結果
| 問題 |
No.891 隣接3項間の漸化式
|
| コンテスト | |
| ユーザー |
 jell
|
| 提出日時 | 2020-01-16 22:51:40 |
| 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 | 13,526 bytes |
| コンパイル時間 | 1,077 ms |
| コンパイル使用メモリ | 94,452 KB |
| 実行使用メモリ | 6,948 KB |
| 最終ジャッジ日時 | 2024-06-24 11:53:55 |
| 合計ジャッジ時間 | 2,192 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 39 |
コンパイルメッセージ
main.cpp:278:1: warning: ISO C++ forbids declaration of 'main' with no type [-Wreturn-type]
278 | main()
| ^~~~
ソースコード
#ifndef Modint_hpp
#define Modint_hpp
#include <cassert>
#include <iostream>
template <int mod>
class modint
{
int val;
public:
constexpr modint() noexcept : val{0} {}
constexpr modint(long long x) noexcept : val((x %= mod) < 0 ? mod + x : x) {}
constexpr long long value() const noexcept { return val; }
constexpr modint operator++(int) noexcept { modint t = *this; return ++val, t; }
constexpr modint operator--(int) noexcept { modint t = *this; return --val, t; }
constexpr modint &operator++() noexcept { return ++val, *this; }
constexpr modint &operator--() noexcept { return --val, *this; }
constexpr modint operator-() const noexcept { return modint(-val); }
constexpr modint &operator+=(const modint &other) noexcept { return (val += other.val) < mod ? 0 : val -= mod, *this; }
constexpr modint &operator-=(const modint &other) noexcept { return (val += mod - other.val) < mod ? 0 : val -= mod, *this; }
constexpr modint &operator*=(const modint &other) noexcept { return val = (long long)val * other.val % mod, *this; }
constexpr modint &operator/=(const modint &other) noexcept { return *this *= inverse(other); }
constexpr modint operator+(const modint &other) const noexcept { return modint(*this) += other; }
constexpr modint operator-(const modint &other) const noexcept { return modint(*this) -= other; }
constexpr modint operator*(const modint &other) const noexcept { return modint(*this) *= other; }
constexpr modint operator/(const modint &other) const noexcept { return modint(*this) /= other; }
constexpr bool operator==(const modint &other) const noexcept { return val == other.val; }
constexpr bool operator!=(const modint &other) const noexcept { return val != other.val; }
constexpr bool operator!() const noexcept { return !val; }
friend constexpr modint operator+(long long x, modint y) noexcept { return modint(x) + y; }
friend constexpr modint operator-(long long x, modint y) noexcept { return modint(x) - y; }
friend constexpr modint operator*(long long x, modint y) noexcept { return modint(x) * y; }
friend constexpr modint operator/(long long x, modint y) noexcept { return modint(x) / y; }
static constexpr modint inverse(const modint &other) noexcept
{
assert(other != 0);
int a{mod}, b{other.val}, u{}, v{1}, t{};
while(b) t = a / b, a ^= b ^= (a -= t * b) ^= b, u ^= v ^= (u -= t * v) ^= v;
return {u};
}
static constexpr modint pow(modint other, long long e) noexcept
{
if(e < 0) e = e % (mod - 1) + mod - 1;
modint res{1};
while(e) { if(e & 1) res *= other; other *= other, e >>= 1; }
return res;
}
friend std::ostream &operator<<(std::ostream &os, const modint &other) noexcept { return os << other.val; }
friend std::istream &operator>>(std::istream &is, modint &other) noexcept { long long val; other = {(is >> val, val)}; return is; }
}; // class modint
template <>
class modint<2>
{
bool val;
public:
constexpr modint(bool x = false) noexcept : val{x} {}
constexpr modint(int x) noexcept : val(x & 1) {}
constexpr modint(long long x) noexcept : val(x & 1) {}
constexpr operator bool() const noexcept { return val; }
constexpr bool value() const noexcept { return val; }
constexpr modint &operator+=(const modint &other) noexcept { return val ^= other.val, *this; }
constexpr modint &operator-=(const modint &other) noexcept { return val ^= other.val, *this; }
constexpr modint &operator*=(const modint &other) noexcept { return val &= other.val, *this; }
constexpr modint &operator/=(const modint &other) noexcept { assert(other.val); return *this; }
constexpr modint operator!() const noexcept { return !val; }
constexpr modint operator-() const noexcept { return *this; }
constexpr modint operator+(const modint &other) const noexcept { return val != other.val; }
