矩阵类的实现

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矩阵类 正常存储：

Design a template class Matrix that has the following private member variables:

  1. int rows
  2. int columns
  3. vector values

where T is the type parameter.
Besides, it has the functions such that the main function runs correctly with the following output.

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EXAMPLE OUTPUT
constructor 1
    0    0    0
    0    0    0
    0    0    0
constructor 2
    1    2    3
    4    5    6
    7    8    9
copy constructor
    1    2    3
    4    5    6
    7    8    9
operator =
    1    2    3
    4    5    6
    7    8    9
getColumn
    2
    5
    8
getRow
    4    5    6
concatenateRows
    0    0    0
    0    0    0
    0    0    0
    1    2    3
    4    5    6
    7    8    9
concatenateColumns
    0    0    0    1    2    3
    0    0    0    4    5    6
    0    0    0    7    8    9
reshape
    0    0    2
    0    0    5
    0    0    8
    0    1    3
    0    4    6
    0    7    9
transpose
    1    4    7
    2    5    8
    3    6    9
operator +
    2    4    6
    8    10    12
    14    16    18
operator +
    11    12    13
    14    15    16
    17    18    19
operator -
    0    2    4
    -2    0    2
    -4    -2    0
operator -
    -9    -8    -7
    -6    -5    -4
    -3    -2    -1
operator *
    66    78    90
    78    93    108
    90    108    126
operator *
    2    4    6
    8    10    12
    14    16    18
max
9
min
1
sum
45
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#include <iostream>
#include <string>
#include <vector>
using namespace std;

