算法数学笔记-二、线性代数

目录

• 二、线性代数
  • 矩阵模板
  • 高斯消元

二、线性代数

矩阵模板

namespace Matrix{
	
	struct matrix{
		int hang, lie;
		vector <vector<int >> num;
		
		matrix(int x = 0, int y = 0){
			
			hang = x;
			lie = y;
			num.resize(x + 1);
			for(int i = 1; i <= x; i ++)
				num[i].resize(y + 1);
		}
		
		void out(){
			for(int i = 1; i <= hang; i ++){
				for(int j = 1; j <= lie; j ++)
					cout << num[i][j] << " ";
				cout << endl;
			}		
		}
	
	}no;
	
	matrix E(int n){
		matrix ret(n, n);
		for(int i = 1; i <= n; i ++)
			ret.num[i][i] = 1;
		return ret;
	}
	
	matrix operator * (matrix a, matrix b){
	
		matrix ret(a.hang, b.lie);
		
		for(int i = 1; i <= ret.hang; i ++)
			for(int j = 1; j <= ret.lie; j ++)
				for(int k = 1; k <= a.lie; k ++)
					ret.num[i][j] = (ret.num[i][j] + 1ll * a.num[i][k] * b.num[k][j]) % mod;
	
		return ret;
	}

	matrix operator * (int k, matrix b){
		
		matrix ret = b;
		
		for(int i = 1; i <= b.hang; i ++)
			for(int j = 1; j <= b.lie; j ++)
				ret.num[i][j] = 1ll * k * b.num[i][j] % mod;
				
		return ret;
	}
	
	matrix operator + (matrix a, matrix b){
		
		matrix ret = a;
		for(int i = 1; i <= a.hang; i ++)
			for(int j = 1; j <= a.lie; j ++){
				ret.num[i][j] = a.num[i][j] + b.num[i][j];
				if(ret.num[i][j] >= mod) ret.num[i][j] -= mod;
			}
				
		return ret;
	}
	
	matrix quickpow(matrix x, int b){
		if(b == 0) return E(x.lie);
		if(b == 1) return x;
		
		matrix l = quickpow(x, b >> 1);
		l = l * l;
		if(b & 1)
			l = l * x;
		return l;
	}

}

高斯消元