constexpr modint operator-(const modint &other) const noexcept { return val != other.val; }
constexpr modint operator*(const modint &other) const noexcept { return val && other.val; }
constexpr modint operator/(const modint &other) const noexcept { assert(other.val); return *this; }
constexpr bool operator==(const modint &other) const noexcept { return val == other.val; }
constexpr bool operator!=(const modint &other) const noexcept { return val != other.val; }
friend constexpr modint operator+(long long x, modint y) noexcept { return x & 1 ? !y : y; }
friend constexpr modint operator-(long long x, modint y) noexcept { return x & 1 ? !y : y; }
friend constexpr modint operator*(long long x, modint y) noexcept { return x & 1 ? y : modint<2>{0}; }
friend constexpr modint operator/(long long x, modint y) noexcept { assert(y.val); return x & 1 ? y : modint<2>{0}; }
friend std::ostream &operator<<(std::ostream &os, const modint &other) noexcept { return os << other.val; }
friend std::istream &operator>>(std::istream &is, modint &other) noexcept { long long val; other.val = (is >> val, val & 1); return is; }
}; // class modint specialization
#endif // Modint_hpp
#include <valarray>
namespace std
{
// hash
template <class T> size_t hash_combine(size_t seed, T const &key) { return seed ^ (hash<T>()(key) + 0x9e3779b9 + (seed << 6) + (seed >> 2)); }
template <class T, class U> struct hash<pair<T, U>> { size_t operator()(pair<T, U> const &pr) const { return hash_combine(hash_combine(0, pr.first), pr.second); } };
template <class tuple_t, size_t index = tuple_size<tuple_t>::value - 1> struct tuple_hash_calc { static size_t apply(size_t seed, tuple_t const &t) { return hash_combine(tuple_hash_calc<tuple_t, index - 1>::apply(seed, t), get<index>(t)); } };
template <class tuple_t> struct tuple_hash_calc<tuple_t, 0> { static size_t apply(size_t seed, tuple_t const &t) { return hash_combine(seed, get<0>(t)); } };
template <class... T> struct hash<tuple<T...>> { size_t operator()(tuple<T...> const &t) const { return tuple_hash_calc<tuple<T...>>::apply(0, t); } };
// iostream
template <class T, class U> istream &operator>>(istream &is, pair<T, U> &p) { return is >> p.first >> p.second; }
template <class T, class U> ostream &operator<<(ostream &os, const pair<T, U> &p) { return os << p.first << ' ' << p.second; }
template <class tuple_t, size_t index> struct tupleis { static istream &apply(istream &is, tuple_t &t) { tupleis<tuple_t, index - 1>::apply(is, t); return is >> get<index>(t); } };
template <class tuple_t> struct tupleis<tuple_t, SIZE_MAX> { static istream &apply(istream &is, tuple_t &t) { return is; } };
template <class... T> istream &operator>>(istream &is, tuple<T...> &t) { return tupleis<tuple<T...>, tuple_size<tuple<T...>>::value - 1>::apply(is, t); }
template <> istream &operator>>(istream &is, tuple<> &t) { return is; }
template <class tuple_t, size_t index> struct tupleos { static ostream &apply(ostream &os, const tuple_t &t) { tupleos<tuple_t, index - 1>::apply(os, t); return os << ' ' << get<index>(t); } };
template <class tuple_t> struct tupleos<tuple_t, 0> { static ostream &apply(ostream &os, const tuple_t &t) { return os << get<0>(t); } };
template <class... T> ostream &operator<<(ostream &os, const tuple<T...> &t) { return tupleos<tuple<T...>, tuple_size<tuple<T...>>::value - 1>::apply(os, t); }
template <> ostream &operator<<(ostream &os, const tuple<> &t) { return os; }
template <class Container, typename Value = typename Container::value_type, enable_if_t<!is_same<decay_t<Container>, string>::value, nullptr_t> = nullptr>
istream& operator>>(istream& is, Container &cont) { for(auto&& e : cont) is >> e; return is; }
template <class Container, typename Value = typename Container::value_type, enable_if_t<!is_same<decay_t<Container>, string>::value, nullptr_t> = nullptr>
ostream& operator<<(ostream& os, const Container &cont) { bool flag = 1; for(auto&& e : cont) flag ? flag = 0 : (os << ' ', 0), os << e; return os; }
} // namespace std
#ifndef Matrix_hpp
#define Matrix_hpp
#include <iostream>
#include <valarray>
#include <vector>
// Field must be a field.
