数据结构-稀疏矩阵

#include <iostream>
#include <stdlib.h>
using namespace std;
const int DefaultSize=100;

template <class T>
struct Trituple{    //三元数组类定义
    int row,col;    //非零元素行号、列号
    T value;
    Trituple<T>& operator=(Trituple<T>& x){row=x.row;col=x.col;value=x.value;}   //结点赋值
}

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

template <class T>
SparseMatrix<T>::SparseMatrix(int maxSz):maxTerms(maxSz){ //构造函数
    if(maxSz<1){
        cerr<<"矩阵初始化值错误！"<<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(SparseMatrix<T>& x){ //复制构造函数
    Rows=x.Rows;
    Cols=x.Cols;
    Terms=x.Terms;
    maxTerms=x.maxTerms;
    smArray=new Trituple<T>[maxTerms];
    if(smArray==NULL){
        cerr<<"分配存储错！"<<endl;
        exit(1);
    }
    for(int i=0;i<Terms;i++)smArray[i]=x.smArray[i];
}

template <class T>
ostream& operator<<(ostream& out, SparseMatrix<T>& M){
    out<<"rows="<<M.Rows<<endl;
    out<<"cols="<<M.Cols<<endl;
    out<<"Nonzero 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 or rows,columns,and terms"<<endl;
    in>>M.Rows>>M.Cols>>M.Terms;
    if (M.Terms>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;
}

template <class T>
SpareMatrix<T> SparseMatrix<T>::Transpose(){
    SparseMatrix<T> b(maxTerms);
    b.Rows = Cols;
    b.Cols = Rows;
    b.Terms = Terms;
    if (Terms > 0){
        int CurrentB = 0;   //存放指针
        for (int k=0; k<Cols; k++)     //按照列号（新行号）进行扫描，扫描Cols次
             for (int i=0; i<Terms; i++)  //在数组中找列号为k的三元组，if语句一共执行次数为O(Cols*Terms)
             if (sumArray[i].col==k){
                 b.smArray[CurrentB].row=k;
                 b.smArray[CurrentB].col=smArray[i].row;
                 b.smArray[CurrentB].value=smArray[i].value;
                 CurrentB++;
             }
    }
    return b;
}

template <class T>
SparseMatrix<T> SparseMatrix<T>::FastTranspose(){
//  程序总时间复杂度为O(Cols+Terms)=O(Cols*Rows),但增加了两个辅助数组
    int *rowSize=new int[Cols];     //辅助数组，统计各列非零元素个数
    int *rowStart=new int[Cols];    //辅助数组，预计转置后各行存放位置
    SparseMatrix<T> b(maxTerms);    //存放转置结果
    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]++;     //每次加入一个元素后，对应行的rowStart加1
        }
    }
    delete []rowStart;
    delete []rowStart;
    return b;
}