結果
問題 | No.1073 無限すごろく |
ユーザー |
|
提出日時 | 2020-07-04 07:47:01 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 2 ms / 2,000 ms |
コード長 | 14,645 bytes |
コンパイル時間 | 2,416 ms |
コンパイル使用メモリ | 206,084 KB |
最終ジャッジ日時 | 2025-01-11 15:26:24 |
ジャッジサーバーID (参考情報) |
judge4 / judge4 |
(要ログイン)
ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 30 |
ソースコード
#define _USE_MATH_DEFINES#include <bits/stdc++.h>using namespace std;template<typename T> class Modular {private:long long value;constexpr static int MOD() { return static_cast<int>(T::value); }public:constexpr Modular() : value() {};constexpr Modular(const Modular& other) : value(other.value) {}template <typename U> constexpr Modular(const U& x) { value = normalize(x); }template <typename U> static long long normalize(const U& x) {long long v;if (-MOD() <= x && x < MOD()) v = static_cast<long long>(x);else v = static_cast<long long>(x % MOD());if (v < 0) v += MOD();return v;}constexpr static long long inverse(long long x) {x = (x % MOD() + MOD()) % MOD();long long y = MOD(), u = 1, v = 0;while(y) {long long t = x / y;x -= t * y; swap(x, y);u -= t * v; swap(u, v);}return (u % MOD() + MOD()) % MOD();}static long long mul(const long long& a, const long long& b) {long long res;#ifdef _WIN32unsigned long long x = a * b;unsigned xh = (unsigned) (x >> 32), xl = (unsigned) x, d, m;asm("divl %4; \n\t": "=a" (d), "=d" (m): "d" (xh), "a" (xl), "r" (MOD()));res = m;#elseres = a * b % MOD();#endifreturn res;}explicit operator long long() const noexcept { return value;}template <typename U> explicit operator U() const noexcept { return static_cast<U>(value); }constexpr Modular& operator=(const Modular& other) & noexcept { value = other.value; return *this; }template <typename U> constexpr Modular& operator=(const U& other) & noexcept { return *this = Modular(other); }constexpr Modular& operator+=(const Modular& other) noexcept { if ((value += other.value) >= MOD()) value -= MOD(); return *this; }template <typename U> constexpr Modular& operator+=(const U& other) noexcept { return *this += Modular(other); }constexpr Modular& operator-=(const Modular& other) noexcept { if ((value -= other.value) < 0) value += MOD(); return *this; }template <typename U> constexpr Modular& operator-=(const U& other) noexcept { return *this -= Modular(other); }constexpr Modular& operator*=(const Modular& other) noexcept { this->value = mul(this->value, other.value); return *this; }template <typename U> constexpr Modular& operator*=(const U& other) noexcept {return *this *= Modular(other); }constexpr Modular& operator/=(const Modular& other) noexcept { return *this *= Modular(inverse(other.value)); }template <typename U> constexpr Modular& operator/=(const U& other) noexcept { return *this *= Modular(inverse(normalize(other))); }constexpr Modular& operator++() noexcept {return *this += 1; }constexpr Modular operator++(int) noexcept { Modular ret(*this); *this += 1; return ret; }constexpr Modular& operator--() noexcept {return *this -= 1; }constexpr Modular operator--(int) noexcept { Modular ret(*this); *this -= 1; return ret; }constexpr Modular operator-() const { return Modular(-value); }friend constexpr bool operator==(const Modular& lhs, const Modular<T>& rhs) noexcept { return lhs.value == rhs.value; }template <typename U> friend constexpr bool operator==(const Modular<T>& lhs, U rhs) noexcept { return lhs == Modular<T>(rhs); }template <typename U> friend constexpr bool operator==(U lhs, const Modular<T>& rhs) noexcept { return Modular<T>(lhs) == rhs; }friend constexpr bool operator!