【矩阵】对称矩阵及稀疏矩阵的压缩存储

1.稀疏矩阵

//稀疏矩阵及其压缩存储#pragma once#include <vector>#include <iostream>using namespace std;template<class T>struct Triple{size_t _r;size_t _c;T _value;Triple(size_t row = 0, size_t col = 0, const T& value = T()):_r(row),_c(col),_value(value){}};template <class T>class SparseMatrix{public:SparseMatrix():_row(0) ,_col(0) ,_illegal(T()){}SparseMatrix(T* arr, size_t row, size_t col, const T& illegal):_row(row),_col(col),_illegal(illegal){for(size_t i = 0; i<row; ++i){for(size_t j = 0; j<col; ++j){if(arr[i*col+j] != illegal){Triple<T> t(i,j,arr[i*col+j]);_matrix.push_back(t);}}}}void Display(){vector<Triple<T> >::iterator iter;iter = _matrix.begin();for(size_t i = 0; i<_row; ++i){for(size_t j = 0; j<_col; ++j){if(iter!=_matrix.end()&&iter->_r == i&&iter->_c == j){cout << iter->_value <<" ";++iter;}else{cout << _illegal <<" ";}}cout << endl;}cout << endl;}//普通转置(行优先存储)//列变行，从0列开始，将列数据一个一个放进转置矩阵SparseMatrix<T> Transpose() {SparseMatrix<T> tm;tm._row = _col;tm._col = _row;tm._illegal = _illegal;tm._matrix.reserve(_matrix.size());for(size_t i = 0; i<_col; ++i){size_t index = 0;while(index < _matrix.size()){if(_matrix[index]._c == i){Triple<T> t(_matrix[index]._c, _matrix[index]._r, _matrix[index]._value);tm._matrix.push_back(t);}++index;}}return tm;}SparseMatrix<T> FastTranspose(){SparseMatrix<T> tm;tm._row = _col;tm._col = _row;tm._illegal = _illegal;tm._matrix.resize(_matrix.size());int* count = new int[_col];//记录每行的元素个数memset(count, 0, sizeof(int)*_col);int* start = new int[_col];//转置矩阵中元素的位置start[0] = 0;size_t index = 0;while(index < _matrix.size()){count[_matrix[index]._c]++;++index;}for(size_t i=1; i<_col; ++i){start[i] = start[i-1] + count[i-1]; }index = 0;while(index < _matrix.size()){Triple<T> t(_matrix[index]._c, _matrix[index]._r, _matrix[index]._value);tm._matrix[start[_matrix[index]._c]++] = t;   //核心代码++index;}delete[] count;delete[] start;return tm;}protected:vector<Triple<T> > _matrix;size_t _row;size_t _col;T _illegal;};

2.对称矩阵

//对称矩阵及其压缩存储#pragma once#include <iostream>using namespace std;template <class T>class SymmetricMatrix{public:SymmetricMatrix(T* arr, size_t n):_n(n),_matrix(new T[n*(n+1)/2]){size_t index = 0;for(size_t i = 0; i<n; ++i){for(size_t j=0; j<n;++j){if(i >= j){_matrix[index] = arr[i*n+j];++index;}else{continue;}}}}void Display(){for(size_t i =0; i < _n; ++i){for(size_t j = 0; j < _n; ++j){/*if(i<j){swap(i,j);cout<<_matrix[i*(i+1)/2+j]<<" ";swap(i,j);}elsecout<<_matrix[i*(i+1)/2+j]<<" ";*/cout << Access(i,j) << " ";}cout << endl;}cout << endl;}T& Access(size_t row, size_t col){if(row<col){swap(row, col);}return _matrix[row*(row+1)/2+col];}~SymmetricMatrix(){if(_matrix != NULL){delete[] _matrix;_matrix = NULL;}}protected:T* _matrix;size_t _n; //对称矩阵的行列大小};