#435023 (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	tkmst201
提出日時	2020-02-26 23:15:20
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	9,091 bytes
コンパイル時間	1,662 ms
コンパイル使用メモリ	179,472 KB
実行使用メモリ	6,820 KB
最終ジャッジ日時	2024-10-13 15:34:28
合計ジャッジ時間	2,882 ms
ジャッジサーバーID （参考情報）	judge4 / judge2

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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 6,816 KB
testcase_01	AC	2 ms 6,816 KB
testcase_02	AC	2 ms 6,816 KB
testcase_03	AC	1 ms 6,816 KB
testcase_04	AC	1 ms 6,820 KB
testcase_05	AC	1 ms 6,816 KB
testcase_06	AC	1 ms 6,816 KB
testcase_07	AC	2 ms 6,816 KB
testcase_08	AC	1 ms 6,816 KB
testcase_09	AC	2 ms 6,816 KB
testcase_10	AC	1 ms 6,816 KB
testcase_11	AC	2 ms 6,816 KB
testcase_12	AC	2 ms 6,816 KB
testcase_13	AC	2 ms 6,820 KB
testcase_14	AC	2 ms 6,820 KB
testcase_15	AC	1 ms 6,816 KB
testcase_16	AC	2 ms 6,816 KB
testcase_17	AC	2 ms 6,816 KB
testcase_18	AC	2 ms 6,816 KB
testcase_19	AC	1 ms 6,820 KB
testcase_20	AC	2 ms 6,816 KB
testcase_21	AC	2 ms 6,816 KB
testcase_22	AC	1 ms 6,816 KB
testcase_23	AC	2 ms 6,820 KB
testcase_24	AC	2 ms 6,816 KB
testcase_25	AC	1 ms 6,816 KB
testcase_26	AC	2 ms 6,820 KB
testcase_27	AC	1 ms 6,820 KB
testcase_28	AC	2 ms 6,816 KB
testcase_29	AC	2 ms 6,816 KB
testcase_30	AC	1 ms 6,816 KB
testcase_31	AC	1 ms 6,816 KB
testcase_32	AC	2 ms 6,816 KB
testcase_33	AC	2 ms 6,820 KB
testcase_34	AC	2 ms 6,820 KB
testcase_35	AC	1 ms 6,820 KB
testcase_36	AC	2 ms 6,816 KB
testcase_37	AC	2 ms 6,816 KB
testcase_38	AC	2 ms 6,820 KB
testcase_39	AC	1 ms 6,820 KB
testcase_40	AC	2 ms 6,816 KB
testcase_41	AC	2 ms 6,820 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

raw source code

#include <bits/stdc++.h>
using namespace std;
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) begin(v),end(v)
#define fi first
#define se second
template<typename A, typename B> inline bool chmax(A &a, B b) { if (a<b) { a=b; return 1; } return 0; }
template<typename A, typename B> inline bool chmin(A &a, B b) { if (a>b) { a=b; return 1; } return 0; }
using ll = long long;
using pii = pair<int, int>;
constexpr ll INF = 1ll<<30;
constexpr ll longINF = 1ll<<60;
constexpr ll MOD = 1000000007;
constexpr bool debug = 0;
//---------------------------------//

template<typename T>
struct Matrix {
public:
	using value_type = T;
	using size_type = std::size_t;
	
	Matrix() {}
	Matrix(size_type h, size_type w, const value_type & x = 0) : h(h), w(w), val(h, std::vector<value_type>(w, x)) {
		assert(h > 0 && w > 0);
	}
	Matrix(std::vector<std::vector<value_type>> val) : h(val.size()), w(val.size() ? val[0].size() : 0), val(val) {
		assert(h > 0 && w > 0);
		for (size_type i = 1; i < h; ++i) assert(val[i].size() == w);
	}
	Matrix(std::initializer_list<std::vector<value_type>> init) : val(init.begin(), init.end()) {
		h = val.size();
		w = val.size() ? val[0].size() : 0;
		assert(h > 0 && w > 0);
		for (size_type i = 1; i < h; ++i) assert(val[i].size() == w);
	}
	std::vector<value_type> & operator [](size_type i) noexcept { return val[i]; }
	const std::vector<value_type> & operator [](size_type i) const noexcept { return val[i]; };
	value_type & operator ()(size_type i, size_type j) noexcept { return val[i][j]; };
	const value_type & operator ()(size_type i, size_type j) const noexcept { return val[i][j]; }
	value_type & at(size_type i, size_type j) {
		assert(i < h && j < w);
		return val[i][j];
	}
	const value_type & at(size_type i, size_type j) const {
		assert(i < h & j < w);
		return val[i][j];
	}
	
