結果

問題 No.718 行列のできるフィボナッチ数列道場 (1)
ユーザー maimai
提出日時 2018-07-27 23:02:25
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 11,120 bytes
コンパイル時間 2,523 ms
コンパイル使用メモリ 217,980 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-07-05 04:32:55
合計ジャッジ時間 3,311 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge1
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
6,940 KB
testcase_05 AC 2 ms
6,940 KB
testcase_06 AC 2 ms
6,940 KB
testcase_07 AC 1 ms
6,940 KB
testcase_08 AC 2 ms
6,944 KB
testcase_09 AC 2 ms
6,940 KB
testcase_10 AC 1 ms
6,944 KB
testcase_11 AC 2 ms
6,944 KB
testcase_12 AC 2 ms
6,940 KB
testcase_13 AC 1 ms
6,940 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
6,944 KB
testcase_19 AC 2 ms
6,940 KB
testcase_20 AC 2 ms
6,940 KB
testcase_21 AC 2 ms
6,940 KB
testcase_22 AC 2 ms
6,940 KB
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 # 

#pragma GCC optimize ("O3")
#include "bits/stdc++.h"

using namespace std;
using ll = long long int;

#define debugos cout
#define debug(v) {printf("L%d %s > ",__LINE__,#v);debugos<<(v)<<endl;}
#define debugv(v) {printf("L%d %s > ",__LINE__,#v);for(auto e:(v)){debugos<<e<<" ";}debugos<<endl;}
#define debuga(m,w) {printf("L%d %s > ",__LINE__,#m);for(int x=0;x<(w);x++){debugos<<(m)[x]<<" ";}debugos<<endl;}
#define debugaa(m,h,w) {printf("L%d %s >\n",__LINE__,#m);for(int y=0;y<(h);y++){for(int x=0;x<(w);x++){debugos<<(m)[y][x]<<" ";}debugos<<endl;}}
#define ALL(v) (v).begin(),(v).end()
#define repeat(cnt,l) for(remove_reference<remove_const<decltype(l)>::type>::type cnt=0;(cnt)<(l);++(cnt))
#define rrepeat(cnt,l) for(auto cnt=(l)-1;0<=(cnt);--(cnt))
#define iterate(cnt,b,e) for(auto cnt=(b);(cnt)!=(e);++(cnt))
#define diterate(cnt,b,e) for(auto cnt=(b);(cnt)!=(e);--(cnt))
const ll MD = 1000000007ll; const long double PI = 3.1415926535897932384626433832795L;
inline void assert_call(bool assertion, function<void()> f) { if (!assertion) { cerr << "assertion fault:" << endl; f(); abort(); } }
template<typename T1, typename T2> inline ostream& operator <<(ostream &o, const pair<T1, T2> p) { o << '(' << p.first << ':' << p.second << ')'; return o; }
template<typename Vec> inline ostream& _ostream_vecprint(ostream& os, const Vec& a) {
    os << '['; for (const auto& e : a) os << ' ' << e << ' '; os << ']'; return os;
}
template<typename T> inline ostream& operator<<(ostream& o, const vector<T>& v) { return _ostream_vecprint(o, v); }
template<typename T, size_t S> inline ostream& operator<<(ostream& o, const array<T, S>& v) { return _ostream_vecprint(o, v); }
template<typename T> inline T& maxset(T& to, const T& val) { return to = max(to, val); }
template<typename T> inline T& minset(T& to, const T& val) { return to = min(to, val); }
void bye(string s, int code = 0) { cout << s << endl; exit(code); }
mt19937_64 randdev(8901016);
template<typename T> inline T rand(T l, T h) { return uniform_int_distribution<T>(l, h)(randdev); }
template<> inline double rand<double>(double l, double h) { return uniform_real_distribution<double>(l, h)(randdev); }
template<> inline float rand<float>(float l, float h) { return uniform_real_distribution<float>(l, h)(randdev); }

