#382064 (C++14) No.891 隣接3項間の漸化式

• 問題: No.891 隣接3項間の漸化式
• ユーザー: polylogK
• 提出日時: 2019-09-21 14:48:34
• 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: 5,305 bytes
• コンパイル時間: 1,830 ms
• コンパイル使用メモリ: 176,768 KB
• 実行使用メモリ: 4,348 KB
• 最終ジャッジ日時: 2023-10-19 02:34:09
• 合計ジャッジ時間: 3,202 ms
• ジャッジサーバーID （参考情報）: judge15 / judge13

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 4,348 KB
testcase_01	AC	2 ms; 4,348 KB
testcase_02	AC	2 ms; 4,348 KB
testcase_03	AC	2 ms; 4,348 KB
testcase_04	AC	2 ms; 4,348 KB
testcase_05	AC	2 ms; 4,348 KB
testcase_06	AC	2 ms; 4,348 KB
testcase_07	AC	2 ms; 4,348 KB
testcase_08	AC	2 ms; 4,348 KB
testcase_09	AC	2 ms; 4,348 KB
testcase_10	AC	2 ms; 4,348 KB
testcase_11	AC	2 ms; 4,348 KB
testcase_12	AC	2 ms; 4,348 KB
testcase_13	AC	2 ms; 4,348 KB
testcase_14	AC	2 ms; 4,348 KB
testcase_15	AC	2 ms; 4,348 KB
testcase_16	AC	2 ms; 4,348 KB
testcase_17	AC	2 ms; 4,348 KB
testcase_18	AC	2 ms; 4,348 KB
testcase_19	AC	2 ms; 4,348 KB
testcase_20	AC	2 ms; 4,348 KB
testcase_21	AC	2 ms; 4,348 KB
testcase_22	AC	2 ms; 4,348 KB
testcase_23	AC	2 ms; 4,348 KB
testcase_24	AC	2 ms; 4,348 KB
testcase_25	AC	2 ms; 4,348 KB
testcase_26	AC	2 ms; 4,348 KB
testcase_27	AC	2 ms; 4,348 KB
testcase_28	AC	2 ms; 4,348 KB
testcase_29	AC	2 ms; 4,348 KB
testcase_30	AC	2 ms; 4,348 KB
testcase_31	AC	2 ms; 4,348 KB
testcase_32	AC	2 ms; 4,348 KB
testcase_33	AC	2 ms; 4,348 KB
testcase_34	AC	2 ms; 4,348 KB
testcase_35	AC	2 ms; 4,348 KB
testcase_36	AC	2 ms; 4,348 KB
testcase_37	AC	2 ms; 4,348 KB
testcase_38	AC	2 ms; 4,348 KB
testcase_39	AC	2 ms; 4,348 KB
testcase_40	AC	2 ms; 4,348 KB
testcase_41	AC	2 ms; 4,348 KB

ソースコード

#include <bits/stdc++.h>
using namespace std::literals::string_literals;
using i64 = long long;
using std::cout;
using std::endl;
using std::cin;

template<typename T>
std::vector<T> make_v(size_t a){return std::vector<T>(a);}

template<typename T,typename... Ts>
auto make_v(size_t a,Ts... ts){
  return std::vector<decltype(make_v<T>(ts...))>(a,make_v<T>(ts...));
}

using namespace std;
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<(int)(1e9 + 7)>;

template<class T>
class square_matrix {
	using value_type = T;
	using i64 = int64_t;
	
	std::vector<std::vector<value_type>> data;

	public:
	square_matrix() {}
	square_matrix(const size_t & n) : data(n, std::vector<value_type>(n, T())) {}
	
	static const square_matrix E(const size_t & n) {
		square_matrix e(n);
		for(size_t i = 0; i < n; i++) e[i][i] = 1;
		return e;
	}
	static const square_matrix O(const size_t & n) {
		return square_matrix(n);
	}
	
	const size_t height() const {
		return data.size();
	}
	const size_t width() const {
		return data.size();
	}
	const T determinant() const {
		square_matrix B(*this);
		T ret = 1;
		for(int i = 0; i < width(); i++) {
			int ind = -1;
			for(int j = i; j < width(); j++) {
				if(B[j][i] == 0) continue;
				ind = j;
			}
			if(ind == -1) return 0;
			if(i != ind) {
				ret *= -1;
				std::swap(B[i], B[ind]);
			}

			ret *= B[i][i];
			for(int j = 0; j < width(); j++) B[i][j] /= B[i][i];
			for(int j = i + 1; j < width(); j++)
				for(int k = 0; k < width(); k++)
					B[j][k] -= B[i][k] * B[j][i];
		}
		return ret;
	}
	
	const std::vector<value_type> & operator[](const size_t & k) const {
		return data.at(k);
	}
	std::vector<value_type> & operator[](const size_t & k) {
		return data.at(k);
	}
	square_matrix & operator+=(const square_matrix & B) {
		assert(height() == B.height());
		for(int i = 0; i < height(); i++)
			for(int j = 0; j < width(); j++)
				(*this)[i][j] += B[i][j];
		return (*this);
	}
	square_matrix & operator-=(const square_matrix & B) {
		assert(height() == B.height());
		for(int i = 0; i < height(); i++)
			for(int j = 0; j < width(); j++)
				(*this)[i][j] -= B[i][j];
		return (*this);
	}
	square_matrix & operator*=(const square_matrix & B) {
		assert(height() == B.height());
		auto C = square_matrix::O(height());
		for(int i = 0; i < height(); i++)
			for(int j = 0; j < width(); j++)
				for(int k = 0; k < height(); k++)
					C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]);
		return (*this) = C;
	}
	square_matrix & operator^=(i64 k) {
		auto B = square_matrix::E(height());
		while(k) {
			if(k & 1) B *= (*this);
			(*this) *= (*this);
			k >>= 1;
		}
		return (*this) = B;
	}
	square_matrix & operator=(const square_matrix & B) {
		(*this).data = B.data;
		return (*this);
	}
	const square_matrix operator+(const square_matrix & B) const {
		return (square_matrix(*this) += B);
	}
	const square_matrix operator-(const square_matrix & B) const {
		return (square_matrix(*this) -= B);
	}
	const square_matrix operator*(const square_matrix & B) const {
		return (square_matrix(*this) *= B);
	}
	const square_matrix operator^(const i64 & k) const {
		return (square_matrix(*this) ^= k);
	}
	const bool operator==(const square_matrix & B) const {
		return (data == B.data);
	}
	friend std::ostream & operator<<(std::ostream & os, square_matrix & p) {
		for(int i = 0; i < height(); i++) {
			os << "[";
			for(int j = 0; j < width(); j++) {
				os << p[i][j] << (j + 1 == width() ? "]\n" : ", ");
			}
		}
		return os;
	}
};

int main() {
	int a, b, n; scanf("%d%d%d", &a, &b, &n);
	if(n == 0) {
		printf("0\n");
		return 0;
	}

	square_matrix<modint> A(2);
	A[0][0] = a; A[0][1] = b; A[1][0] = 1;
	A ^= n - 1;
	
	printf("%d\n", A[0][0]);
	return 0;
}