#562945 (C++14) No.720 行列のできるフィボナッチ数列道場 (2)

• 問題: No.720 行列のできるフィボナッチ数列道場 (2)
• ユーザー: 🍮かんプリン
• 提出日時: 2020-10-06 16:27:27
• 言語: C++14 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 2 ms / 2,000 ms
• コード長: 6,166 bytes
• コンパイル時間: 1,685 ms
• コンパイル使用メモリ: 175,344 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-07-20 02:06:39
• 合計ジャッジ時間: 2,369 ms
• ジャッジサーバーID （参考情報）: judge4 / judge3

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	2 ms; 5,376 KB
testcase_05	AC	2 ms; 5,376 KB
testcase_06	AC	2 ms; 5,376 KB
testcase_07	AC	2 ms; 5,376 KB
testcase_08	AC	2 ms; 5,376 KB
testcase_09	AC	2 ms; 5,376 KB
testcase_10	AC	2 ms; 5,376 KB
testcase_11	AC	2 ms; 5,376 KB
testcase_12	AC	2 ms; 5,376 KB
testcase_13	AC	2 ms; 5,376 KB
testcase_14	AC	2 ms; 5,376 KB
testcase_15	AC	2 ms; 5,376 KB
testcase_16	AC	2 ms; 5,376 KB
testcase_17	AC	2 ms; 5,376 KB
testcase_18	AC	2 ms; 5,376 KB
testcase_19	AC	1 ms; 5,376 KB
testcase_20	AC	2 ms; 5,376 KB
testcase_21	AC	1 ms; 5,376 KB
testcase_22	AC	1 ms; 5,376 KB

ソースコード

/**
 *   @FileName	a.cpp
 *   @Author	kanpurin
 *   @Created	2020.10.06 16:27:22
**/

#include "bits/stdc++.h" 
using namespace std; 
typedef long long ll;

