C++模版类实现稀疏矩阵（转置运算和快速转置运算）

在完成稀疏矩阵的实现时，主要遇到了两个问题：

1. 复制构造函数传参数一般应该为const引用类型，否则在SparseMatrix<T> b(a.Transpose())等情况下会出问题，重载赋值符号时也一样，参数应设为const引用类型。（似乎和左右值有关？待深入研究）
2. 在转置函数和快速转置函数中，数组元素三元组中的行和列都是我们输入的值，是从1开始的，而在数组中是从0开始的，这一点要千万注意。

1、SparseMatrix.h

#ifndef SparseMatrix_h
#define SparseMatrix_h
#include <iostream>
using std::ostream;
using std::istream;
const int DefaultSize = 100;

template <class T>
struct Trituple{
    int row, col;
    T value;
    Trituple<T>& operator=(Trituple<T>& x){
        row = x.row;
        col = x.col;
        value = x.value;
        return *this;
    }
};

template <class T>
class SparseMatrix{
private:
    int Rows, Cols, Terms;
    Trituple<T>* smArray;
    int maxTerms;
public:
    SparseMatrix(int maxSz = DefaultSize);
    SparseMatrix(const SparseMatrix<T>& x);
    ~SparseMatrix(){delete []smArray;}
    SparseMatrix<T>& operator=(const SparseMatrix<T>& x);
    SparseMatrix<T> Transpose();
    SparseMatrix<T> FastTranspose();
    //SparseMatrix<T> Add(SparseMatrix<T>& b);
    //SparseMatrix<T> Multiply(SparseMatrix<T>& b);
    template <class U> friend ostream& operator<<(ostream& out, SparseMatrix<U>& M);
    template <class U> friend istream& operator>>(istream& in, SparseMatrix<U>& M);
};

#endif /* SparseMatrix_h */

2、SparseMatrix.cpp

#include <stdio.h>
#include "SparseMatrix.h"
using std::endl;
using std::cerr;
using std::cout;

template <class T>
SparseMatrix<T>::SparseMatrix(int maxSz) : maxTerms(maxSz){
    if(maxSz < 1){cerr << "矩阵初始化值错！" << endl; exit(1);}
    smArray = new Trituple<T>[maxSz];
    if(smArray == NULL){cerr << "存储分配错！" << endl; exit(1);}
    Rows = Cols = Terms = 0;
}

template <class T>
SparseMatrix<T>::SparseMatrix(const SparseMatrix<T>& x){
    Rows = x.Rows;
    Cols = x.Cols;
    Terms = x.Terms;
    maxTerms = x.maxTerms;
    smArray = new Trituple<T>[maxTerms];
    if(smArray == NULL){cerr << "存储分配错误！" << endl; exit(1);}
    for(int i = 0; i < Terms; i++)
        smArray[i] = x.smArray[i];
}

template <class T>
SparseMatrix<T>& SparseMatrix<T>::operator=(const SparseMatrix<T>& x){
    Rows = x.Rows;
    Cols = x.Cols;
    Terms = x.Terms;
    maxTerms = x.maxTerms;
    for(int i = 0; i < Terms; i++)
        smArray[i] = x.smArray[i];
    return *this;
}

template <class T>
ostream& operator<<(ostream& out, SparseMatrix<T>& M){
    out << "row = " << M.Rows << endl;
    out << "cols = " << M.Cols << endl;
    out << "Nozero terms = " << M.Terms << endl;
    for(int i = 0; i < M.Terms; i ++)
        out << "M[" << M.smArray[i].row << "][" << M.smArray[i].col << "] = " << M.smArray[i].value << endl;
    return out;
}

template <class T>
istream& operator>>(istream& in, SparseMatrix<T>& M){
    cout << "Enter number of rows, columns, and terms" << endl;
    in >> M.Rows >> M.Cols >> M.Terms;
    if(M.Terms > M.maxTerms){cerr << "Number of terms overflow!" << endl; exit(1);}
    for(int i = 0; i < M.Terms; i++){
        cout << "Enter row, column, and value of term:" << i+1 << endl;
        in >> M.smArray[i].row >> M.smArray[i].col >> M.smArray[i].value;
    }
    return in;
}

//稀疏矩阵转置算法
template <class T>
SparseMatrix<T> SparseMatrix<T>::Transpose(){
    SparseMatrix<T> b(maxTerms);
    b.Rows = Cols;
    b.Cols = Rows;
    b.Terms = Terms;
    if(Terms > 0){
        int k, i, CurrentB = 0;
        for(k = 0; k < Cols; k ++)
            for(i = 0; i < Terms; i ++)
                if(smArray[i].col == k+1){
                    b.smArray[CurrentB].row = k;
                    b.smArray[CurrentB].col = smArray[i].row;
                    b.smArray[CurrentB].value = smArray[i].value;
                    CurrentB ++;
                }
    }
    return b;
}

//稀疏矩阵快速转置算法
template <class T>
SparseMatrix<T> SparseMatrix<T>::FastTranspose(){
    int* rowSize = new int[Cols];
    int* rowStart = new int[Cols];
    SparseMatrix<T> b(maxTerms);
    b.Rows = Cols;
    b.Cols = Rows;
    b.Terms = Terms;
    if(Terms > 0){
        int i, j;
        for(i = 0; i < Cols; i ++) rowSize[i] = 0;
        for(i = 0; i < Terms; i ++) rowSize[--smArray[i].col]++;
        rowStart[0] = 0;
        for(i = 1; i < Cols; i++)
            rowStart[i] = rowStart[i-1] + rowSize[i-1];
        for(i = 0; i < Terms; i ++){
            j = rowStart[smArray[i].col];
            b.smArray[j].row = smArray[i].col;
            b.smArray[j].col = smArray[i].row;
            b.smArray[j].value = smArray[i].value;
            rowStart[smArray[i].col]++;
        }
    }
    delete []rowStart;
    delete []rowSize;
    return b;
}

3、main.cpp

#include <iostream>
#include "SparseMatrix.cpp"
using std::cin;

int main(){
    SparseMatrix<int> a(100);
    cin >> a;
    cout << a;
    SparseMatrix<int> b(100);
    SparseMatrix<int> c(100);
    b = a.Transpose();
    c = a.FastTranspose();
    cout << b;
    cout << c;
    return 0;
}