#if defined(_WIN32) || defined(_WIN64)
#define getchar_unlocked _getchar_nolock
#define putchar_unlocked _putchar_nolock
#elif defined(__GNUC__)
#else
#define getchar_unlocked getchar
#define putchar_unlocked putchar
#endif
namespace {
#define isvisiblechar(c) (0x21<=(c)&&(c)<=0x7E)
    class MaiScanner {
    public:
        template<typename T> void input_integer(T& var) {
            var = 0; T sign = 1;
            int cc = getchar_unlocked();
            for (; cc<'0' || '9'<cc; cc = getchar_unlocked())
                if (cc == '-') sign = -1;
            for (; '0' <= cc && cc <= '9'; cc = getchar_unlocked())
                var = (var << 3) + (var << 1) + cc - '0';
            var = var * sign;
        }
        inline int c() { return getchar_unlocked(); }
        inline MaiScanner& operator>>(int& var) { input_integer<int>(var); return *this; }
        inline MaiScanner& operator>>(long long& var) { input_integer<long long>(var); return *this; }
        inline MaiScanner& operator>>(string& var) {
            int cc = getchar_unlocked();
            for (; !isvisiblechar(cc); cc = getchar_unlocked());
            for (; isvisiblechar(cc); cc = getchar_unlocked())
                var.push_back(cc);
            return *this;
        }
        template<typename IT> void in(IT begin, IT end) { for (auto it = begin; it != end; ++it) *this >> *it; }
    };
    class MaiPrinter {
    public:
        template<typename T>
        void output_integer(T var) {
            if (var == 0) { putchar_unlocked('0'); return; }
            if (var < 0)
                putchar_unlocked('-'),
                var = -var;
            char stack[32]; int stack_p = 0;
            while (var)
                stack[stack_p++] = '0' + (var % 10),
                var /= 10;
            while (stack_p)
                putchar_unlocked(stack[--stack_p]);
        }
        inline MaiPrinter& operator<<(char c) { putchar_unlocked(c); return *this; }
        inline MaiPrinter& operator<<(int var) { output_integer<int>(var); return *this; }
        inline MaiPrinter& operator<<(long long var) { output_integer<long long>(var); return *this; }
        inline MaiPrinter& operator<<(char* str_p) { while (*str_p) putchar_unlocked(*(str_p++)); return *this; }
        inline MaiPrinter& operator<<(const string& str) {
            const char* p = str.c_str();
            const char* l = p + str.size();
            while (p < l) putchar_unlocked(*p++);
            return *this;
        }
        template<typename IT> void join(IT begin, IT end, char sep = ' ') { for (bool b = 0; begin != end; ++begin, b = 1) b ? *this << sep << *begin : *this << *begin; }
    };
}
MaiScanner scanner;
MaiPrinter printer;

template<typename T>
// typedef double T;
class Matrix {
public:
    size_t height_, width_;
    valarray<T> data_;
    Matrix(size_t height, size_t width) :height_(height), width_(width), data_(height*width) {}
    Matrix(size_t height, size_t width, const valarray<T>& data) :height_(height), width_(width), data_(data) {}

    inline T& operator()(size_t y, size_t x) { return data_[y*width_ + x]; }
    inline T operator() (size_t y, size_t x) const { return data_[y*width_ + x]; }
    inline T& at(size_t y, size_t x) { return data_[y*width_ + x]; }
    inline T at(size_t y, size_t x) const { return data_[y*width_ + x]; }
    inline void resize(size_t h, size_t w) { height_ = h; width_ = w; data_.resize(h*w); }
    inline void resize(size_t h, size_t w, T val) { height_ = h; width_ = w; data_.resize(h*w, val); }
    inline void fill(T val) { data_ = val; }
    Matrix<T>& setDiag(T val) { for (size_t i = 0, en = min(width_, height_); i < en; ++i)at(i, i) = val; return *this; }

    void print(ostream& os) {
        os << "- - -" << endl; //  << setprecision(3)
        for (size_t y = 0; y < height_; ++y) {
            for (size_t x = 0; x < width_; ++x) {
                os << setw(7) << at(y, x) << ' ';
            }os << endl;
        }
    }
    valarray<valarray<T>> to_valarray() const {
        valarray<valarray<T>> work(height_);
        for (size_t i = 0; i < height_; ++i) {
            auto &v = work[i]; v.resize(height_);
            for (size_t j = 0; j < width_; ++j)
                v[j] = at(i, j);
        } return work;
    }
    // mathematics
    Matrix<T> pow(long long);
    double det() const; T tr();
    Matrix<T>& transpose_self(); Matrix<T> transpose() const;
    struct LU {
        size_t size;
        vector<int> pivot;
        vector<T> elem;
    };
};

// IO
template<typename T> inline ostream& operator << (ostream& os, Matrix<T> mat) { mat.print(os); return os; }

