結果

問題 No.891 隣接3項間の漸化式
コンテスト
ユーザー siro53
提出日時 2019-09-20 23:36:15
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 6,435 bytes
コンパイル時間 1,708 ms
コンパイル使用メモリ 172,824 KB
実行使用メモリ 5,376 KB
最終ジャッジ日時 2024-09-14 20:26:17
合計ジャッジ時間 2,908 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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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 # 

#include <bits/stdc++.h>
using namespace std;
template <class T>
inline bool chmax(T &a, T b)
{
    if (a < b)
    {
        a = b;
        return 1;
    }
    return 0;
}
template <class T>
inline bool chmin(T &a, T b)
{
    if (a > b)
    {
        a = b;
        return 1;
    }
    return 0;
}
typedef long long int ll;

#define ALL(v) (v).begin(), (v).end()
#define RALL(v) (v).rbegin(), (v).rend()
#define endl "\n"
const double EPS = 1e-7;
const int INF = 1 << 30;
const ll LLINF = 1LL << 60;
const double PI = acos(-1);
const int MOD = 1000000007;
const int dx[4] = {1, 0, -1, 0};
const int dy[4] = {0, 1, 0, -1};

//-------------------------------------

template <int mod>
struct ModInt
{
    int x;

    ModInt() : x(0) {}

    ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

    ModInt &operator+=(const ModInt &p)
    {
        if ((x += p.x) >= mod)
            x -= mod;
        return *this;
    }

    ModInt &operator-=(const ModInt &p)
    {
        if ((x += mod - p.x) >= mod)
            x -= mod;
        return *this;
    }

    ModInt &operator*=(const ModInt &p)
    {
        x = (int)(1LL * x * p.x % mod);
        return *this;
    }

    ModInt &operator/=(const ModInt &p)
    {
        *this *= p.inverse();
        return *this;
    }

    ModInt operator-() const { return ModInt(-x); }

    ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }

    ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }

    ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }

    ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }

    bool operator==(const ModInt &p) const { return x == p.x; }

    bool operator!=(const ModInt &p) const { return x != p.x; }

    ModInt inverse() const
    {
        int a = x, b = mod, u = 1, v = 0, t;
        while (b > 0)
        {
            t = a / b;
            swap(a -= t * b, b);
            swap(u -= t * v, v);
        }
        return ModInt(u);
    }

    ModInt pow(int64_t n) const
    {
        ModInt ret(1), mul(x);
        while (n > 0)
        {
            if (n & 1)
                ret *= mul;
            mul *= mul;
            n >>= 1;
        }
        return ret;
    }

    friend ostream &operator<<(ostream &os, const ModInt &p)
    {
        return os << p.x;
    }

    friend istream &operator>>(istream &is, ModInt &a)
    {
        int64_t t;
        is >> t;
        a = ModInt<mod>(t);
        return (is);
    }

    static int get_mod() { return mod; }
};

using modint = ModInt<MOD>;

template <class T>
struct Matrix
{
    vector<vector<T>> A;

    Matrix() {}

    Matrix(size_t n, size_t m) : A(n, vector<T>(m, 0)) {}

    Matrix(size_t n) : A(n, vector<T>(n, 0)){};

    size_t height() const
    {
        return (A.size());
    }

    size_t width() const
    {
        return (A[0].size());
    }

    inline const vector<T> &operator[](int k) const
    {
        return (A.at(k));
    }

    inline 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());
        vector<vector<T>> C(n, 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^=(long long k)
    {
        Matrix B = Matrix::I(height());
        while (k > 0)
        {
            if (k & 1)
                B *= *this;
            *this *= *this;
            k >>= 1LL;
        }
        A.swap(B.A);
        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);
    }

    Matrix operator^(const long long k) const
    {
        return (Matrix(*this) ^= k);
    }

    friend ostream &operator<<(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);
    }
};

int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);
    ll p,q,r;
    cin>>p>>q>>r;
    modint a(p),b(q);
    Matrix<modint> mat(2);
    mat[0][0]=a;
    mat[0][1]=b;
    mat[1][0]=1;
    mat[1][1]=0;
    mat^=(r);
    modint ans = mat[1][0];
    cout << ans << endl;
}
0