#418016 (C++14) No.891 隣接3項間の漸化式

提出ソース

結果

問題	No.891 隣接3項間の漸化式
ユーザー	jell
提出日時	2020-01-16 22:12:06
言語	C++14 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	3 ms / 2,000 ms
コード長	14,050 bytes
コンパイル時間	1,326 ms
コンパイル使用メモリ	94,484 KB
実行使用メモリ	6,944 KB
最終ジャッジ日時	2024-06-24 09:39:30
合計ジャッジ時間	2,204 ms
ジャッジサーバーID （参考情報）	judge1 / judge5

このコードへのチャレンジ
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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	2 ms 6,812 KB
testcase_01	AC	2 ms 6,940 KB
testcase_02	AC	2 ms 6,940 KB
testcase_03	AC	2 ms 6,940 KB
testcase_04	AC	2 ms 6,944 KB
testcase_05	AC	2 ms 6,940 KB
testcase_06	AC	2 ms 6,940 KB
testcase_07	AC	2 ms 6,944 KB
testcase_08	AC	2 ms 6,944 KB
testcase_09	AC	2 ms 6,944 KB
testcase_10	AC	2 ms 6,944 KB
testcase_11	AC	3 ms 6,944 KB
testcase_12	AC	2 ms 6,940 KB
testcase_13	AC	2 ms 6,944 KB
testcase_14	AC	2 ms 6,940 KB
testcase_15	AC	2 ms 6,940 KB
testcase_16	AC	2 ms 6,940 KB
testcase_17	AC	2 ms 6,940 KB
testcase_18	AC	2 ms 6,940 KB
testcase_19	AC	2 ms 6,940 KB
testcase_20	AC	2 ms 6,944 KB
testcase_21	AC	2 ms 6,944 KB
testcase_22	AC	2 ms 6,940 KB
testcase_23	AC	1 ms 6,944 KB
testcase_24	AC	2 ms 6,944 KB
testcase_25	AC	2 ms 6,944 KB
testcase_26	AC	2 ms 6,940 KB
testcase_27	AC	2 ms 6,940 KB
testcase_28	AC	2 ms 6,940 KB
testcase_29	AC	2 ms 6,940 KB
testcase_30	AC	2 ms 6,944 KB
testcase_31	AC	2 ms 6,944 KB
testcase_32	AC	2 ms 6,940 KB
testcase_33	AC	2 ms 6,940 KB
testcase_34	AC	2 ms 6,940 KB
testcase_35	AC	2 ms 6,944 KB
testcase_36	AC	2 ms 6,940 KB
testcase_37	AC	2 ms 6,940 KB
testcase_38	AC	2 ms 6,944 KB
testcase_39	AC	2 ms 6,940 KB
testcase_40	AC	2 ms 6,944 KB
testcase_41	AC	2 ms 6,944 KB

権限があれば一括ダウンロードができます

コンパイルメッセージ

main.cpp:279:1: warning: ISO C++ forbids declaration of 'main' with no type [-Wreturn-type]
  279 | main()
      | ^~~~

ソースコード

raw source code

#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];
        }
        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)
        {
            row_type row_copy{data[i]};
            for(size_t j = 0; j != other.h; ++j) data[i][j] = (row_copy * 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)
                {
                    if(piv)
                    {
                        const Field r = data[i][j];
                        data[i] -= data[rank] * r;
                        // for(size_t k = j; k != w; ++k) data[i][k] -= data[rank][k] * r;
                    }
                    else
                    {
                        swap(data[rank], data[i]);
                        Field r = data[rank][j];
                        data[rank] /= r;
                        // for(size_t k = j; k != w; ++k) data[rank][k] /= r;
                        for(size_t k = 0; k != rank; ++k)
                        {
                            r = data[k][j];
                            data[k] -= data[rank] * r;
                            // for(size_t l = j; l != w; ++l) data[k][l] -= data[rank][l] * r;
                        }
                        piv = true;
                    }
                }
            }
            if(piv)
            {
                ++rank;
                pivots.emplace_back(j);
            }
        }
        return pivots;
    }
    Field determinant() const
    {
        matrix<Field> x(*this);
        assert(is_square());
        size_t n = height();
        Field res(1);
        for(size_t j = 0; j < n; ++j)
        {
            bool piv = false;
            for(size_t i = j; i < n; ++i)
            {
                if(x[i][j] != Field{})
                {
                    if(piv)
                    {
                        const Field r = -x[i][j];
                        for(size_t k = j; k < n; ++k) x[i][k] += x[j][k] * r;
                    }
                    else
                    {
                        swap(x[i], x[j]);
                        if(i != j) res = -res;
                        const Field r = x[j][j];
                        res *= r;
                        for(size_t k = j; k < n; ++k) x[j][k] /= r;
                        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";
}

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