結果

問題 No.720 行列のできるフィボナッチ数列道場 (2)
コンテスト
ユーザー sntea
提出日時 2018-08-20 00:46:52
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 6,937 bytes
コンパイル時間 1,995 ms
コンパイル使用メモリ 183,976 KB
実行使用メモリ 6,820 KB
最終ジャッジ日時 2024-11-22 04:22:18
合計ジャッジ時間 2,885 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge1
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 20
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 # 

#ifdef LOCAL111
	#define _GLIBCXX_DEBUG
#else
	#define NDEBUG
#endif
#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
const int INF = 1e9;
using namespace std;
template<typename T, typename U> ostream& operator<< (ostream& os, const pair<T,U>& p) { os << '(' << p.first << ' ' << p.second << ')'; return os; }

#define endl '\n'
#define ALL(a)  (a).begin(),(a).end()
#define SZ(a) int((a).size())
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define RFOR(i,a,b) for (int i=(b)-1;i>=(a);i--)
#define REP(i,n)  FOR(i,0,n)
#define RREP(i,n) for (int i=(n)-1;i>=0;i--)
#ifdef LOCAL111
	#define DEBUG(x) cout<<#x<<": "<<(x)<<endl
	template<typename T> void dpite(T a, T b){ for(T ite = a; ite != b; ite++) cout << (ite == a ? "" : " ") << *ite; cout << endl;}
#else
	#define DEBUG(x) true
	template<typename T> void dpite(T a, T b){ return; }
#endif
#define F first
#define S second
#define SNP string::npos
#define WRC(hoge) cout << "Case #" << (hoge)+1 << ": "
template<typename T> void pite(T a, T b){ for(T ite = a; ite != b; ite++) cout << (ite == a ? "" : " ") << *ite; cout << endl;}
template<typename T> bool chmax(T& a, T b){if(a < b){a = b; return true;} return false;}
template<typename T> bool chmin(T& a, T b){if(a > b){a = b; return true;} return false;}

typedef long long int LL;
typedef unsigned long long ULL;
typedef pair<int,int> P;

void ios_init(){
	//cout.setf(ios::fixed);
	//cout.precision(12);
#ifdef LOCAL111
	return;
#endif
	ios::sync_with_stdio(false); cin.tie(0);
}


template<long long MOD>
class ModInt {
public:
	const static long long mod = MOD;
	long long x;
	
	ModInt() {
		x = 0;
	}

	ModInt(long long x) {
		x %= mod;
		this->x = x < 0 ? x+mod : x;
	}

	int get() const {
		return (int)x;
	}

	ModInt &operator+=(ModInt that) {
		if((x += that.get()) >= mod) x -= mod;
		return *this;
	}

	ModInt &operator-=(ModInt that) {
		if((x += mod-that.get()) >= mod) x -= mod;
		return *this;
	}

	ModInt &operator*=(ModInt that) {
		x = x*that.get()%mod;
		return *this;
	}

	ModInt &operator/=(ModInt that) {
		return *this *= that.inverse();
	}

	ModInt operator+(ModInt that) const {
		return ModInt(*this) += that;
	}

	ModInt operator-(ModInt that) const {
		return ModInt(*this) -= that;
	}

	ModInt operator*(ModInt that) const {
		return ModInt(*this) *= that;
	}

	ModInt operator/(ModInt that) const {
		return ModInt(*this) /= that;
	}

	ModInt inverse() const {
		using std::swap;
		long long a = x, b = mod, u = 1, v = 0;
		while(b) {
			long long t = a/b;
			a -= t*b; swap(a,b);
			u -= t*v; swap(u,v);
		}
		return ModInt(u);
	}

	ModInt pow(int n) const{
		ModInt b = *this;
		ModInt res = 1;
		while(n != 0) {
			if(n&1){
				res *= b;
			}
			b *= b;
			n >>= 1;
		}
		return res;
	}

	bool operator==(ModInt that) const { return x == that.get(); }
	bool operator!=(ModInt that) const { return x != that.get(); }
	ModInt operator-() const { return x == 0 ? 0 : ModInt(mod-x); }
};

template<long long MOD> ostream& operator<< (ostream& os, const ModInt<MOD>& m) { os << m.get(); return os; }
template<long long MOD> istream& operator>> (istream& is, ModInt<MOD>& m){ long long n; is >> n; m = n; return is;}
typedef ModInt<1000000007> mint;


#define EPS 1e-9

//library
template<typename T>
class Matrix {
public:
	vector<vector<T> > v;
	int n,m;
	Matrix(int n){
		this->n = this->m = n;
		v.resize(n,vector<T>(n,0));
	}