// 掛け算
template<typename T> Matrix<T> multiply(const Matrix<T>& mat1, const Matrix<T>& mat2) {
    assert(mat1.width_ == mat2.height_);
    Matrix<T> result(mat1.height_, mat2.width_);
    for (size_t i = 0; i < mat1.height_; i++) {
        for (size_t j = 0; j < mat2.width_; j++) {
            for (size_t k = 0; k < mat1.width_; k++) {
                result(i, j) += mat1(i, k) * mat2(k, j);
            }
        }
    }
    return result;
}
template<typename T> valarray<T> multiply(const Matrix<T>& mat1, const valarray<T>& vec2) {
    assert(mat1.width_ == vec2.size());
    valarray<T> result(mat1.height_);
    for (size_t i = 0, j; i < mat1.height_; i++) {
        for (j = 0; j < mat1.width_; j++) {
            result[i] += mat1(i, j) * vec2[j];
        }
    }
    return result;
}
template<typename T> inline Matrix<T>& operator*=(Matrix<T>& mat1, Matrix<T>& mat2) { mat1 = multiply(mat1, mat2); return mat1; }
template<typename T> inline Matrix<T> operator*(Matrix<T>& mat1, Matrix<T>& mat2) { return multiply(mat1, mat2); }


// スカラー
template<typename T> inline Matrix<T>& operator+=(Matrix<T>& mat, T val) { mat.data_ += val; return mat; }
template<typename T> inline Matrix<T>& operator*=(Matrix<T>& mat, T val) { mat.data_ *= val; return mat; }
template<typename T> inline Matrix<T>& operator/=(Matrix<T>& mat, T val) { mat.data_ /= val; return mat; }
template<typename T> inline Matrix<T>& operator^=(Matrix<T>& mat, T val) { mat.data_ ^= val; return mat; }

// 行列
template<typename T> inline Matrix<T>& operator+=(Matrix<T>& mat1, Matrix<T>& mat2) { mat1.data_ += mat2.data_; return mat1; }
template<typename T> inline Matrix<T> operator+(Matrix<T>& mat1, Matrix<T>& mat2) { return Matrix<T>(mat1.height_, mat1.width_, mat1.data_ + mat2.data_); }


template<typename T> Matrix<T> Matrix<T>::pow(long long p) {
    assert(height_ == width_);
    Matrix<T> a = *this;
    Matrix<T> b(height_, height_); b.setDiag(1);

    while (0 < p) {
        if (p % 2) {
            b *= a;
        }
        a *= a; p /= 2;
    }
    return b;
}


class llmod {
private:
    ll val_;
    inline ll cut(ll v) const { return ((v%MOD) + MOD) % MOD; }
public:
    static const ll MOD = MD; // <= 

    llmod() : val_(0) {}
    llmod(ll num) :val_(cut(num)) {}
    llmod(const llmod& lm) : val_(lm.val_) {}

    inline operator ll() const { return val_; }
    inline ll operator *() const { return val_; }
    inline llmod& operator=(const llmod& lm) { val_ = lm.val_; return *this; }
    inline llmod& operator=(ll v) { val_ = cut(v); return *this; }

    inline llmod& operator+=(ll v) { val_ = cut(val_ + v); return *this; }
    inline llmod& operator+=(const llmod& l) { val_ = cut(val_ + l.val_); return *this; }
    inline llmod& operator-=(ll v) { val_ = cut(val_ - v); return *this; }
    inline llmod& operator-=(const llmod& l) { val_ = cut(val_ - l.val_); return *this; }
    inline llmod& operator*=(ll v) { val_ = cut(val_ * v); return *this; }
    inline llmod& operator*=(const llmod& l) { val_ = cut(val_ * l.val_); return *this; }
    inline llmod& operator++() { val_ = (val_ + 1) % MOD; return *this; }
    inline llmod operator++(int) { llmod t = *this; val_ = (val_ + 1) % MOD; return t; }
};
inline ostream& operator<<(ostream& os, const llmod& l) { os << *l; return os; }

inline llmod operator+(llmod t, const llmod& r) { return t += r; }
inline llmod operator-(llmod t, const llmod& r) { return t -= r; }
inline llmod operator*(llmod t, const llmod& r) { return t *= r; }



// MEMO : 逆元...powm(n,MD-2)
llmod pow(llmod x, ll p) {
    llmod y = 1;
    while (0 < p) {
        if (p % 2)
            y *= x;
        x *= x;
        p /= 2;
    }
    return y;
}

inline llmod& operator/=(llmod& l, const llmod& r) { return l *= pow(r, llmod::MOD - 2); }


int main() {

    ll N;
    cin >> N;

    if (N < 3) {
        vector<int> hoge = {0,1,2};
        cout << hoge[N] << endl;
        return 0;
    }

    Matrix<llmod> mat(4, 4, {
        1,1,2,0,
        1,0,0,0,
        1,0,1,0,
        1,1,2,1});

    auto mp = mat.pow(N-2);

    valarray<llmod> v = {1,1,1,2};
    auto w = multiply(mp, v);

    cout << *w[3] << endl;


    return 0;
}
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