結果

問題 No.891 隣接3項間の漸化式
ユーザー noshi91noshi91
提出日時 2019-09-20 21:30:33
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 9,124 bytes
コンパイル時間 816 ms
コンパイル使用メモリ 79,440 KB
実行使用メモリ 5,376 KB
最終ジャッジ日時 2024-09-14 16:26:59
合計ジャッジ時間 2,018 ms
ジャッジサーバーID
(参考情報)
judge5 / judge1
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 * 39
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 NDEBUG
#include <cstddef>
#include <cstdint>
#include <iostream>
#include <iterator>
#include <vector>
namespace n91 {
using i8 = std::int_fast8_t;
using i32 = std::int_fast32_t;
using i64 = std::int_fast64_t;
using u8 = std::uint_fast8_t;
using u32 = std::uint_fast32_t;
using u64 = std::uint_fast64_t;
using isize = std::ptrdiff_t;
using usize = std::size_t;
constexpr usize operator"" _z(unsigned long long x) noexcept {
return static_cast<usize>(x);
}
template <class T> class integral_iterator {
public:
using difference_type = T;
using value_type = T;
using pointer = const value_type *;
using reference = value_type;
using iterator_category = std::random_access_iterator_tag;
private:
using self_type = integral_iterator<value_type>;
value_type i;
public:
constexpr integral_iterator() noexcept : i() {}
explicit constexpr integral_iterator(const value_type i) noexcept : i(i) {}
constexpr self_type operator++(int) noexcept { return self_type(i++); }
constexpr self_type operator--(int) noexcept { return self_type(i--); }
constexpr self_type operator[](const difference_type rhs) const noexcept {
return self_type(i + rhs);
}
constexpr self_type &operator++() noexcept {
++i;
return *this;
}
constexpr self_type &operator--() noexcept {
--i;
return *this;
}
constexpr reference operator*() const noexcept { return i; }
constexpr self_type operator+(const difference_type rhs) const noexcept {
return self_type(i + rhs);
}
constexpr self_type operator-(const difference_type rhs) const noexcept {
return self_type(i - rhs);
}
constexpr difference_type operator-(const self_type rhs) const noexcept {
return i - rhs.i;
}
constexpr bool operator<(const self_type rhs) const noexcept {
return i < rhs.i;
}
constexpr bool operator<=(const self_type rhs) const noexcept {
return i <= rhs.i;
}
constexpr bool operator>(const self_type rhs) const noexcept {
return i > rhs.i;
}
constexpr bool operator>=(const self_type rhs) const noexcept {
return i >= rhs.i;
}
constexpr bool operator==(const self_type rhs) const noexcept {
return i == rhs.i;
}
constexpr bool operator!=(const self_type rhs) const noexcept {
return i != rhs.i;
}
constexpr self_type &operator+=(const difference_type rhs) noexcept {
i += rhs;
return *this;
}
constexpr self_type &operator-=(const difference_type rhs) noexcept {
i -= rhs;
return *this;
}
};
template <class T>
constexpr integral_iterator<T> make_int_itr(const T i) noexcept {
return integral_iterator<T>(i);
}
class rep {
const usize f, l;
public:
constexpr rep(const usize f, const usize l) noexcept : f(f), l(l) {}
constexpr auto begin() const noexcept { return make_int_itr(f); }
constexpr auto end() const noexcept { return make_int_itr(l); }
};
class revrep {
const usize f, l;
public:
revrep(const usize f, const usize l) noexcept : f(l), l(f) {}
auto begin() const noexcept {
return std::make_reverse_iterator(make_int_itr(f));
}
auto end() const noexcept {
return std::make_reverse_iterator(make_int_itr(l));
}
};
template <class T> auto md_vec(const usize n, const T &value) {
return std::vector<T>(n, value);
}
template <class... Args> auto md_vec(const usize n, Args... args) {
return std::vector<decltype(md_vec(args...))>(n, md_vec(args...));
}
template <class T> constexpr T difference(const T &a, const T &b) {
return a < b ? b - a : a - b;
}
template <class T> T scan() {
T ret;
std::cin >> ret;
return ret;
}
} // namespace n91
#include <algorithm>
#include <array>
#include <cassert>
#include <cstddef>
#include <initializer_list>
namespace n91 {
template <class T, std::size_t M, std::size_t N>
class array_matrix : public std::array<std::array<T, N>, M> {
public:
array_matrix() {
std::for_each(this->begin(), this->end(), [](auto &row) {
std::fill(row.begin(), row.end(), static_cast<T>(0));
});
}
array_matrix(std::initializer_list<std::initializer_list<T>> il) {
assert(il.size() == M);
auto ar_itr = this->begin();
const auto ar_end = this->end();
auto il_itr = il.begin();
while (ar_itr != ar_end) {
