= 1);_val = ((long long) x % _mod + _mod) % _mod;};friend constexpr mint operator+(const mint& l, const mint& r) { return mint(l._val + r._val); }friend constexpr mint operator-(const mint& l, const mint& r) { return mint(l._val + l._mod - r._val); }friend constexpr mint operator*(const mint& l, const mint& r) { return mint((long long) l._val * r._val); }friend constexpr mint operator/(const mint& l, const mint& r) { return l * r.inv(); }constexpr mint operator+() const { return *this; }constexpr mint operator-() const { return 0 - *this; }constexpr mint& operator+=(const mint& other) { return *this = *this + other; }constexpr mint& operator-=(const mint& other) { return *this = *this - other; }constexpr mint& operator*=(const mint& other) { return *this = *this * other; }constexpr mint& operator/=(const mint& other) { return *this = *this / other; }constexpr mint& operator++() { return *this += 1; }constexpr mint& operator--() { return *this -= 1; }constexpr mint operator++(int) {mint res = *this;++*this;return res;}constexpr mint operator--(int) {mint res = *this;--*this;return res;}friend constexpr bool operator==(const mint& l, const mint& r) { return l._val == r._val && l._mod == r._mod; }friend constexpr bool operator!=(const mint& l, const mint& r) { return !(l == r); }friend constexpr bool operator<(const mint& l, const mint& r) { return l._val < r._val; }template<integral T>constexpr mint pow(T x) const {assert(x >= 0);mint res = 1, base = *this;while (x) {if (x & 1) res *= base;base *= base;x >>= 1;}return res;}constexpr mint inv() const {if (gcd(_val, _mod) != 1) throw invalid_argument("Modular inverse does not exist");return mint(asalib::math::extgcd<long long>(_val, _mod, 1).value().first);}constexpr unsigned int val() const { return _val; }constexpr static unsigned int mod() { return _mod; }constexpr static void set_mod(unsigned int mod) {assert(mod >= 1);_mod = mod;}private:unsigned int _val;static inline unsigned int _mod;};} // namespace ds} // namespace asalib#line 7 "library\\data_structure\\matrix.hpp"namespace asalib {namespace ds {namespace internal {template<typename T>concept matval = integral_or_modint<T> || floating_point<T>;}template<internal::matval T>class Matrix {public:constexpr Matrix(): _n_row(0), _n_col(0) {};constexpr Matrix(size_t n_row, size_t n_col): _n_row(n_row), _n_col(n_col), _data(n_row * n_col) {};constexpr Matrix(size_t n_row, size_t n_col, T x): _n_row(n_row), _n_col(n_col), _data(n_row * n_col, x) {};// constexpr T& operator[](size_t i, size_t j) { return _data[i * _n_col + j]; }// constexpr const T& operator[](size_t i, size_t j) const { return _data[i * _n_col + j]; }// 使えないっぽいので at で代用constexpr inline T& at(size_t i, size_t j) { return _data[i * _n_col + j]; }constexpr T at(size_t i, size_t j) const { return _data[i * _n_col + j]; }constexpr valarray<T> row(size_t i) const { return valarray<T>(_data[slice(i * _n_col, _n_col, 1)]); }constexpr valarray<T> col(size_t j) const { return valarray<T>(_data[slice(j, _n_row, _n_col)]); }constexpr Matrix operator+=(const T& x) {_data += x;return *this;}constexpr Matrix operator-=(const T& x) {_data -= x;return *this;}constexpr Matrix operator*=(const T& x) {_data *= x;return *this;}constexpr Matrix operator/=(const T& x) {_data /= x;return *this;}constexpr Matrix operator%=(const T& x) {_data %= x;return *this;}constexpr Matrix operator+(const T& x) const { return Matrix(*this) += x; }constexpr Matrix operator-(const T& x) const { return Matrix(*this) -= x; }constexpr Matrix operator*(const T& x) const { return Matrix(*this) *= x; }constexpr Matrix operator/(const T& x) const { return Matrix(*this) /= x; }constexpr Matrix operator%(const T& x) const { return Matrix(*this) %= x; }constexpr Matrix operator+=(const Matrix& x) {assert(_n_row == x._n_row);assert(_n_col == x._n_col);_data += x._data;return *this;}constexpr Matrix operator-=(const Matrix& x) {assert(_n_row == x._n_row);assert(_n_col == x._n_col);_data -= x._data;return *this;}constexpr Matrix operator*=(const Matrix& x) {assert(_n_col == x._n_row);Matrix res(_n_row, x._n_col);for (size_t i = 0; i < _n_row; ++i) {for (size_t j = 0; j < x._n_col; ++j) {res.at(i, j) = (this->row(i) * x.col(j)).sum();}}return *this = res;}constexpr Matrix operator+(const Matrix& x) const { return Matrix(*this) += x; }constexpr Matrix operator-(const Matrix& x) const { return Matrix(*this) -= x; }constexpr Matrix operator*(const Matrix& x) const { return Matrix(*this) *= x; }constexpr bool operator==(const Matrix& x) const { return _n_row == x._n_row && _n_col == x._n_col && _data == x._data; }constexpr bool operator!=(const Matrix& x) const { return !(*this == x); }constexpr bool operator<(const Matrix& x) const { return _data < x._data; }constexpr const Matrix transpose() const {Matrix res(_n_col, _n_row);for (size_t i = 0; i < _n_row; ++i) res._data[slice(i, _n_col, _n_row)] = _data[slice(i * _n_col, _n_col, 1)];return res;}template<integral U>constexpr Matrix pow(U x) {assert(_n_row == _n_col);Matrix res = I(_n_row);Matrix a(*this);while (x) {if (x & 1) res *= a;a *= a;x >>= 1;}return res;}constexpr static Matrix I(size_t n) {Matrix res(n, n);res._data[std::slice(0, n, n + 1)] = 1;return res;}constexpr size_t n_row() const { return _n_row; }constexpr size_t n_col() const { return _n_col; }private:size_t _n_row, _n_col;valarray<T> _data;};} // namespace ds} // namespace asalib#line 8 "main.cpp"#define PROBLEM "https://yukicoder.me/problems/no/2441"int main() {cin.tie(nullptr)->sync_with_stdio(false);asalib::ds::Matrix<ll> a(2, 2);rep(i, 2) rep(j, 2) cin >> a.at(i, j);auto ans = a.pow(3);rep(i, 2) {rep(j, 2) cout << ans.at(i, j) << " \n"[j == 1];}return 0;}