template< int MOD >
struct mint {
public:
    long long x;
    mint(long long x = 0) :x((x%MOD+MOD)%MOD) {}
    mint(std::string &s) {
        long long z = 0;
        for (int i = 0; i < s.size(); i++) {
            z *= 10;
            z += s[i] - '0';
            z %= MOD;
        }
        this->x = z;
    }
    mint& operator+=(const mint &a) {
        if ((x += a.x) >= MOD) x -= MOD;
        return *this;
    }
    mint& operator-=(const mint &a) {
        if ((x += MOD - a.x) >= MOD) x -= MOD;
        return *this;
    }
    mint& operator*=(const mint &a) {
        (x *= a.x) %= MOD;
        return *this;
    }
    mint& operator/=(const mint &a) {
        long long n = MOD - 2;
        mint u = 1, b = a;
        while (n > 0) {
            if (n & 1) {
                u *= b;
            }
            b *= b;
            n >>= 1;
        }
        return *this *= u;
    }
    mint operator+(const mint &a) const {
        mint res(*this);
        return res += a;
    }
    mint operator-() const {return mint() -= *this; }
    mint operator-(const mint &a) const {
        mint res(*this);
        return res -= a;
    }
    mint operator*(const mint &a) const {
        mint res(*this);
        return res *= a;
    }
    mint operator/(const mint &a) const {
        mint res(*this);
        return res /= a;
    }
    friend std::ostream& operator<<(std::ostream &os, const mint &n) {
        return os << n.x;
    }
    friend std::istream &operator>>(std::istream &is, mint &n) {
        long long x;
        is >> x;
        n = mint(x);
        return is;
    }
    bool operator==(const mint &a) const {
        return this->x == a.x;
    }
    mint pow(long long k) const {
        mint ret = 1;
        mint p = this->x;
        while (k > 0) {
            if (k & 1) {
                ret *= p;
            }
            p *= p;
            k >>= 1;
        }
        return ret;
    }
};
constexpr int MOD = 1e9 + 7;
template< class T >
struct Matrix {
    std::vector< std::vector< T > > A;
    Matrix() {}
    Matrix(size_t n, size_t m) : A(n, std::vector< T >(m, 0)) {}
    Matrix(size_t n) : A(n, std::vector< T >(n, 0)) {};
    size_t height() const {
        return (A.size());
    }
    size_t width() const {
        return (A[0].size());
    }
    inline const std::vector< T > &operator[](int k) const {
        return (A.at(k));
    }
    inline std::vector< T > &operator[](int k) {
        return (A.at(k));
    }
    static Matrix I(size_t n) {
        Matrix mat(n);
        for (int i = 0; i < n; i++) mat[i][i] = 1;
        return (mat);
    }
    Matrix &operator+=(const Matrix &B) {
        size_t n = height(), m = width();
        assert(n == B.height() && m == B.width());
        for (int i = 0; i < n; i++)
            for (int j = 0; j < m; j++)
                (*this)[i][j] += B[i][j];
        return (*this);
    }
    Matrix &operator-=(const Matrix &B) {
        size_t n = height(), m = width();
        assert(n == B.height() && m == B.width());
        for (int i = 0; i < n; i++)
            for (int j = 0; j < m; j++)
                (*this)[i][j] -= B[i][j];
        return (*this);
    }
    Matrix &operator*=(const Matrix &B) {
        size_t n = height(), m = B.width(), p = width();
        assert(p == B.height());
        std::vector< std::vector< T > > C(n, std::vector< T >(m, 0));
        for (int i = 0; i < n; i++)
            for (int j = 0; j < m; j++)
                for (int k = 0; k < p; k++)
                    C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]);
        A.swap(C);
        return (*this);
    }
    Matrix operator+(const Matrix &B) const {
        return (Matrix(*this) += B);
    }
    Matrix operator-(const Matrix &B) const {
        return (Matrix(*this) -= B);
    }
    Matrix operator*(const Matrix &B) const {
        return (Matrix(*this) *= B);
    }
    bool operator==(const Matrix &B) const {
        assert(this->A.size() == B.A.size() && this->A[0].size() == B.A[0].size());
        int n = this->A.size();
        int m = this->A[0].size();
        for (int i = 0; i < n; i++)
            for (int j = 0; j < m; j++)
                if (this->A[i][j] != B.A[i][j]) return false;
        return true;
    }
    bool operator!=(const Matrix &B) const {
        return !(*this == B);
    }
    friend std::ostream &operator<<(std::ostream &os, Matrix &p) {
        size_t n = p.height(), m = p.width();
        for (int i = 0; i < n; i++) {
            os << "[";
            for (int j = 0; j < m; j++) {
                os << p[i][j] << (j + 1 == m ? "]\n" : ",");
            }
        }
        return (os);
    }
    
    T determinant() {
        Matrix B(*this);
        assert(width() == height());
        T ret = 1;
        for (int i = 0; i < width(); i++) {
            int idx = -1;
            for (int j = i; j < width(); j++) {
                if (B[j][i] != 0) idx = j;
            }
            if (idx == -1) return (0);
            if (i != idx) {
                ret *= -1;
                swap(B[i], B[idx]);
            }
            ret *= B[i][i];
            T vv = B[i][i];
            for (int j = 0; j < width(); j++) {
                B[i][j] /= vv;
            }
            for (int j = i + 1; j < width(); j++) {
                T a = B[j][i];
                for (int k = 0; k < width(); k++) {
                    B[j][k] -= B[i][k] * a;
                }
            }
        }
        return (ret);
    }
    
    
    Matrix pow(ll k) const {
        auto res = I(A.size());
        auto M = *this;
        while (k > 0) {
            if (k & 1) {
                res *= M;
            }
            M *= M;
            k >>= 1;
        }
        return res;
    }
};
int main() {
    ll n,m;cin >> n >> m;
    Matrix<mint<MOD>> mat1(3),mat2(3);
    mat1[0][0] = mat1[1][1] = mat1[2][0] = mat1[2][2] = 1;
    mat2[0][0] = mat2[0][1] = mat2[1][0] = mat2[2][2] = 1;
    mat1 = (mat1 * mat2.pow(m)).pow(n);
    cout << mat1[2][1] << endl;
    return 0;
}