結果
問題 | No.1073 無限すごろく |
ユーザー |
![]() |
提出日時 | 2020-06-05 21:48:41 |
言語 | C++17(gcc12) (gcc 12.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 2 ms / 2,000 ms |
コード長 | 7,174 bytes |
コンパイル時間 | 2,733 ms |
コンパイル使用メモリ | 112,608 KB |
最終ジャッジ日時 | 2025-01-10 22:27:01 |
ジャッジサーバーID (参考情報) |
judge4 / judge4 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 30 |
ソースコード
#include <iostream>#include <algorithm>#include <utility>#include <numeric>#include <vector>#include <array>template <class T, class U>inline bool chmin(T &lhs, const U &rhs) {if (lhs > rhs) { lhs = rhs; return true; }return false;}template <class T, class U>inline bool chmax(T &lhs, const U &rhs) {if (lhs < rhs) { lhs = rhs; return true; }return false;}struct range {using itr = int64_t;struct iterator {itr i;constexpr iterator(itr i_): i(i_) { }constexpr void operator ++ () { ++i; }constexpr itr operator * () const { return i; }constexpr bool operator != (iterator x) const { return i != x.i; }};const iterator l, r;constexpr range(itr l_, itr r_): l(l_), r(std::max(l_, r_)) { }constexpr iterator begin() const { return l; }constexpr iterator end() const { return r; }};struct revrange {using itr = int64_t;struct iterator {itr i;constexpr iterator(itr i_): i(i_) { }constexpr void operator ++ () { --i; }constexpr itr operator * () const { return i; }constexpr bool operator != (iterator x) const { return i != x.i; }};const iterator l, r;constexpr revrange(itr l_, itr r_): l(l_ - 1), r(std::max(l_, r_) - 1) { }constexpr iterator begin() const { return r; }constexpr iterator end() const { return l; }};template <uint32_t Modulus>class modular {public:using value_type = uint32_t;using max_type = uint64_t;static constexpr value_type mod = Modulus;static_assert(mod >= 2, "invalid mod :: smaller than 2");static_assert(mod < (value_type(1) << 31), "invalid mod :: over 2^31");template <class T>static constexpr value_type normalize(T value_) {if (value_ < 0) {value_ = -value_;value_ %= mod;if (value_ == 0) return 0;return mod - value_;}return value_ % mod;}private:value_type value;public:constexpr modular(): value(0) { }template <class T>explicit constexpr modular(T value_): value(normalize(value_)) { }template <class T>explicit constexpr operator T() { return static_cast<T>(value); }constexpr value_type get() const { return value; }constexpr modular operator - () const { return modular(mod - value); }constexpr modular operator ~ () const { return inverse(); }constexpr value_type &extract() { return value; }constexpr modular inverse() const { return power(mod - 2); }constexpr modular power(max_type exp) const {modular res(1), mult(*this);while (exp > 0) {if (exp & 1) res *= mult;mult *= mult;exp >>= 1;}return res;}constexpr modular operator + (const modular &rhs) const { return modular(*this) += rhs; }constexpr modular& operator += (const modular &rhs) {if ((value += rhs.value) >= mod) value -= mod;return *this;}constexpr modular operator - (const modular &rhs) const { return modular(*this) -= rhs; }constexpr modular& operator -= (const modular &rhs) {if ((value += mod - rhs.value) >= mod) value -= mod;return *this;}constexpr modular operator * (const modular &rhs) const { return modular(*this) *= rhs; }constexpr modular& operator *= (const modular &rhs) {value = (max_type) value * rhs.value % mod;return *this;}constexpr modular operator / (const modular &rhs) const { return modular(*this) /= rhs; }constexpr modular& operator /= (const modular &rhs) { return (*this) *= rhs.inverse(); }constexpr bool zero() const { return value == 0; }constexpr bool operator == (const modular &rhs) const { return value == rhs.value; }constexpr bool operator != (const modular &rhs) const { return value != rhs.value; }friend std::ostream& operator << (std::ostream &stream, const modular &rhs) {return stream << rhs.value;}};using m32 = modular<1000000007>;template <class T, size_t H, size_t W>class matrix {public:using value_type = typename T::value_type;using size_type = size_t;static inline auto add = typename T::addition();static inline auto mult = typename T::multiplication();static constexpr size_type height = H;static constexpr size_type width = W;private:std::array<std::array<value_type, W>, H> data;public:matrix(const value_type &value_ = add.identity) { fill(value_); }matrix(const std::array<std::array<value_type, W>, H> &data_): data(data_) { }std::array<value_type, W> &operator [] (size_type idx) { return data[idx]; }const std::array<value_type, W> &operator [] (size_type idx) const { return data[idx]; }matrix operator + (const matrix &rhs) const { return matrix(*this) += rhs; }matrix &operator += (const matrix &rhs) {for (size_type i = 0; i < H; ++i) {for (size_type j = 0; j < W; ++j) {data[i][j] = add(data[i][j], rhs[i][j]);}}return *this;}matrix &operator *= (const matrix<T, W, W> &rhs) { return (*this) = (*this) * rhs; }template <size_t K>matrix<T, H, K> operator * (const matrix<T, W, K> &rhs) const {matrix<T, H, K> res;for (size_type i = 0; i < H; ++i) {for (size_type j = 0; j < K; ++j) {for (size_type k = 0; k < W; ++k) {res[i][j] = add(res[i][j], mult(data[i][k], rhs[k][j]));}}}return res;}matrix operator * (const value_type &rhs) const { return matrix(*this) *= rhs; }matrix &operator *= (const value_type &rhs) {for (size_type i = 0; i < H; ++i) {for (size_type j = 0; j < W; ++j) {data[i][j] = mult(data[i][j], rhs);}}return *this;}void fill(const value_type &val) {for (auto &arr: data) { arr.fill(val); }}/* typename std::enable_if<H == W, matrix>::type */matrix power(uint64_t exp) const {matrix res, use(*this);for (size_type i = 0; i < H; ++i) {res[i][i] = mult.identity;}while (exp > 0) {if (exp & 1) res *= use;use *= use;exp >>= 1;}return res;}};template <class T>struct number {using value_type = T;struct addition {value_type identity = value_type(0);value_type operator () (const value_type &x, const value_type &y) const {return x + y;}};struct multiplication {value_type identity = value_type(1);value_type operator () (const value_type &x, const value_type &y) const {return x * y;}};};using i32 = int32_t;using i64 = int64_t;using u32 = uint32_t;using u64 = uint64_t;constexpr i32 inf32 = (i32(1) << 30) - 1;constexpr i64 inf64 = (i64(1) << 62) - 1;int main() {u64 N;std::cin >> N;matrix<number<m32>, 1, 6> start;start[0][0] = m32(6).inverse();for (auto i: range(0, 6)) {start[0][i] = m32(6).inverse();for (auto j: range(0, i)) {start[0][i] += start[0][j] / m32(6);}}if (N <= 6) {std::cout << start[0][N - 1] << '\n';return 0;}matrix<number<m32>, 6, 6> power;for (auto i: range(0, 6)) {power[i][5] = m32(6).inverse();}for (auto i: range(0, 5)) {power[i + 1][i] = m32(1);}start *= power.power(N - 6);std::cout << start[0][5] << '\n';return 0;}