template <typename E>
class Matrix{
private:
	int rows;
	int columns;
	vector<E> values;
public:
	Matrix(int r, int c):rows(r),columns(c){
		this->values.clear();
		this->values.resize(r*c);
	}
	Matrix(int r, int c, vector<E>& v):rows(r),columns(c){
		this->values.clear();
		this->values.resize(r*c);
		for(int i=0; i<r*c; i++)
			values[i] = v[i];
	}
	Matrix(const Matrix & m)
	{
		this->columns = m.columns;
		this->rows = m.rows;
		this->values.clear();
		this->values.resize(m.rows*m.columns);
		for(int i=0; i<m.rows*m.columns; i++)
			this->values[i] = m.values[i];
	}
	Matrix & operator = (const Matrix & m)
	{
		this->rows = m.rows;
		this->columns = m.columns;
		this->values.clear();
		this->values.resize(m.rows*m.columns);
		for(int i=0; i<m.rows*m.columns; i++)
			this->values[i] = m.values[i];
		return *this;
	}
	~Matrix()
	{
		this->values.clear();
	}
	void print()
	{
		for(int i=0; i<this->rows; i++)
		{
			for(int j=0; j<this->columns; j++)
				cout << "    " << values[i*this->columns+j];
			cout << endl;
		}
	}
	Matrix getColumn(int c)
	{
		Matrix rem(this->rows, 1);
		for(int i=0; i<this->rows; i++)
			rem.values[i] = this->values[i*this->columns+c-1];
		return rem;
	}
	Matrix getRow(int r)
	{
		Matrix rem(1, this->columns);
		for(int i=0; i<this->columns; i++)
			rem.values[i] = this->values[(r-1)*this->columns+i];
		return rem;
	}
	Matrix concatenateRows(const Matrix & m)
	{
		Matrix rem(this->rows+m.rows, this->columns);
		for(int i=0; i<this->rows*this->columns; i++)
			rem.values[i] = this->values[i];
		for(int i=0; i<m.rows*m.columns; i++)
			rem.values[this->rows*this->columns+i] = m.values[i];
		return rem;
	}
	Matrix concatenateColumns(const Matrix & m)
	{
		Matrix rem(this->rows, this->columns+m.columns);
		int z = 0;
		for(int i=0; i<this->rows; i++)
		{
			for(int j=0; j<this->columns; j++)
				rem.values[z++] = this->values[i*this->columns+j];
			for(int j=0; j<m.columns; j++)
				rem.values[z++] = m.values[i*m.columns+j];
		}
		return rem;
	}
	Matrix reshape(int r, int c)
	{
		Matrix rem(r, c);
		E arr[r*c];
		int z = 0;
		for(int i=0; i<this->columns; i++)
		{
			for(int j=0; j<this->rows; j++)
			{
				arr[z++] = this->values[j*this->columns+i];
			}
		}
		z = 0;
		for(int i=0; i<c; i++)
		{
			for(int j=0; j<r; j++)
			{
				rem.values[j*c+i] = arr[z++];
			}
		}
		return rem;
	}
	Matrix transpose()
	{
		Matrix rem(this->columns, this->rows);
		for(int i=0; i<rem.rows; i++)
		{
			for(int j=0; j<rem.columns; j++)
			{
				rem.values[i*rem.columns+j] = this->values[j*this->columns+i];
			}
		}
		return rem;
	}
	Matrix operator + (int n)
	{
		Matrix rem(this->rows, this->columns);
		for(int i=0; i<this->rows*this->columns; i++)
		{
			rem.values[i] = this->values[i] + n;
		}
		return rem;
	}
	Matrix operator + (Matrix &n)
	{
		Matrix rem(this->rows, this->columns);
		for(int i=0; i<this->rows*this->columns; i++)
		{
			rem.values[i] = this->values[i] + n.values[i];
		}
		return rem;
	}
	Matrix operator - (int n)
	{
		Matrix rem(this->rows, this->columns);
		for(int i=0; i<this->rows*this->columns; i++)
		{
			rem.values[i] = this->values[i] - n;
		}
		return rem;
	}
	Matrix operator - (Matrix &n)
	{
		Matrix rem(this->rows, this->columns);
		for(int i=0; i<this->rows*this->columns; i++)
		{
			rem.values[i] = this->values[i] - n.values[i];
		}
		return rem;
	}
	Matrix operator * (int n)
	{
		Matrix rem(this->rows, this->columns);
		for(int i=0; i<this->rows*this->columns; i++)
		{
			rem.values[i] = this->values[i] * n;
		}
		return rem;
	}
	Matrix operator * (const Matrix & matrix2) const{
		Matrix rem(this->rows, matrix2.columns);
		for(int i=0; i<this->rows; i++)
		{
			for(int j=0; j<matrix2.columns; j++)
			{
				int sum = 0;
				for(int x=0; x<this->columns; x++)
				{
				sum += this->values[i*this->columns+x]*matrix2.values[x*matrix2.columns+j];
			
				}
				rem.values[i*matrix2.columns+j] = sum;
			}
		}
		return rem;
	}
	E& get(int r, int c)
	{
		int nr = r-1;
		int nc = c-1;
		return this->values[nr*this->columns+nc];
	}
	Matrix sum() const{
		Matrix rem(1, this->columns);
		if(this->rows == 1)
		{
			rem.columns = 1;
			for(int i=0; i<this->columns; i++)
			{
				rem.values[0] += this->values[i];
			}
		}
		else
		{
			for(int i=0; i<this->columns; i++)
			{
				for(int j=0; j<this->rows; j++)
				{
					rem.values[i] += this->values[j*this->columns+i];	
				}	
			}
		}
		return rem;
	}
	Matrix max()const {
		Matrix rem(1, this->columns);
		if(this->rows == 1)
		{
			rem.columns = 1;
			for(int i=0; i<this->columns; i++)
			{
				rem.values[0] = rem.values[0]>this->values[i] ? rem.values[0] : this->values[i];
			}
		}
		else
		{
			for(int i=0; i<this->columns; i++)
			{
				for(int j=0; j<this->rows; j++)
				{
					rem.values[i] = rem.values[i] > this->values[j*this->columns+i] ? rem.values[i]: this->values[j*this->columns+i];	
				}	
			}
		}
		return rem;
	}
	Matrix min()const {
		Matrix rem(1, this->columns);
		if(this->rows == 1)
		{
			rem.columns = 1;
			rem.values[0] = this->values[0];
			for(int i=0; i<this->columns; i++)
			{
				rem.values[0] = rem.values[0]<this->values[i] ? rem.values[0] : this->values[i];
			}
		}
		else
		{
			for(int i=0; i<this->columns; i++)
			{
				rem.values[i] = this->values[i];
				for(int j=0; j<this->rows; j++)
				{
					rem.values[i] = rem.values[i] < this->values[j*this->columns+i] ? rem.values[i]: this->values[j*this->columns+i];	
				}	
			}
		}
		return rem;
	}
};

