結果
| 問題 |
No.793 うし数列 2
|
| ユーザー |
 a01sa01to
|
| 提出日時 | 2025-05-08 00:39:00 |
| 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 | 12,372 bytes |
| コンパイル時間 | 3,352 ms |
| コンパイル使用メモリ | 279,768 KB |
| 実行使用メモリ | 7,844 KB |
| 最終ジャッジ日時 | 2025-05-08 00:39:04 |
| 合計ジャッジ時間 | 4,348 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge4 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 21 |
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 "my-library\\library\\data-structure\\matrix.hpp"
#line 4 "my-library\\library\\data-structure\\matrix.hpp"
using namespace std;
#line 2 "my-library\\library\\_internal\\types.hpp"
#include <concepts>
#include <type_traits>
using namespace std;
#line 2 "my-library\\library\\_internal\\modint-base.hpp"
#line 5 "my-library\\library\\_internal\\modint-base.hpp"
using namespace std;
namespace asalib {
namespace _internal {
class modint_base {};
template<typename T>
concept is_modint = is_base_of_v<modint_base, T>;
}
}
#line 8 "my-library\\library\\_internal\\types.hpp"
namespace asalib {
namespace _internal {
template<class T>
concept integral_like = integral<T> || is_modint<T>;
template<class T>
concept floating_like = floating_point<T>;
template<class T>
concept numeric_like = integral_like<T> || floating_like<T>;
template<class T>
T plus(T a, T b) { return a + b; }
template<class T>
T minus(T a, T b) { return a - b; }
template<class T>
T zero() { return 0; }
}
}
#line 7 "my-library\\library\\data-structure\\matrix.hpp"
namespace asalib {
namespace matrix {
template<_internal::numeric_like 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 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->_data[slice(i * _n_col, _n_col, 1)] * x._data[slice(j, x._n_row, x._n_col)]).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[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;
public:
constexpr T determinant() const;
template<_internal::numeric_like U>
constexpr U determinant() const;
};
}
}
#line 2 "my-library\\library\\data-structure\\modint.hpp"
#line 6 "my-library\\library\\data-structure\\modint.hpp"
using namespace std;
#line 2 "my-library\\library\\math\\extgcd.hpp"
#line 4 "my-library\\library\\math\\extgcd.hpp"
#include <optional>
#line 6 "my-library\\library\\math\\extgcd.hpp"
using namespace std;
namespace asalib {
namespace math {
template<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);
}
}
}
#line 10 "my-library\\library\\data-structure\\modint.hpp"
namespace asalib {
namespace ds {
template<unsigned int mod>
requires(mod >= 1)
class static_modint: private _internal::modint_base {
using mint = static_modint;
public:
constexpr static_modint(): _val(0) {};
template<integral T>
constexpr static_modint(T x) {
long long y = x % (long long) mod;
if (y < 0) y += mod;
_val = y;
}
friend constexpr mint operator+(const mint& l, const mint& r) { return mint(l) += r; }
friend constexpr mint operator-(const mint& l, const mint& r) { return mint(l) -= r; }
friend constexpr mint operator*(const mint& l, const mint& r) { return mint(l) *= r; }
friend constexpr mint operator/(const mint& l, const mint& r) { return mint(l) /= r; }
constexpr mint operator+() const { return *this; }
constexpr mint operator-() const { return 0 - *this; }
constexpr mint& operator+=(const mint& other) {
_val += other._val;
if (_val >= mod) _val -= mod;
return *this;
}
constexpr mint& operator-=(const mint& other) {
_val -= other._val;
if (_val >= mod) _val += mod;
return *this;
}
constexpr mint& operator*=(const mint& other) {
unsigned long long z = _val;
z *= other._val;
_val = z % mod;
return *this;
}
constexpr mint& operator/=(const mint& other) { return *this = *this * other.inv(); }
constexpr mint& operator++() {
_val++;
if (_val == mod) _val = 0;
return *this;
}
constexpr mint& operator--() {
if (_val == 0) _val = mod;
_val--;
return *this;
}
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 _internal::modint_base {
using mint = dynamic_modint;
public:
constexpr dynamic_modint(): _val(0) {}
template<integral T>
constexpr dynamic_modint(T x) {
assert(_mod >= 1);
long long y = x % (long long) _mod;
if (y < 0) y += _mod;
_val = y;
};
friend constexpr mint operator+(const mint& l, const mint& r) { return mint(l) += r; }
friend constexpr mint operator-(const mint& l, const mint& r) { return mint(l) -= r; }
friend constexpr mint operator*(const mint& l, const mint& r) { return mint(l) *= r; }
friend constexpr mint operator/(const mint& l, const mint& r) { return mint(l) /= r; }
constexpr mint operator+() const { return *this; }
constexpr mint operator-() const { return 0 - *this; }
constexpr mint& operator+=(const mint& other) {
_val += other._val;
if (_val >= _mod) _val -= _mod;
return *this;
}
constexpr mint& operator-=(const mint& other) {
_val -= other._val;
if (_val >= _mod) _val += _mod;
return *this;
}
constexpr mint& operator*=(const mint& other) {
unsigned long long z = _val;
z *= other._val;
_val = z % _mod;
return *this;
}
constexpr mint& operator/=(const mint& other) { return *this = *this * other.inv(); }
constexpr mint& operator++() {
_val++;
if (_val == _mod) _val = 0;
return *this;
}
constexpr mint& operator--() {
if (_val == 0) _val = _mod;
_val--;
return *this;
}
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(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;
};
}
}
#line 9 "main.cpp"
using mint = asalib::ds::static_modint<1'000'000'007>;
int main() {
cin.tie(nullptr)->sync_with_stdio(false);
ll n;
cin >> n;
asalib::matrix::Matrix<mint> A(2, 2);
A.at(0, 0) = 10, A.at(0, 1) = 3, A.at(1, 0) = 0, A.at(1, 1) = 1;
asalib::matrix::Matrix<mint> b(2, 1);
b.at(0, 0) = 1, b.at(1, 0) = 1;
cout << (A.pow(n) * b).at(0, 0).val() << '\n';
return 0;
}