template <class Field>
class matrix
{
size_t h, w;
using row_type = std::valarray<Field>;
using data_type = std::valarray<std::valarray<Field>>;
data_type data;
friend std::istream &operator>>(std::istream &is, matrix &x)
{
for(size_t i = 0; i != x.h; ++i)
{
for(size_t j = 0; j != x.w; ++j) is >> x[i][j];
}
return is;
}
friend std::ostream &operator<<(std::ostream &os, const matrix &x)
{
for(size_t i = 0; i != x.h; ++i)
{
if(i) os << "\n";
for(size_t j = 0; j != x.w; ++j) os << (j ? " " : "") << x.data[i][j];
os << " x.w: " << x.w;
}
return os;
}
friend matrix transpose(const matrix &x)
{
matrix res(x.w, x.h);
for(size_t i = 0; i != x.w; ++i)
for(size_t j = 0; j != x.h; ++j)
res[i][j] = x.data[j][i];
return res;
}
friend matrix pow(matrix x, long long n)
{
assert(x.is_square());
if(n < 0) x = inverse(x), n = -n;
matrix res{identity(x.h)};
while(n)
{
if(n & 1) res *= x;
x *= x, n >>= 1;
}
return res;
}
friend matrix inverse(const matrix &x)
{
assert(x.is_square());
matrix ext_x(x.h, x.h * 2), res(x.h);
for(size_t i = 0; i != x.h; ++i) ext_x.data[i][std::slice(0, x.h, 1)] = x.data[i], ext_x.data[i][i + x.h] = 1;
if(ext_x.row_canonicalize().size() != x.h) return matrix{0};
for(size_t i = 0; i != x.h; ++i) res[i] = ext_x.data[i][std::slice(x.h, x.h, 1)];
return res;
}
public:
explicit matrix(size_t _n = 0) : h(_n), w(_n) { resize(_n, _n);}
matrix(size_t _h, size_t _w) : h(_h), w(_w) { resize(_h, _w); }
matrix(const data_type &_data) : h(_data.size()), w(_data.size() ? _data[0].size() : 0), data(_data) {}
operator data_type() const { return data; }
size_t height() const { return h; }
size_t width() const { return w; }
bool is_square() const { return h == w; }
void resize(size_t h, size_t w, const Field val = Field(0)) { data.resize(h, std::valarray<Field>(val, w)); }
row_type &operator[](const size_t i) { assert(i < data.size()); return data[i]; }
static matrix identity(const size_t n)
{
data_type data(row_type(n), n);
for(size_t i = 0; i != n; ++i) data[i][i] = 1;
return data;
}
matrix operator-() const { return {-data}; }
matrix &operator+=(const matrix &other) { data += other.data; return *this; }
matrix &operator-=(const matrix &other) { data -= other.data; return *this; }
matrix &operator*=(matrix other)
{
other = transpose(other);
for(size_t i = 0; i != h; ++i)
{
const row_type copied{data[i]};
for(size_t j = 0; j != other.h; ++j) data[i][j] = (copied * other.data[j]).sum();
}
return *this;
}
matrix operator+(const matrix &x) const { return matrix(*this) += x; }
matrix operator-(const matrix &x) const { return matrix(*this) -= x; }
matrix operator*(const matrix &x) const { return matrix(*this) *= x; }
std::vector<size_t> row_canonicalize()
{
std::vector<size_t> pivots;
for(size_t j = 0, rank = 0; j != w; ++j)
{
bool piv = false;
for(size_t i = rank; i != h; ++i)
{
if(data[i][j] != 0)
{
const Field coef = data[i][j];
if(piv) data[i] -= data[rank] * coef;
else
{
swap(data[rank], data[i]);
data[rank] /= coef;
piv = true;
}
}
}
if(piv)
{
for(size_t k = 0; k != rank; ++k)
{
const Field coef = data[k][j];
data[k] -= data[rank] * coef;
}
++rank;
pivots.emplace_back(j);
}
}
return pivots;
}
Field determinant() const
{
assert(is_square());
data_type copied{data};
Field res{1};
for(size_t j = 0; j != w; ++j)
{
bool piv = false;
for(size_t i = j; i != h; ++i)
{
if(copied[i][j] != 0)
{
const Field coef = copied[i][j];
if(piv) copied[i] -= copied[j] * coef;
else
{
swap(copied[i], copied[j]);
if(i != j) res = -res;
res *= coef;
copied[j] /= coef;
piv = true;
}
}
}
if(!piv) return Field{0};
}
return res;
}
};
#endif
main()
{
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
using namespace std;
using mint=modint<(int)1e9+7>;
int n,a,b; cin>>a>>b>>n;
matrix<mint> c({
{a,b},
{1,0},
});
auto ans{pow(c,n)*transpose(matrix<mint>({{1,0}}))};
cout << ans[1][0] << "\n";
}