#524185 (C++17) No.658 テトラナッチ数列 Hard

• 問題: No.658 テトラナッチ数列 Hard
• ユーザー: Mister
• 提出日時: 2020-08-04 01:31:19
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 64 ms / 2,000 ms
• コード長: 5,942 bytes
• コンパイル時間: 957 ms
• コンパイル使用メモリ: 76,008 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-09-13 20:31:44
• 合計ジャッジ時間: 1,582 ms
• ジャッジサーバーID （参考情報）: judge5 / judge1

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 5,248 KB
testcase_01	AC	2 ms; 5,376 KB
testcase_02	AC	2 ms; 5,376 KB
testcase_03	AC	2 ms; 5,376 KB
testcase_04	AC	24 ms; 5,376 KB
testcase_05	AC	27 ms; 5,376 KB
testcase_06	AC	34 ms; 5,376 KB
testcase_07	AC	37 ms; 5,376 KB
testcase_08	AC	43 ms; 5,376 KB
testcase_09	AC	64 ms; 5,376 KB
testcase_10	AC	63 ms; 5,376 KB

ソースコード

#include <iostream>
#include <array>
#include <vector>

template <int MOD>
struct ModInt {
    using lint = long long;
    int val;

    // constructor
    ModInt(lint v = 0) : val(v % MOD) {
        if (val < 0) val += MOD;
    };

    // unary operator
    ModInt operator+() const { return ModInt(val); }
    ModInt operator-() const { return ModInt(MOD - val); }
    ModInt inv() const { return this->pow(MOD - 2); }

    // arithmetic
    ModInt operator+(const ModInt& x) const { return ModInt(*this) += x; }
    ModInt operator-(const ModInt& x) const { return ModInt(*this) -= x; }
    ModInt operator*(const ModInt& x) const { return ModInt(*this) *= x; }
    ModInt operator/(const ModInt& x) const { return ModInt(*this) /= x; }
    ModInt pow(lint n) const {
        auto x = ModInt(1);
        auto b = *this;
        while (n > 0) {
            if (n & 1) x *= b;
            n >>= 1;
            b *= b;
        }
        return x;
    }

    // compound assignment
    ModInt& operator+=(const ModInt& x) {
        if ((val += x.val) >= MOD) val -= MOD;
        return *this;
    }
    ModInt& operator-=(const ModInt& x) {
        if ((val -= x.val) < 0) val += MOD;
        return *this;
    }
    ModInt& operator*=(const ModInt& x) {
        val = lint(val) * x.val % MOD;
        return *this;
    }
    ModInt& operator/=(const ModInt& x) { return *this *= x.inv(); }

    // compare
    bool operator==(const ModInt& b) const { return val == b.val; }
    bool operator!=(const ModInt& b) const { return val != b.val; }
    bool operator<(const ModInt& b) const { return val < b.val; }
    bool operator<=(const ModInt& b) const { return val <= b.val; }
    bool operator>(const ModInt& b) const { return val > b.val; }
    bool operator>=(const ModInt& b) const { return val >= b.val; }

    // I/O
    friend std::istream& operator>>(std::istream& is, ModInt& x) noexcept { return is >> x.val; }
    friend std::ostream& operator<<(std::ostream& os, const ModInt& x) noexcept { return os << x.val; }
};

template <class T, int D>
struct Vector {
    using V = std::array<T, D>;

    V vec;

    // constructor
    Vector() = default;
    Vector(T val) { vec.fill(val); }

    // getter
    T& operator[](int i) { return vec[i]; }
    T operator[](int i) const { return vec[i]; }
    typename V::iterator begin() { return vec.begin(); }
    typename V::iterator end() { return vec.end(); }

    // arithmetic
    Vector operator+(const Vector& v) const { return Matrix(*this) += v; }
    Vector operator-(const Vector& v) const { return Matrix(*this) -= v; }
    T operator*(const Vector& v) const {
        T ret(0);
        for (int i = 0; i < D; ++i) ret += vec[i] * v[i];
        return ret;
    }

    // compound assignment
    Vector& operator+=(const Vector& v) {
        for (int i = 0; i < D; ++i) vec[i] += v[i];
        return *this;
    }
    Vector& operator-=(const Vector& v) {
        for (int i = 0; i < D; ++i) vec[i] -= v[i];
        return *this;
    }
};

template <class T, int D>
struct Matrix {
    using M = std::array<std::array<T, D>, D>;

    M mat;

    // constructor
    Matrix() = default;
    Matrix(T val) {
        for (auto& v : mat) v.fill(val);
    }

    static Matrix id() {
        Matrix m;
        for (int i = 0; i < D; ++i) m[i][i] = 1;
        return m;
    }

    // getter
    std::array<T, D>& operator[](int i) { return mat[i]; }
    std::array<T, D> operator[](int i) const { return mat[i]; }
    typename M::iterator begin() { return mat.begin(); }
    typename M::iterator end() { return mat.end(); }

    // arithmetic
    Matrix operator+(const Matrix& m) const { return Matrix(*this) += m; }
    Matrix operator-(const Matrix& m) const { return Matrix(*this) -= m; }
    Matrix operator*(const Matrix& m) const { return Matrix(*this) *= m; }

    template <class U>
    Matrix pow(U k) {
        Matrix ret = id();
        Matrix a = *this;

        while (k > 0) {
            if (k & 1) ret *= a;
            a *= a;
            k >>= 1;
        }
        return ret;
    }

    // compound assignment
    Matrix& operator+=(const Matrix& m) {
        for (int i = 0; i < D; ++i) {
            for (int j = 0; j < D; ++j) {
                mat[i][j] += m[i][j];
            }
        }
        return *this;
    }
    Matrix& operator-=(const Matrix& m) {
        for (int i = 0; i < D; ++i) {
            for (int j = 0; j < D; ++j) {
                mat[i][j] -= m[i][j];
            }
        }
        return *this;
    }
    Matrix& operator*=(const Matrix& m) {
        M nmat;
        for (int i = 0; i < D; ++i) {
            for (int j = 0; j < D; ++j) {
                for (int k = 0; k < D; ++k) {
                    nmat[i][j] += mat[i][k] * m[k][j];
                }
            }
        }
        mat = nmat;
        return *this;
    }

    // arithmetic with vector
    using Vec = Vector<T, D>;
    Vec operator*(const Vec& v) {
        Vec ret;
        for (int i = 0; i < D; ++i) {
            for (int j = 0; j < D; ++j) {
                ret[i] += mat[i][j] * v[j];
            }
        }
        return ret;
    }
};

constexpr int MOD = 17;
using mint = ModInt<MOD>;
using lint = long long;
using Mat = Matrix<mint, 4>;
using Vec = Vector<mint, 4>;

void solve() {
    std::vector<Mat> ms(60);
    {
        auto& m = ms[0];
        for (int i = 0; i < 3; ++i) m[i][i + 1] = 1;
        for (int i = 0; i < 4; ++i) m[3][i] = 1;

        for (int i = 1; i < 60; ++i) {
            ms[i] = ms[i - 1] * ms[i - 1];
        }
    }

    Vec v;
    v[3] = 1;

    int q;
    std::cin >> q;
    while (q--) {
        lint n;
        std::cin >> n;
        --n;

        Mat m = Mat::id();
        for (int i = 0; i < 60; ++i) {
            if ((n >> i) & 1) m *= ms[i];
        }

        std::cout << (m * v)[0] << "\n";
    }
}

int main() {
    std::cin.tie(nullptr);
    std::ios::sync_with_stdio(false);

    solve();

    return 0;
}