经典数据结构之稀疏矩阵

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数据的存储形式，不外乎链表和类数组两种。使用二维数组存储矩阵，如果该矩阵是稀疏的，那么会浪费很多空间。例如一个4*4的对角阵，很明显，只有主对角线上才有元素。那么使用二维数组存储需要16个单位的存储空间。然而通过定义一个结构体：

template<typename T>struct SDataType{    friend class CSparseMatrix<T>;    int m_nRow;    int m_nCol;    T m_nVal;};

然后将其存放于数组，所需要的空间则为[(sizeof(T) +2*sizeof(int))* 4]相对于[sizeof(T) * 16]来说，会节约很多空间。故我们通常使用这种方式存储稀疏矩阵。然而矩阵的存储，可以是基于行的，或者是基于列的。下面以基于行来示例代码：

.h文件

#ifndef CSPARSEMATRIX_HHH#define CAPARSEMATRIX_HHH#include <iostream>#include <cassert>template<typename T>class CSparseMatrix;template<typename T>struct SDataType{    friend class CSparseMatrix<T>;    int m_nRow;int m_nCol;T m_nVal;};template <typename T>class CSparseMatrix{private:// members;SDataType<T>* m_pArray;int m_nLength;int m_nMaxSize;int m_nRows;int m_nCols;public:// constructors;CSparseMatrix(const int& maxSize);~CSparseMatrix();// methods;friend std::ostream& operator<< (std::ostream& out, const CSparseMatrix<T>& matrix){out << "rows = " << matrix.m_nRows << " columns = " << matrix.m_nCols << std::endl;out << "length = " << matrix.m_nLength << std::endl;out << "row" << '\t' << "col" << '\t' <<  "val" << std::endl;for(int i = 0; i < matrix.m_nLength; i ++)out << matrix.m_pArray[i].m_nRow << '\t' << matrix.m_pArray[i].m_nCol << '\t' << matrix.m_pArray[i].m_nVal << std::endl;return out;}friend std::istream& operator>> (std::istream& in, CSparseMatrix<T>& matrix){std::cout << "number of rows, columns, length" << std::endl;in >> matrix.m_nRows >> matrix.m_nCols >> matrix.m_nLength;assert(matrix.m_nLength <= matrix.m_nMaxSize);for(int i = 0; i < matrix.m_nLength; i ++){std::cout << "row number, column number, value" << std::endl;in >> matrix.m_pArray[i].m_nRow >> matrix.m_pArray[i].m_nCol >> matrix.m_pArray[i].m_nVal;}return in;}    // append;void mAdd(const CSparseMatrix<T>& aMatrix, CSparseMatrix<T>& bMatrix);void mTranpose(CSparseMatrix<T>& aMatrix);private:    void mAppend(const SDataType<T>& data);};template<typename T>CSparseMatrix<T>::CSparseMatrix(const int& maxSize = 10):    m_nMaxSize(maxSize){    assert(m_nMaxSize > 0);m_nLength = m_nCols = m_nRows = 0;m_pArray = new SDataType<T>[m_nMaxSize];}template<typename T>CSparseMatrix<T>::~CSparseMatrix(){delete [] m_pArray;}template<typename T>void CSparseMatrix<T>::mAppend(const SDataType<T>& data){if(m_nLength >= m_nMaxSize)printf("the matrix is full, cannot append any more\n");else{        m_pArray[m_nLength] = data;m_nLength ++;}}template<typename T>void CSparseMatrix<T>::mAdd(const CSparseMatrix<T>& aMatrix, CSparseMatrix<T>& bMatrix){    if(aMatrix.m_nRows != m_nRows || aMatrix.m_nCols != m_nCols)printf("the matrix is not compatable\n");bMatrix.m_nCols = m_nCols;bMatrix.m_nRows = m_nRows;bMatrix.m_nLength = 0;    int i = 0;    // indicator of self;int j = 0;    // indicator of aMatrix;    while(i < m_nLength && j < aMatrix.m_nLength){if(bMatrix.m_nLength == bMatrix.m_nMaxSize){printf("Not enough size to add");return;}int ipos = m_pArray[i].m_nRow * m_pArray[i].m_nCol + m_pArray[i].m_nCol;int jpos = aMatrix.m_pArray[j].m_nRow * aMatrix.m_pArray[j].m_nCol  + aMatrix.m_pArray[j].m_nCol;        if(ipos < jpos){bMatrix.mAppend(m_pArray[i]);i ++;}else if(ipos > jpos){bMatrix.mAppend(aMatrix.m_pArray[j]);j ++;}else{SDataType<T> data;data.m_nVal = m_pArray[i].m_nVal + aMatrix.m_pArray[j].m_nVal;data.m_nRow = m_pArray[i].m_nRow;data.m_nCol = m_pArray[i].m_nCol;bMatrix.mAppend(data);i ++;j ++;}bMatrix.m_nLength ++;}while(i < m_nLength){if(bMatrix.m_nLength == bMatrix.m_nMaxSize){printf("Not enough size to add");return;}bMatrix.mAppend(m_pArray[i]);i ++;}while(j < bMatrix.m_nLength){if(bMatrix.m_nLength == bMatrix.m_nMaxSize){printf("Not enough size to add");return;}    bMatrix.m_pArray[j];j ++;}}template<typename T>void CSparseMatrix<T>::mTranpose(CSparseMatrix<T>& matrix){if(m_nLength > matrix.m_nMaxSize){printf("Not enough mem\n");return;}    matrix.m_nCols = m_nRows;matrix.m_nRows = m_nCols;    matrix.m_nLength = m_nLength;    int* numberInCol = new int[m_nCols + 1];int* nextOrderByRow = new int[m_nRows + 1];// initializefor(int i = 0; i < m_nCols; i ++)numberInCol[i] = 0;nextOrderByRow[1] = 0;nextOrderByRow[0] = 0;for(int i = 1; i <= m_nLength; i ++)numberInCol[m_pArray[i].m_nCol] ++;for(int j = 2; j <= m_nCols; j ++) // row start;nextOrderByRow[j] = nextOrderByRow[j - 1] + numberInCol[j - 1];        for(int i = 0; i < m_nLength; i ++){int pos = nextOrderByRow[m_pArray[i].m_nCol] ++;matrix.m_pArray[pos].m_nRow = m_pArray[i].m_nCol;matrix.m_pArray[pos].m_nCol = m_pArray[i].m_nRow;matrix.m_pArray[pos].m_nVal = m_pArray[i].m_nVal;}}#endif




	
					
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