int main() { 
    cout << "constructor 1" << endl; 
    Matrix<double> matrix1(3, 3); 
    matrix1.print(); 
     
    const double values1[] = { 
        1, 2, 3, 
        4, 5, 6, 
        7, 8, 9, 
    }; 
    vector<double> values2; 
    for (int i = 0; i < 9; ++ i) { 
        values2.push_back(values1[i]); 
    } 
     
    cout << "constructor 2" << endl; 
    Matrix<double> matrix2(3, 3, values2); 
    matrix2.print(); 
     
    cout << "copy constructor" << endl; 
    Matrix<double> matrix3 = matrix2; 
    matrix3.print(); 
     
    cout << "operator =" << endl; 
    matrix3.get(1, 1) = 10.0; 
    matrix3 = matrix2; 
    matrix3.print(); 
     
    cout << "getColumn" << endl; 
    matrix2.getColumn(2).print(); 
    cout << "getRow" << endl; 
    matrix2.getRow(2).print(); 
     
    cout << "concatenateRows" << endl; 
    matrix1.concatenateRows(matrix2).print(); 
    cout << "concatenateColumns" << endl; 
    matrix1.concatenateColumns(matrix2).print(); 
     
    cout << "reshape" << endl; 
    matrix1.concatenateColumns(matrix2). 
        reshape(6, 3).print(); 
     
    cout << "transpose" << endl; 
    matrix2.transpose().print(); 
     
    cout << "operator +" << endl; 
    (matrix2 + matrix2).print(); 
    cout << "operator +" << endl; 
    (matrix2 + 10).print(); 
    cout << "operator -" << endl; 
    (matrix2.transpose() - matrix2).print(); 
    cout << "operator -" << endl; 
    (matrix2 - 10).print(); 
     
    cout << "operator *" << endl; 
    (matrix2.transpose() * matrix2).print(); 
    cout << "operator *" << endl; 
    (matrix2 * 2).print(); 
     
    cout << "max" << endl; 
    cout << matrix2.max().max().get(1, 1) << endl; 
    cout << "min" << endl; 
    cout << matrix2.min().min().get(1, 1) << endl; 
    cout << "sum" << endl; 
    cout << matrix2.sum().sum().get(1, 1) << endl;         
}

矩阵类 稀疏矩阵存储：

Design a class Sparse that implements interface Matrix: Sparse should has the following public object functions in addition:

A constructor Sparse(int rows, int column), which initializes all elements in the matrix to 0's.

A function Sparse Sparse::operator * (Sparse & sparse2), which returns the product of two sparse matrixes.

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EXAMPLE INPUT
1000000 2000000 3000000

1 1 10
1 2000000 50
1000000 2000000 20

1 3000000 30
2000000 1 40
1 1 -10
EXAMPLE OUTPUT
(1,1,1900)
(1,3000000,300)
(1000000,1,800)
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#include <iostream>
#include <vector>
using namespace std;

class Entry 
{ 
public: 
    int row; 
    int column; 
    double value; 
}; 
     
class Matrix 
{     
public: 
    virtual int size(int dimension) const = 0; 
     
    virtual void set(int row, int column,  
    double value) = 0; 
     
    virtual double get(int row, int column)  
    const = 0; 
     
    virtual void print() = 0; 
     
