number/matrix.yukicoder-1073.test.cpp

• View this file on GitHub
• Last update: 2021-08-30 04:35:37+09:00
• Problem: https://yukicoder.me/problems/no/1073

Depends on

• quotient ring / 剰余環 $\mathbb{Z}/n\mathbb{Z}$ (modulus/mint.hpp)
• modulus/modinv.hpp
• modulus/modpow.hpp
• number/matrix.hpp
• utils/macros.hpp

Code

#define PROBLEM "https://yukicoder.me/problems/no/1073"
#include "../number/matrix.hpp"
#include "../modulus/mint.hpp"
#include <iostream>
using namespace std;


constexpr int MOD = 1000000007;
mint<MOD> solve(int64_t n) {
    vector<vector<mint<MOD> > > f = {
        vector<mint<MOD> >{ 0, 0, 0, 0, 0, mint<MOD>(6).inv() },
        vector<mint<MOD> >{ 1, 0, 0, 0, 0, mint<MOD>(6).inv() },
        vector<mint<MOD> >{ 0, 1, 0, 0, 0, mint<MOD>(6).inv() },
        vector<mint<MOD> >{ 0, 0, 1, 0, 0, mint<MOD>(6).inv() },
        vector<mint<MOD> >{ 0, 0, 0, 1, 0, mint<MOD>(6).inv() },
        vector<mint<MOD> >{ 0, 0, 0, 0, 1, mint<MOD>(6).inv() },
    };
    vector<mint<MOD> > x = {
        0,
        0,
        0,
        0,
        0,
        1,
    };
    return (matpow(f, n) * x)[5];
}

int main() {
    int64_t n; cin >> n;
    auto ans = solve(n);
    cout << ans << endl;
    return 0;
}

#line 1 "number/matrix.yukicoder-1073.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1073"
#line 2 "number/matrix.hpp"
#include <cstdint>
#include <vector>
#line 2 "utils/macros.hpp"
#define REP(i, n) for (int i = 0; (i) < (int)(n); ++ (i))
#define REP3(i, m, n) for (int i = (m); (i) < (int)(n); ++ (i))
#define REP_R(i, n) for (int i = (int)(n) - 1; (i) >= 0; -- (i))
#define REP3R(i, m, n) for (int i = (int)(n) - 1; (i) >= (int)(m); -- (i))
#define ALL(x) std::begin(x), std::end(x)
#line 5 "number/matrix.hpp"

template <typename T>
std::vector<std::vector<T> > operator * (const std::vector<std::vector<T> >& a, const std::vector<std::vector<T> >& b) {
    int n = a.size();
    std::vector<std::vector<T> > c(n, std::vector<T>(n));
    REP (y, n) {
        REP (z, n) {
            REP (x, n) {
                c[y][x] += a[y][z] * b[z][x];
            }
        }
    }
    return c;
}

template <typename T>
std::vector<T> operator * (const std::vector<std::vector<T> >& a, const std::vector<T>& b) {
    int n = a.size();
    std::vector<T> c(n);
    REP (y, n) {
        REP (z, n) {
            c[y] += a[y][z] * b[z];
        }
    }
    return c;
}

template <typename T>
std::vector<std::vector<T> > unit_matrix(int n) {
    auto e = std::vector<std::vector<T> >(n, std::vector<T>(n));
    REP (i, n) {
        e[i][i] = 1;
    }
    return e;
}

template <typename T>
std::vector<std::vector<T> > zero_matrix(int n) {
    return std::vector<std::vector<T> >(n, std::vector<T>(n));
}

template <typename T>
std::vector<std::vector<T> > matpow(std::vector<std::vector<T> > x, int64_t y) {
    int n = x.size();
    auto z = unit_matrix<T>(n);
    for (int64_t i = 1; i <= y; i <<= 1) {
        if (y & i) {
            z = z * x;
        }
        x = x * x;
    }
    return z;
}
#line 3 "modulus/mint.hpp"
#include <iostream>
#line 2 "modulus/modpow.hpp"
#include <cassert>
#line 4 "modulus/modpow.hpp"

inline int32_t modpow(uint_fast64_t x, uint64_t k, int32_t MOD) {
    assert (/* 0 <= x and */ x < (uint_fast64_t)MOD);
    uint_fast64_t y = 1;
    for (; k; k >>= 1) {
        if (k & 1) (y *= x) %= MOD;
        (x *= x) %= MOD;
    }
    assert (/* 0 <= y and */ y < (uint_fast64_t)MOD);
    return y;
}
#line 2 "modulus/modinv.hpp"
#include <algorithm>
#line 5 "modulus/modinv.hpp"

