結果

問題 No.1073 無限すごろく
ユーザー KoDKoD
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
このコードへのチャレンジ
(要ログイン)
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

#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;
}
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