=(const Modular<T>& lhs, const Modular<T>& rhs) noexcept { return !(lhs == rhs); }template <typename U> friend constexpr bool operator!=(const Modular<T>& lhs, U rhs) noexcept { return !(lhs == rhs); }template <typename U> friend constexpr bool operator!=(U lhs, const Modular<T> rhs) noexcept { return !(lhs == rhs); }friend constexpr bool operator<(const Modular<T>& lhs, const Modular<T>& rhs) noexcept { return lhs.value < rhs.value; }template <typename U> friend constexpr bool operator<(const Modular<T> &lhs, U rhs) noexcept { return lhs.value < rhs; }template <typename U> friend constexpr bool operator<(U lhs, const Modular<T> &rhs) noexcept { return lhs < rhs.value; }friend constexpr bool operator>(const Modular<T>& lhs, const Modular<T>& rhs) noexcept { return rhs.value < lhs.value; }template <typename U> friend constexpr bool operator>(const Modular<T> &lhs, U rhs) noexcept { return rhs.value < lhs; }template <typename U> friend constexpr bool operator>(U lhs, const Modular<T> &rhs) noexcept { return rhs < lhs.value; }friend constexpr bool operator<=(const Modular<T>& lhs, const Modular<T>& rhs) noexcept { return !(lhs.value > rhs.value); }template <typename U> friend constexpr bool operator<=(const Modular<T> &lhs, U rhs) noexcept { return !(lhs.value > rhs); }template <typename U> friend constexpr bool operator<=(U lhs, const Modular<T> &rhs) noexcept { return !(lhs < rhs.value); }friend constexpr bool operator>=(const Modular<T>& lhs, const Modular<T>& rhs) noexcept { return !(lhs.value < rhs.value); }template <typename U> friend constexpr bool operator>=(const Modular<T> &lhs, U rhs) noexcept { return !(lhs.value < rhs); }template <typename U> friend constexpr bool operator>=(U lhs, const Modular<T> &rhs) noexcept { return !(lhs < rhs.value); }friend constexpr Modular<T> operator+(const Modular<T>& lhs, const Modular<T>& rhs) noexcept { return Modular<T>(lhs) += rhs; }template <typename U> friend constexpr Modular<T> operator+(const Modular<T>& lhs, U rhs) noexcept { return Modular<T>(lhs) += rhs; }template <typename U> friend constexpr Modular<T> operator+(U lhs, const Modular<T> &rhs) noexcept { return Modular<T>(lhs) += rhs; }friend constexpr Modular<T> operator-(const Modular<T>& lhs, const Modular<T>& rhs) noexcept { return Modular<T>(lhs) -= rhs; }template <typename U> friend constexpr Modular<T> operator-(const Modular<T>& lhs, U rhs) noexcept { return Modular<T>(lhs) -= rhs; }template <typename U> friend constexpr Modular<T> operator-(U lhs, const Modular<T> &rhs) noexcept { return Modular<T>(lhs) -= rhs; }friend constexpr Modular<T> operator*(const Modular<T>& lhs, const Modular<T>& rhs) noexcept { return Modular<T>(lhs) *= rhs; }template <typename U> friend constexpr Modular<T> operator*(const Modular<T>& lhs, U rhs) noexcept { return Modular<T>(lhs) *= rhs; }template <typename U> friend constexpr Modular<T> operator*(U lhs, const Modular<T> &rhs) noexcept { return Modular<T>(lhs) *= rhs; }friend constexpr Modular<T> operator/(const Modular<T>& lhs, const Modular<T>& rhs) noexcept { return Modular<T>(lhs) /= rhs; }template <typename U> friend constexpr Modular<T> operator/(const Modular<T>& lhs, U rhs) noexcept { return Modular<T>(lhs) /= rhs; }template <typename U> friend constexpr Modular<T> operator/(U lhs, const Modular<T> &rhs) noexcept { return Modular<T>(lhs) /= rhs; }friend std::ostream& operator<<(std::ostream& stream, const Modular<T>& number) noexcept { return stream << number.value; }friend std::istream& operator>>(std::istream& stream, Modular<T>& number) { long long in; stream >> in; number.value = Modular<T>::normalize(in);return stream; }constexpr int getmod() const { return MOD(); }};template<typename T, typename U> Modular<T> power(const Modular<T>& x, const U& y) {assert(y >= 0);Modular<T> k = x, result = 1;U p = y;while (p > 0) {if (p & 1) result *= k;k *= k;p >>= 1;}return result;}template<typename T> class BinaryCoefficients {private:vector<Modular<T>> fact_, inv_, finv_;long long MOD = static_cast<long long>(T::value);public:constexpr BinaryCoefficients(int n = 2020200) : fact_(n, 1), inv_(n, 1), finv_(n, 1) {for (int i = 2; i < n; i++) {fact_[i] = fact_[i - 1] * i;inv_[i] = -inv_[MOD % i] * (MOD / i);finv_[i] = finv_[i - 1] * inv_[i];}}constexpr Modular<T> comb(int n, int k) const noexcept { if (n < k || n < 0 || k < 0) return 0; return fact_[n] * finv_[k] * finv_[n - k]; }constexpr Modular<T> fact(int n) const noexcept { if (n < 0) return 0; return fact_[n]; }constexpr Modular<T> inv(int n) const noexcept { if (n < 0) return 0; return inv_[n]; }constexpr Modular<T> finv(int n) const noexcept { if (n < 0) return 0; return finv_[n]; }};constexpr int mod = 1e9 + 7;//constexpr int mod = 998244353;using mint = Modular<std::integral_constant<decay<decltype(mod)>::type, mod>>;using bicoef = BinaryCoefficients<std::integral_constant<decay<decltype(mod)>::type, mod>>;// struct modValue { static int value; };// int modValue::value;// int& mod = modValue::value;// using mint = Modular<modValue>;// using bicoef = BinaryCoefficients<modValue>;template <typename T> class Matrix {private:vector<vector<T>> matrix;template<typename U> using ET = enable_if<is_floating_point<U>::value>;template<typename U> using EF = enable_if<!is_floating_point<U>::value>;template<typename U, typename ET<U>::type* = nullptr> static constexpr bool is_zero (const U& x) { return abs(x) < 1e-8; }template<typename U, typename EF<U>::type* = nullptr> static constexpr bool is_zero (const U& x) { return x == U(0); }public:constexpr Matrix () {}constexpr Matrix (int h, int w) : matrix(vector<vector<T>>(h, vector<T>(w))) {}constexpr Matrix (int h, int w, T val) : matrix(vector<vector<T>>(h, vector<T>(w, val))) {}constexpr Matrix (const vector<vector<T>>& mat) : matrix(mat) {}constexpr Matrix (const Matrix<T>& mat) : matrix(mat.matrix) {}constexpr size_t height () const noexcept { return matrix.size(); }constexpr size_t width () const noexcept { assert(!empty()); return matrix[0].size(); }constexpr bool empty() const noexcept { return matrix.empty(); }vector<T>& operator[] (size_t row) { assert(matrix.size() > row); return matrix[row]; }const vector<T>& operator[] (size_t row) const { assert(matrix.size() > row); return matrix[row]; }static Matrix identity (int n) {Matrix res(n, n);for (int i = 0; i < n; ++i) res[i][i] = T(1);return res;}Matrix identity () { assert(height() == width()); return identity(height()); };constexpr Matrix<T>& operator= (const Matrix<T>& lhs) & noexcept {//int h = lhs.matrix.size();// assert(!lhs.matrix.empty());matrix = lhs.matrix;return *this;// int w = lhs.matrix[0].size();// matrix = vector<vector<T>>(h, vector<T>(w, T()));// for (int i = 0; i < h; i++) for (int j = 0; j < w; j++) matrix[i][j] = lhs.matrix[i][j];// return *this;}constexpr Matrix<T>& operator= (const vector<vector<T>>& lhs) & noexcept { return *this = Matrix(lhs); }constexpr Matrix<T>& operator+= (const Matrix<T>& lhs) noexcept {assert(height() == lhs.matrix.size());assert(width() == lhs.matrix[0].sizse());for (int i = 0; i < height(); ++i) for (int j = 0; j < width(); ++j) matrix[i][j] += lhs[i][j];return (*this);}constexpr Matrix<T>& operator+= (const vector<vector<T>>& lhs) noexcept { return *this += Matrix(lhs); }constexpr Matrix<T>& operator-= (const Matrix<T>& lhs) noexcept {assert(height() == lhs.matrix.size());assert(width() == lhs.matrix[0].sizse());for (int i = 0; i < height(); ++i) for (int j = 0; j < width(); ++j) matrix[i][j] -= lhs[i][j];return (*this);}constexpr Matrix<T>& operator-= (const vector<vector<T>>& lhs) noexcept { return *this -= Matrix(lhs); }constexpr Matrix<T>& operator*= (const Matrix<T>& lhs) noexcept {Matrix res(height(), lhs[0].size());for (int i = 0; i < (int) height(); ++i) for (int j = 0; j < (int) lhs[0].size(); ++j) for (int k = 0; k < (int) width(); k++) {res[i][j] += matrix[i][k] * lhs[k][j];}matrix.swap(res.matrix);return (*this);}constexpr Matrix<T>& operator*= (const vector<vector<T>>& lhs) noexcept { return *this *= Matrix(lhs); }friend constexpr bool operator==(const Matrix<T>& lhs, const Matrix<T>& rhs) noexcept { return lhs.matrix == rhs.matrix; }friend constexpr bool operator==(const Matrix<T>& lhs, const vector<vector<T>>& rhs) noexcept { return lhs == Matrix(rhs); }friend constexpr bool operator==(const vector<vector<T>>& lhs, const Matrix<T>& rhs) noexcept { return Matrix(lhs) == rhs; }friend constexpr Matrix<T> operator+(const Matrix<T>& lhs, const Matrix<T>& rhs) noexcept { return Matrix(lhs) += rhs; }friend constexpr Matrix<T> operator+(const Matrix<T>& lhs, const vector<vector<T>>& rhs) noexcept { return Matrix(lhs) += rhs; }friend constexpr Matrix<T> operator+(const vector<vector<T>>& lhs, const Matrix<T>& rhs) noexcept { return Matrix(lhs) += rhs; }friend constexpr Matrix<T> operator-(const Matrix<T>& lhs, const Matrix<T>& rhs) noexcept { return Matrix(lhs) -= rhs; }friend constexpr Matrix<T> operator-(const Matrix<T>& lhs, const vector<vector<T>>& rhs) noexcept { return Matrix(lhs) -= rhs; }friend constexpr Matrix<T> operator-(const vector<vector<T>>& lhs, const Matrix<T>& rhs) noexcept { return Matrix(lhs) -= rhs; }friend constexpr Matrix<T> operator*(const Matrix<T>& lhs, const Matrix<T>& rhs) noexcept { return Matrix(lhs) *= rhs; }friend constexpr Matrix<T> operator*(const Matrix<T>& lhs, const vector<vector<T>>& rhs) noexcept { return Matrix(lhs) *= rhs; }friend constexpr Matrix<T> operator*(const vector<vector<T>>& lhs, const Matrix<T>& rhs) noexcept { return Matrix(lhs) *= rhs; }template <typename U> Matrix<T> power(U n) {Matrix x(*this), res = identity(height());while (n) {if (n & 1) res *= x;x *= x;n >>= 1;}return res;}T determinant() {Matrix a(*this);assert(a.height() == a.width());T res = 1;for (int i = 0; i < width(); ++i) {int pivot = -1;for (int j = i; j < width(); ++j) if (!is_zero(a[j][i])) pivot = j;if (pivot == -1) return T(0);if (i != pivot) {res *= -1;swap(a[i], a[pivot]);}res *= a[i][i];T div = a[i][i];for (int j = 0; j < width(); ++j) a[i][j] /= div;for (int j = i + 1; j < width(); ++j) {T b = a[j][i];for (int k = 0; k < width(); ++k) {a[j][k] -= a[i][k] * b;}}}return res;}};signed main() {ios::sync_with_stdio(false); cin.tie(0);long long n;cin >> n;Matrix<mint> m(6, 1);m[0][0] = 1;Matrix<mint> v(6, 6);for (int i = 0; i < 6; i++) v[0][i] = mint(1) / 6;for (int i = 1; i < 6; i++) v[i][i - 1] = 1;v = v.power(n);Matrix<mint> res = v * m;cout << res[0][0] << endl;return 0;}