inline int32_t modinv_nocheck(int32_t value, int32_t MOD) {
    assert (0 <= value and value < MOD);
    if (value == 0) return -1;
    int64_t a = value, b = MOD;
    int64_t x = 0, y = 1;
    for (int64_t u = 1, v = 0; a; ) {
        int64_t q = b / a;
        x -= q * u; std::swap(x, u);
        y -= q * v; std::swap(y, v);
        b -= q * a; std::swap(b, a);
    }
    if (not (value * x + MOD * y == b and b == 1)) return -1;
    if (x < 0) x += MOD;
    assert (0 <= x and x < MOD);
    return x;
}

inline int32_t modinv(int32_t x, int32_t MOD) {
    int32_t y = modinv_nocheck(x, MOD);
    assert (y != -1);
    return y;
}
#line 6 "modulus/mint.hpp"

/**
 * @brief quotient ring / 剰余環 $\mathbb{Z}/n\mathbb{Z}$
 */
template <int32_t MOD>
struct mint {
    int32_t value;
    mint() : value() {}
    mint(int64_t value_) : value(value_ < 0 ? value_ % MOD + MOD : value_ >= MOD ? value_ % MOD : value_) {}
    mint(int32_t value_, std::nullptr_t) : value(value_) {}
    explicit operator bool() const { return value; }
    inline mint<MOD> operator + (mint<MOD> other) const { return mint<MOD>(*this) += other; }
    inline mint<MOD> operator - (mint<MOD> other) const { return mint<MOD>(*this) -= other; }
    inline mint<MOD> operator * (mint<MOD> other) const { return mint<MOD>(*this) *= other; }
    inline mint<MOD> & operator += (mint<MOD> other) { this->value += other.value; if (this->value >= MOD) this->value -= MOD; return *this; }
    inline mint<MOD> & operator -= (mint<MOD> other) { this->value -= other.value; if (this->value <    0) this->value += MOD; return *this; }
    inline mint<MOD> & operator *= (mint<MOD> other) { this->value = (uint_fast64_t)this->value * other.value % MOD; return *this; }
    inline mint<MOD> operator - () const { return mint<MOD>(this->value ? MOD - this->value : 0, nullptr); }
    inline bool operator == (mint<MOD> other) const { return value == other.value; }
    inline bool operator != (mint<MOD> other) const { return value != other.value; }
    inline mint<MOD> pow(uint64_t k) const { return mint<MOD>(modpow(value, k, MOD), nullptr); }
    inline mint<MOD> inv() const { return mint<MOD>(modinv(value, MOD), nullptr); }
    inline mint<MOD> operator / (mint<MOD> other) const { return *this * other.inv(); }
    inline mint<MOD> & operator /= (mint<MOD> other) { return *this *= other.inv(); }
};
template <int32_t MOD> mint<MOD> operator + (int64_t value, mint<MOD> n) { return mint<MOD>(value) + n; }
template <int32_t MOD> mint<MOD> operator - (int64_t value, mint<MOD> n) { return mint<MOD>(value) - n; }
template <int32_t MOD> mint<MOD> operator * (int64_t value, mint<MOD> n) { return mint<MOD>(value) * n; }
template <int32_t MOD> mint<MOD> operator / (int64_t value, mint<MOD> n) { return mint<MOD>(value) / n; }
template <int32_t MOD> std::istream & operator >> (std::istream & in, mint<MOD> & n) { int64_t value; in >> value; n = value; return in; }
template <int32_t MOD> std::ostream & operator << (std::ostream & out, mint<MOD> n) { return out << n.value; }
#line 5 "number/matrix.yukicoder-1073.test.cpp"
using namespace std;


constexpr int MOD = 1000000007;
mint<MOD> solve(int64_t n) {
    vector<vector<mint<MOD> > > f = {
        vector<mint<MOD> >{ 0, 0, 0, 0, 0, mint<MOD>(6).inv() },
        vector<mint<MOD> >{ 1, 0, 0, 0, 0, mint<MOD>(6).inv() },
        vector<mint<MOD> >{ 0, 1, 0, 0, 0, mint<MOD>(6).inv() },
        vector<mint<MOD> >{ 0, 0, 1, 0, 0, mint<MOD>(6).inv() },
        vector<mint<MOD> >{ 0, 0, 0, 1, 0, mint<MOD>(6).inv() },
        vector<mint<MOD> >{ 0, 0, 0, 0, 1, mint<MOD>(6).inv() },
    };
    vector<mint<MOD> > x = {
        0,
        0,
        0,
        0,
        0,
        1,
    };
    return (matpow(f, n) * x)[5];
}

int main() {
    int64_t n; cin >> n;
    auto ans = solve(n);
    cout << ans << endl;
    return 0;
}

Back to top page