	bool empty() const { return !(h || w); }
	std::pair<size_type, size_type> type() const { return std::make_pair(h, w); }
	bool match_type(const Matrix & rhs) const noexcept { return h == rhs.h && w == rhs.w; }
	bool is_square() const { return h == w; }
	const std::vector<std::vector<value_type>> & get() const noexcept { return val; }
	
	bool operator ==(const Matrix & rhs) const noexcept { return match_type(rhs) && val == rhs.val; }
	bool operator !=(const Matrix & rhs) const noexcept { return !(*this == rhs); }
	Matrix operator +() const { return Matrix(*this); }
	Matrix operator -() const { return Matrix(h, w) - Matrix(*this); }
	Matrix operator +(const Matrix & rhs) const { return Matrix(*this) += rhs; }
	Matrix operator -(const Matrix & rhs) const { return Matrix(*this) -= rhs; }
	Matrix operator *(const Matrix & rhs) const {
		assert(w == rhs.h);
		Matrix res(h, rhs.w);
		for (size_type i = 0; i < h; ++i) for (size_type j = 0; j < rhs.w; ++j) for (size_type k = 0; k < w; ++k)
			res.val[i][j] += val[i][k] * rhs.val[k][j];
		return res;
	}
	Matrix operator /(const Matrix & rhs) const { return Matrix(*this) /= rhs; }
	friend Matrix operator *(const value_type & lhs, const Matrix & rhs) {
		Matrix res(rhs.val);
		for (size_type i = 0; i < res.h; ++i) for (size_type j = 0; j < res.w; ++j)
			res.val[i][j] = lhs * res.val[i][j];
		return res;
	}
	Matrix operator *(const value_type & rhs) const {
		Matrix res(val);
		for (size_type i = 0; i < h; ++i) for (size_type j = 0; j < w; ++j)
			res.val[i][j] *= rhs;
		return res;
	}
	Matrix operator /(const value_type & rhs) const {
		Matrix res(val);
		for (size_type i = 0; i < h; ++i) for (size_type j = 0; j < w; ++j)
			res.val[i][j] /= rhs;
		return res;
	}
	Matrix & operator +=(const Matrix & rhs) {
		assert(match_type(rhs));
		for (size_type i = 0; i < h; ++i) for (size_type j = 0; j < w; ++j)
			val[i][j] += rhs.val[i][j];
		return *this;
	}
	Matrix & operator -=(const Matrix & rhs) {
		assert(match_type(rhs));
		for (size_type i = 0; i < h; ++i) for(size_type j = 0; j < w; ++j)
			val[i][j] -= rhs.val[i][j];
		return *this;
	}
	Matrix & operator *=(const Matrix & rhs) {
		*this = *this * rhs;
		return *this;
	}
	Matrix & operator /=(const Matrix & rhs) {
		*this *= rhs.inverse();
		return *this;
	}
	
	Matrix pow(long long n) const {
		Matrix res = identity(h), x(*this);
		if (n < 0) { x = x.inverse(); n = -n; }
		while (n) { if (n & 1) res *= x; x *= x; n >>= 1; }
		return res;
	}
	
	Matrix trans() const {
		Matrix res(w, h);
		for (size_type i = 0; i < h; ++i) for (size_type j = 0; j < w; ++j)
			res.val[j][i] = val[i][j];
		return res;
	}
	
	Matrix inverse() const {
		assert(is_square());
		Matrix aug_mat = this->hstack(identity(h));
		if (aug_mat.gauss_jordan() != h) return Matrix();
		return aug_mat.submat(0, w, h, 2 * w);
	}
	
	Matrix vstack(const Matrix & A) const {
		assert(w == A.w);
		Matrix res(h + A.h, w);
		std::copy(val.begin(), val.end(), res.val.begin());
		std::copy(A.val.begin(), A.val.end(), res.val.begin() + h);
		return res;
	}
	
	Matrix hstack(const Matrix & A) const {
		assert(h == A.h);
		Matrix res(h, w + A.w);
		for (int i = 0; i < h; ++i) {
			std::copy(val[i].begin(), val[i].end(), res.val[i].begin());
			std::copy(A.val[i].begin(), A.val[i].end(), res.val[i].begin() + w);
		}
		return res;
	}
	