assert(il_itr->size() == N);
std::copy(il_itr->begin(), il_itr->end(), ar_itr->begin());
++ar_itr;
++il_itr;
}
}
array_matrix &operator*=(const array_matrix<T, N, N> &rhs) {
return *this = *this * rhs;
}
};
template <class T, std::size_t L, std::size_t M, std::size_t N>
array_matrix<T, L, N> operator*(const array_matrix<T, L, M> &lhs,
const array_matrix<T, M, N> &rhs) {
array_matrix<T, L, N> ret = {};
for (std::size_t i = static_cast<std::size_t>(0); i != L; ++i) {
for (std::size_t j = static_cast<std::size_t>(0); j != M; ++j) {
for (std::size_t k = static_cast<std::size_t>(0); k != N; ++k) {
ret[i][k] += lhs[i][j] * rhs[j][k];
}
}
}
return ret;
}
template <class T, std::size_t N> array_matrix<T, N, N> matrix_identity() {
array_matrix<T, N, N> ret;
for (std::size_t i = static_cast<std::size_t>(0); i != N; ++i) {
ret[i][i] = static_cast<T>(1);
}
return ret;
}
} // namespace n91
#include <cstdint>
namespace n91 {
constexpr std::uint_fast64_t totient(std::uint_fast64_t x) noexcept {
using u64 = std::uint_fast64_t;
u64 ret = x;
for (u64 i = static_cast<u64>(2); i * i <= x; ++i) {
if (x % i == static_cast<u64>(0)) {
ret -= ret / i;
x /= i;
while (x % i == static_cast<u64>(0)) {
x /= i;
}
}
}
if (x != static_cast<u64>(1)) {
ret -= ret / x;
}
return ret;
}
template <std::uint_fast64_t Modulus,
std::uint_fast64_t InverseExp =
totient(Modulus) - static_cast<std::uint_fast64_t>(1)>
class modint {
using u64 = std::uint_fast64_t;
static_assert(Modulus < static_cast<u64>(1) << static_cast<u64>(32),
"Modulus must be less than 2**32");
u64 a;
constexpr modint &negate() noexcept {
if (a != static_cast<u64>(0)) {
a = Modulus - a;
}
return *this;
}
public:
constexpr modint(const u64 x = static_cast<u64>(0)) noexcept
: a(x % Modulus) {}
constexpr u64 &value() noexcept { return a; }
constexpr const u64 &value() const noexcept { return a; }
constexpr modint operator+() const noexcept { return modint(*this); }
constexpr modint operator-() const noexcept { return modint(*this).negate(); }
constexpr modint operator+(const modint rhs) const noexcept {
return modint(*this) += rhs;
}
constexpr modint operator-(const modint rhs) const noexcept {
return modint(*this) -= rhs;
}
constexpr modint operator*(const modint rhs) const noexcept {
return modint(*this) *= rhs;
}
constexpr modint operator/(const modint rhs) const noexcept {
return modint(*this) /= rhs;
}
constexpr modint &operator+=(const modint rhs) noexcept {
a += rhs.a;
if (a >= Modulus) {
a -= Modulus;
}
return *this;
}
constexpr modint &operator-=(const modint rhs) noexcept {
if (a < rhs.a) {
a += Modulus;
}
a -= rhs.a;
return *this;
}
constexpr modint &operator*=(const modint rhs) noexcept {
a = a * rhs.a % Modulus;
return *this;
}
constexpr modint &operator/=(modint rhs) noexcept {
u64 exp = InverseExp;
while (exp) {
if (exp % static_cast<u64>(2) != static_cast<u64>(0)) {
*this *= rhs;
}
rhs *= rhs;
exp /= static_cast<u64>(2);
}
return *this;
}
constexpr bool operator==(const modint rhs) const noexcept {
return a == rhs.a;
}
constexpr bool operator!=(const modint rhs) const noexcept {
return a != rhs.a;
}
};
template <class T, std::uint_fast64_t v> class modint_constant {
public:
static constexpr T value = static_cast<T>(v);
using value_type = T;
};
} // namespace n91
#include <functional>
#include <utility>
namespace n91 {
template <class T, class U, class Operate = std::multiplies<T>>
constexpr T power(T base, U exp, const Operate &oper = Operate(),
T iden = static_cast<T>(1)) {
while (exp != static_cast<U>(0)) {
if (exp % static_cast<U>(2) != static_cast<U>(0)) {
iden = oper(iden, base);
}
exp /= static_cast<U>(2);
base = oper(base, base);
}
return iden;
}
} // namespace n91
#include <algorithm>
#include <iostream>
#include <utility>
namespace n91 {
void main_() {
using mint = modint<static_cast<u64>(1000000007)>;
using mat = array_matrix<mint, 2_z, 2_z>;
const mint a = static_cast<mint>(scan<u64>());
const mint b = static_cast<mint>(scan<u64>());
const u64 n = scan<u64>();
mat step = {{a, static_cast<mint>(1)}, {b, static_cast<mint>(0)}};
array_matrix<mint, 1_z, 2_z> init = {
{static_cast<mint>(1), static_cast<mint>(0)}};
std::cout << (init * power(step, n, std::multiplies<mat>(),
matrix_identity<mint, 2_z>()))[0_z][1_z]
.value()
<< std::endl;
}
} // namespace n91
int main() {
n91::main_();
return 0;
}
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