	Matrix(int n, int m){
		this -> n = n;
		this -> m = m;
		v.resize(n,vector<T>(m,0));
	}

	size_t size() const {
		return v.size();
	}

	int row() const {
		return n;
	}

	int col() const {
		return m;
	}

	Matrix operator+ (Matrix x) const {
		Matrix res(n,m);
		for(int i = 0; i < n; i++){
			for(int j = 0; j < m; j++){
				res.v[i][j] = x.v[i][j]+v[i][j];
			}
		}
		return res;
	}

	Matrix operator-(Matrix x) const {
		Matrix res(n,m);
		for(int i = 0; i < n; i++){
			for(int j = 0; j < m; j++){
				res.v[i][j] = v[i][j]-x.v[i][j];
			}
		}
	}

	Matrix operator*(Matrix x) const {
		Matrix res(n,x.m);
		for(int i = 0; i < n; i++){
			for(int j = 0; j < x.m; j++){
				for(int k = 0; k < m; k++){
					res.v[i][j] += v[i][k]*x.v[k][j];
				}
			}
		}
		return res;
	}

	Matrix operator-() const  {
		Matrix res = *this;
		for(int i = 0; i < (int)v.size(); ++i) {
			for(int j = 0; j < (int)v[i].size(); ++j) {
				res [i][j] *= -1;
			}
		}
		return res;
	}

	vector<T> operator*(vector<T> x) const {
		assert(x.size() == v.size());
		vector<T> res(v.size());
		for(int i = 0; i < n; i++){
			T tmp = 0;
			for(int j = 0; j < m; j++){
				tmp += v[i][j]*x[j];
			}
			res[i] = tmp;
		}
		return res;
	}

	Matrix pow(long long x) const {
		assert(n == m);
		Matrix m = (*this);
		Matrix res(n);
		for(int i = 0; i < n; i++) res[i][i] = 1;
		while(x != 0) {
			if(x&1) {
				res = res*m;
			}
			m = m*m;
			x >>= 1;
		}
		return res;
	}

	vector<T>& operator[](int x){
		return v[x];
	}

	const vector<T>& operator[](int x) const {
		return v[x];
	}

	Matrix<T> inverse() const{
		assert(n == m);
		Matrix res(n);
		for(int i = 0; i < n; ++i) {
			res[i][i] = 1;
		}
		
		// vector<pair<int,int>> swap_log;
		Matrix<T> mat = *this;
		for(int k = 0; k < n; ++k) {
			T max_val = abs(mat[k][k]);
			int max_point = k;
			for(int i = k+1; i < n; ++i) {
				if(max_val < abs(mat[i][k])){
					max_val = abs(mat[i][k]);
					max_point = i;
				}
			}
			swap(mat[k],mat[max_point]);
			swap(res[k],res[max_point]);
			// swap_log.emplace_back(k,max_point);
			for(int i = k+1; i < n; ++i) {
				T m = mat[i][k]/mat[k][k];
				for(int j = 0; j < n; ++j) {
					mat[i][j] -= m*mat[k][j];
					res[i][j] -= m*res[k][j];
				}
			}
		}
		
		for(int k = n-1; k >= 0; --k) {
			for(int i = 0; i < k; ++i) {
				T m = mat[i][k]/mat[k][k];
				for(int j = 0; j < n; ++j) {
					// mat[i][j] -= mat[k][j]*m;
					res[i][j] -= res[k][j]*m;
				}
			}
		}
		for(int i = 0; i < n; ++i) {
			for(int j = 0; j < n; ++j) {
				res[i][j] /= mat[i][i];
			}
		}
		// for(auto&& e : swap_log) {
		// 	swap(res[e.first],res[e.second]);
		// }
		return res;
	}

	T det() const {
		Matrix<T> mat = *this;
		T res = 1;
		for(int k = 0; k < n; ++k) {
			T max_val = abs(mat[k][k]);
			int max_point = k;
			for(int i = k+1; i < n; ++i) {
				if(max_val < abs(mat[i][k])){
					max_val = abs(mat[i][k]);
					max_point = i;
				}
			}
			swap(mat[k],mat[max_point]);
			if(k != max_point) res *= -1;
			for(int i = k+1; i < n; ++i) {
				T m = mat[i][k]/mat[k][k];
				for(int j = 0; j < n; ++j) {
					mat[i][j] -= m*mat[k][j];
				}
			}
		}
		for(int i = 0; i < n; ++i) {
			res *= mat[i][i];
		}
		return res;
	}
};
//libary


int main()
{
	ios_init();
	LL n, m;
	while(cin >> n >> m) {
		Matrix<mint> A(3);
		Matrix<mint> B(2);
		B[0] = {1, 1};
		B[1] = {1, 0};
		B = B.pow(m);
		A[0] = {1, 0, 1};
		A[1] = {0, 0, 0};
		A[2] = {0, 0, 0};
		REP(i, 2) REP(j, 2) A[i+1][j+1] = B[i][j];
		vector<mint> v = {0, 1, 0};
		auto ans = A.pow(n+1) * v;
		cout << ans[0] << endl;
	}
	return 0;
}
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