	Matrix submat(size_type i1, size_type j1, size_type i2, size_type j2) const {
		assert(i1 < i2 && j1 < j2 && i2 <= h && j2 <= w);
		Matrix res(i2 - i1, j2 - j1);
		for (size_type i = 0; i < i2 - i1; ++i)
			std::copy(val[i + i1].begin() + j1, val[i + i1].begin() + j2, res.val[i].begin());
		return res;
	}
	
	static Matrix identity(size_type n) {
		Matrix res(n, n);
		for (size_type i = 0; i < n; ++i) res(i, i) = 1;
		return res;
	}
	
	size_type gauss_jordan(size_type colnum = -1) {
		if (colnum == -1) colnum = w;
		size_type rank = 0;
		
		for (size_type k = 0; k < colnum; ++k) {
			size_type pivot = -1;
			for (size_type i = rank; i < h; ++i) {
				if (val[i][k] != 0) {
					pivot = i;
					break;
				}
			}
			if (pivot == -1) continue;
			if (pivot != rank) std::swap(val[rank], val[pivot]);
			
			value_type div = static_cast<value_type>(1) / val[rank][k];
			for (size_type j = k; j < w; ++j) val[rank][j] *= div;
			
			for (size_type i = 0; i < h; ++i) if (i != rank) {
				for (size_type j = k + 1; j < w; ++j) val[i][j] -= val[rank][j] * val[i][k];
					val[i][k] = 0;
			}
			++rank;
		}
		return rank;
	}
	
	friend std::ostream & operator <<(std::ostream & os, const Matrix & rhs) {
		os << "type = (" << rhs.h << "," << rhs.w << ") [\n";
		for (size_type i = 0; i < rhs.h; ++i) for (size_type j = 0; j < rhs.w; ++j)
			os << (j == 0 ? " " : "") << rhs.val[i][j] << (j + 1 == rhs.w ? '\n' : ' ');
		return os << "]";
	}
	
private:
	size_type h, w;
	std::vector<std::vector<value_type>> val;
};

template<int M>
struct ModInt {
public:
	using value_type = long long;
	
	ModInt(value_type val = 0) : val(val < 0 ? (M - (-val % M)) % M : val % M) {}
	
	explicit operator bool() const noexcept { return val; }
	bool operator ==(const ModInt & rhs) const noexcept { return val == rhs.val; }
	bool operator !=(const ModInt & rhs) const noexcept { return !(*this == rhs); }
	ModInt operator +() const noexcept { return ModInt(*this); }
	ModInt operator -() const noexcept { return ModInt(0) -= *this; }
	ModInt operator +(const ModInt & rhs) const noexcept { return ModInt(*this) += rhs; }
	ModInt operator -(const ModInt & rhs) const noexcept { return ModInt(*this) -= rhs; }
	ModInt operator *(const ModInt & rhs) const noexcept { return ModInt(*this) *= rhs; }
	ModInt operator /(const ModInt & rhs) const noexcept { return ModInt(*this) /= rhs; }
	
	ModInt & operator +=(const ModInt & rhs) noexcept {
		val += rhs.val;
		if (val >= M) val -= M;
		return *this;
	}
	ModInt & operator -=(const ModInt & rhs) noexcept {
		if (val < rhs.val) val += M;
		val -= rhs.val;
		return *this;
	}
	ModInt & operator *=(const ModInt & rhs) noexcept {
		val = val * rhs.val % M;
		return *this;
	}
	ModInt & operator /=(const ModInt & rhs) noexcept {
		*this *= rhs.inverse();
		return *this;
	}
	
	ModInt pow(value_type n) const {
		ModInt res = 1, x = val;
		if (n < 0) { x = x.inverse(); n = -n; }
		while (n) { if (n & 1) res *= x; x *= x; n >>= 1; }
		return res;
	}
	
	ModInt inverse() const {
		value_type a = val, a1 = 1, a2 = 0, b = M, b1 = 0, b2 = 1;
		while (b > 0) {
			value_type q = a / b, r = a % b;
			value_type nb1 = a1 - q * b1, nb2 = a2 - q * b2;
			a = b; b = r;
			a1 = b1; b1 = nb1;
			a2 = b2; b2 = nb2;
		}
		assert(a == 1);
		return a1;
	}
	
	const value_type & get() const noexcept { return val; }
	static decltype(M) get_mod() noexcept { return M; }
	
	friend std::ostream & operator <<(std::ostream & os, const ModInt & rhs) { return os << rhs.val; }
	friend std::istream & operator >>(std::istream & is, ModInt & rhs) {
		value_type x;
		is >> x;
		rhs = ModInt(x);
		return is;
	}
private:
	value_type val;
};
using mint = ModInt<MOD>;


int main() {
	ll a, b, n;
	cin >> a >> b >> n;
	
	mint ans;
	if (n <= 1) ans = n;
	else {
		Matrix<mint> A{{a, b}, {1, 0}};
		Matrix<mint> b{{1}, {0}};
		ans = (A.pow(n - 1) * b)[0][0];
	}
	cout << ans << endl;
	return 0;
}

yukicoder

結果

テストケース

ソースコード