結果

問題 No.1073 無限すごろく
ユーザー MayimgMayimg
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
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 30
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#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 _WIN32
unsigned 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;
#else
res = a * b % MOD();
#endif
return 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;
}
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