#381531 (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	a
提出日時	2019-09-20 22:06:48
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	5,708 bytes
コンパイル時間	1,976 ms
コンパイル使用メモリ	176,816 KB
実行使用メモリ	5,376 KB
最終ジャッジ日時	2024-09-14 17:44:25
合計ジャッジ時間	3,192 ms
ジャッジサーバーID （参考情報）	judge4 / judge5

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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 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	2 ms 5,376 KB
testcase_20	AC	2 ms 5,376 KB
testcase_21	AC	2 ms 5,376 KB
testcase_22	AC	2 ms 5,376 KB
testcase_23	AC	2 ms 5,376 KB
testcase_24	AC	2 ms 5,376 KB
testcase_25	AC	2 ms 5,376 KB
testcase_26	AC	2 ms 5,376 KB
testcase_27	AC	2 ms 5,376 KB
testcase_28	AC	2 ms 5,376 KB
testcase_29	AC	2 ms 5,376 KB
testcase_30	AC	2 ms 5,376 KB
testcase_31	AC	2 ms 5,376 KB
testcase_32	AC	2 ms 5,376 KB
testcase_33	AC	2 ms 5,376 KB
testcase_34	AC	2 ms 5,376 KB
testcase_35	AC	2 ms 5,376 KB
testcase_36	AC	2 ms 5,376 KB
testcase_37	AC	2 ms 5,376 KB
testcase_38	AC	2 ms 5,376 KB
testcase_39	AC	2 ms 5,376 KB
testcase_40	AC	2 ms 5,376 KB
testcase_41	AC	2 ms 5,376 KB

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ソースコード

raw source code

#include "bits/stdc++.h"

using namespace std;

using namespace std;

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

    Matrix(size_t n) : A(n, vector<T>(n, 0)) {}
    Matrix(size_t h, size_t w) : A(h, vector<T>(w, 0)) {}
    Matrix(vector<vector<T>> &X) : A(X) {}

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

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

    //ex)auto E = Matrix<int>::E(3);
    static Matrix E(int n)
    {
        Matrix e(n);
        for (int i = 0; i < n; i++)
            e[i][i] = 1;
        return e;
    }

    Matrix operator+(const Matrix &B) const
    {
        size_t h = this->height(), w = this->width();
        assert(h == B.height() && w == B.width());
        Matrix C(h, w);
        for (int i = 0; i < h; i++)
            for (int j = 0; j < w; j++)
            {
                C[i][j] = (*this)[i][j] + B[i][j];
            }
        return C;
    }

    Matrix operator-(const Matrix &B)
    {
        size_t h = this->height(), w = this->width();
        assert(h == B.height() && w == B.width());
        Matrix C(h, w);
        for (int i = 0; i < h; i++)
            for (int j = 0; j < w; j++)
            {
                C[i][j] = (*this)[i][j] - B[i][j];
            }
        return C;
    }

    Matrix operator*(const Matrix &B)
    {
        size_t h = this->height(), x = this->width(), w = B.width();
        assert(x == B.height());
        Matrix C(h, w);
        for (size_t i = 0; i < h; i++)
            for (size_t k = 0; k < x; k++)
                for (size_t j = 0; j < w; j++)
                {
                    C[i][j] += (*this)[i][k] * B[k][j];
                }
        return C;
    }

    Matrix &operator+=(const Matrix &B) { return (*this) = (*this) + B; }
    Matrix &operator-=(const Matrix &B) { return (*this) = (*this) - B; }
    Matrix &operator*=(const Matrix &B) { return (*this) = (*this) * B; }

    Matrix power(long k)
    {
        auto n = this->height();
        assert(k >= 0 && this->width() == n);
        auto R = Matrix<T>::E(n), C = Matrix(*this);
        while (k)
        {
            if (k & 1)
                R *= C;
            C *= C;
            k >>= 1;
        }
        return R;
    }

    friend ostream &operator<<(ostream &o, const Matrix &A)
    {
        for (int i = 0; i < A.height(); i++)
        {
            for (int j = 0; j < A.width(); j++)
            {
                o << A[i][j] << " ";
            }
            o << endl;
        }
        return o;
    }
};

template <int p>
struct Modint
{
    int value;

    Modint() : value(0) {}
    Modint(long x) : value(x >= 0 ? x % p : (p + x % p) % p) {}

    inline Modint &operator+=(const Modint &b)
    {
        if ((this->value += b.value) >= p)
            this->value -= p;
        return (*this);
    }
    inline Modint &operator-=(const Modint &b)
    {
        if ((this->value += p - b.value) >= p)
            this->value -= p;
        return (*this);
    }
    inline Modint &operator*=(const Modint &b)
    {
        this->value = (int)((1LL * this->value * b.value) % p);
        return (*this);
    }
    inline Modint &operator/=(const Modint &b)
    {
        (*this) *= b.inverse();
        return (*this);
    }

    Modint operator+(const Modint &b) const { return Modint(*this) += b; }
    Modint operator-(const Modint &b) const { return Modint(*this) -= b; }
    Modint operator*(const Modint &b) const { return Modint(*this) *= b; }
    Modint operator/(const Modint &b) const { return Modint(*this) /= b; }

    inline Modint &operator++(int) { return (*this) += 1; }
    inline Modint &operator--(int) { return (*this) -= 1; }

    inline bool operator==(const Modint &b) const
    {
        return this->value == b.value;
    }
    inline bool operator!=(const Modint &b) const
    {
        return this->value != b.value;
    }
    inline bool operator<(const Modint &b) const
    {
        return this->value < b.value;
    }
    inline bool operator<=(const Modint &b) const
    {
        return this->value <= b.value;
    }
    inline bool operator>(const Modint &b) const
    {
        return this->value > b.value;
    }
    inline bool operator>=(const Modint &b) const
    {
        return this->value >= b.value;
    }

    // requires that "this->value and p are co-prime"
    // a_i * v + a_(i+1) * p = r_i
    // r_i = r_(i+1) * q_(i+1) * r_(i+2)
    // q == 1 (i > 1)
    // reference: https://atcoder.jp/contests/agc026/submissions/2845729
    // (line:93)
    inline Modint inverse() const
    {
        assert(this->value != 0);
        int r0 = p, r1 = this->value, a0 = 0, a1 = 1;
        while (r1)
        {
            int q = r0 / r1;
            r0 -= q * r1;
            swap(r0, r1);
            a0 -= q * a1;
            swap(a0, a1);
        }
        return Modint(a0);
    }

    friend istream &operator>>(istream &is, Modint<p> &a)
    {
        long t;
        is >> t;
        a = Modint<p>(t);
        return is;
    }
    friend ostream &operator<<(ostream &os, const Modint<p> &a)
    {
        return os << a.value;
    }
};

/*
verified @ https://atcoder.jp/contests/abc034/submissions/4316971
*/

const int MOD = 1e9 + 7;

using Int = Modint<MOD>;

void solve()
{
    Int a, b, n;
    cin >> a >> b >> n;
    if (n.value == 0)
    {
        cout << 0 << endl;
        return;
    }
    Matrix<Int> v(2, 1), m(2, 2);
    v[0][0] = 1;
    m[0][0] = a;
    m[0][1] = b;
    m[1][0] = 1;
    m = m.power(n.value - 1);
    v = m * v;
    cout << v[0][0] << endl;
}

int main()
{
    solve();
    return 0;
}

yukicoder

結果

テストケース

ソースコード