}; 


class Sparse : public Matrix
{
	private:
		int rows;
		int column;
		vector<Entry> mmatrix;
	public:
		Sparse(int rows, int column)
		{
			this->rows = rows;
			this->column = column;
		}
		virtual int size(int dimension) const
		{
			if(dimension == 1) return this->rows;
			if(dimension == 2) return this->column;
		}
		virtual void set(int row, int column, double value) 
		{
			int flag = 0;
			for(int i=0; i<mmatrix.size(); i++)
			{
				if(mmatrix[i].row == row && mmatrix[i].column == column)
				{
					flag = 1;
					mmatrix[i].value = value;
					break;
				}
			}
			if(!flag)
			{
				Entry rem;
				rem.row = row;
				rem.column = column;
				rem.value = value;
				mmatrix.push_back(rem);
			}
		}
		virtual double get(int row, int column)const
		{
			for(int i=0; i<mmatrix.size(); i++)
			{
				if(mmatrix[i].row == row && mmatrix[i].column == column)
				{
					return mmatrix[i].value;
				}
			}
			return -1;
		}
		virtual void print()
		{
			for(int i=0; i<mmatrix.size()-1; i++)
			{
				for(int j=0; j<mmatrix.size()-1-i; j++)
				{
					if(mmatrix[j].row>mmatrix[j+1].row)
					{
						Entry temp = mmatrix[j];
						mmatrix[j] = mmatrix[j+1];
						mmatrix[j+1] = temp;
					}
					else if(mmatrix[j].row==mmatrix[j+1].row)
					{
						if(mmatrix[j].column>mmatrix[j+1].column)
						{
						Entry temp = mmatrix[j];
						mmatrix[j] = mmatrix[j+1];
						mmatrix[j+1] = temp;
						}
					}
				}
			}
			for(int i=0; i<mmatrix.size(); i++)
			{
				cout << "(" << mmatrix[i].row << "," << mmatrix[i].column << "," << mmatrix[i].value << ")" << endl;				
			}
		}
		Sparse operator * (Sparse &sparse2) 
		{
			Sparse rem(this->rows, sparse2.column);
			vector<Entry> ttt;
			for(int i=0; i<this->mmatrix.size(); i++)
			{
				for(int j=0; j<sparse2.mmatrix.size(); j++)
				{
					if(this->mmatrix[i].column == sparse2.mmatrix[j].row)
					{
						Entry rrr;
						rrr.row = this->mmatrix[i].row;
						rrr.column = sparse2.mmatrix[j].column;
						rrr.value = this->mmatrix[i].value * sparse2.mmatrix[j].value;
						ttt.push_back(rrr);
					}
					
				}
			} 
			int num[ttt.size()] = {0};
			for(int i=0; i<ttt.size(); i++)
			{
				if(num[i]==0)
				{
					int sum = ttt[i].value;
					num[i] = 1;
					for(int j=0; j<ttt.size(); j++)
					{
						if(ttt[i].row == ttt[j].row && ttt[i].column == ttt[j].column && i != j)
						{
							sum += ttt[j].value;
							num[j] = 1;
						}
					}
					if(sum != 0)
					{
						Entry zzz;
						zzz.row = ttt[i].row;
						zzz.column = ttt[i].column;
						zzz.value = sum;
						rem.mmatrix.push_back(zzz);
					}
				}
			}
			return rem;
		}
};

 
void print(Matrix & matrix) { 
    matrix.print(); 
} 
 
void readAndSetElement(Matrix & matrix) { 
    int row; 
    int column; 
    double value; 
    cin >> row >> column >> value; 
    matrix.set(row, column, value); 
} 
 
void readAndSetMultipleElements(Matrix & matrix, int count) { 
    for (int i = 0; i < count; ++ i) { 
        readAndSetElement(matrix); 
    } 
} 
 
int main() { 
    int rows; 
    int columns; 
    int & rows2 = columns; 
    int columns2; 
     
    cin >> rows >> columns >> columns2; 
     
    Sparse sparse1(rows, columns); 
    readAndSetMultipleElements(sparse1, 3); 
     
    Sparse sparse2(rows2, columns2); 
    readAndSetMultipleElements(sparse2, 3); 
 
    Sparse sparse3 = sparse1 * sparse2; 
    print(sparse3); 
}
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