《数据结构、算法与应用C++语言描述》使用C++语言实现二维数组下三角矩阵

下三角矩阵定义

如下图所示：

代码实现

_11lowerTriangularMatrix.h

模板类

/*
Project name :			allAlgorithmsTest
Last modified Date:		2022年8月13日17点38分
Last Version:			V1.0
Descriptions:			数组存储的下三角矩阵类头文件
*/
#pragma once
#ifndef _LOWERTRIANGULARMATRIX_H_
#define _LOWERTRIANGULARMATRIX_H_
#include "_1myExceptions.h"
using namespace std;
void lowerTriangularMatrixTest();//测试函数

template<class T>
class lowerTriangularMatrix 
{
   public:
      lowerTriangularMatrix(int theN = 10);
      ~lowerTriangularMatrix() {delete [] element;}
      T get(int, int) const;
      void set(int, int, const T&);
   private:
      int n;       // matrix dimension
      T *element;  // 1D array for lower triangle
};


template<class T>
lowerTriangularMatrix<T>::lowerTriangularMatrix(int theN)
{// Constructor.
   // validate theN
   if (theN < 1)
       throw illegalParameterValue("Matrix size must be > 0");

   n = theN;
   element = new T [n * (n + 1) / 2];
}
   
template <class T>
T lowerTriangularMatrix<T>::get(int i, int j) const
{// Return (i,j)th element of matrix.
   // validate i and j
   if ( i < 1 || j < 1 || i > n || j > n)
       throw matrixIndexOutOfBounds();

   // (i,j) in lower triangle if i >= j
   if (i >= j)
      return element[i * (i - 1) / 2 + j - 1];
   else
      return 0;
}

template<class T>
void lowerTriangularMatrix<T>::set(int i, int j, const T& newValue)
{// Store newValue as (i,j)th element.
   // validate i and j
   if ( i < 1 || j < 1 || i > n || j > n)
       throw matrixIndexOutOfBounds();

   // (i,j) in lower triangle iff i >= j
   if (i >= j)
      element[i * (i - 1) / 2 + j - 1] = newValue;
   else
      if (newValue != 0)
         throw illegalParameterValue
               ("elements not in lower triangle must be zero");
}

#endif

_11lowerTriangularMatrix.cpp

/*
Project name :			allAlgorithmsTest
Last modified Date:		2022年8月13日17点38分
Last Version:			V1.0
Descriptions:			测试_11lowerTriangularMatrix.h头文件中的所有函数(下三角矩阵)
*/
#include <iostream>
#include "_11lowerTriangularMatrix.h"
using namespace std;

void lowerTriangularMatrixTest()
{
	cout << endl << "****************************lowerTriangularMatrixTest()函数开始*******************************" << endl;
	lowerTriangularMatrix<int> x(20);
	x.set(1, 1, 22);
	x.set(5, 3, 44);
	x.set(8, 5, 0);
	x.set(10, 2, 55);
	x.set(8, 5, 0);
	cout << x.get(10, 2) << endl;
	cout << x.get(5, 3) << endl;
	cout << x.get(1, 1) << endl;
	cout << x.get(10, 14) << endl;
	cout << x.get(8, 5) << endl;
	cout << "*******************************diagonalMatrixTest()函数结束***********************************" << endl;   
}

_1main.cpp

主函数

/*
Project name :			allAlgorithmsTest
Last modified Date:		2022年8月13日17点38分
Last Version:			V1.0
Descriptions:			main()函数，控制运行所有的测试函数
*/
#include <iostream>
#include "_11lowerTriangularMatrix.h"

int main()
{
	lowerTriangularMatrixTest();	
	return 0;
}

_1myExceptions.h

异常类汇总

/*
Project name :			allAlgorithmsTest
Last modified Date:		2022年8月13日17点38分
Last Version:			V1.0
Descriptions:			综合各种异常
*/
#pragma once
#ifndef _MYEXCEPTIONS_H_
#define _MYEXCEPTIONS_H_
#include <string>
#include<iostream>

using namespace std;

// illegal parameter value
class illegalParameterValue 
{
   public:
      illegalParameterValue(string theMessage = "Illegal parameter value")
            {message = theMessage;}
      void outputMessage() {cout << message << endl;}
   private:
      string message;
};

// illegal input data
class illegalInputData 
{
   public:
      illegalInputData(string theMessage = "Illegal data input")
            {message = theMessage;}
      void outputMessage() {cout << message << endl;}
   private:
      string message;
};

// illegal index
class illegalIndex 
{
   public:
      illegalIndex(string theMessage = "Illegal index")
            {message = theMessage;}
      void outputMessage() {cout << message << endl;}
   private:
      string message;
};

// matrix index out of bounds
class matrixIndexOutOfBounds 
{
   public:
      matrixIndexOutOfBounds
            (string theMessage = "Matrix index out of bounds")
            {message = theMessage;}
      void outputMessage() {cout << message << endl;}
   private:
      string message;
};

// matrix size mismatch
class matrixSizeMismatch 
{
   public:
      matrixSizeMismatch(string theMessage = 
                   "The size of the two matrics doesn't match")
            {message = theMessage;}
      void outputMessage() {cout << message << endl;}
   private:
      string message;
};

// stack is empty
class stackEmpty
{
   public:
      stackEmpty(string theMessage = 
                   "Invalid operation on empty stack")
            {message = theMessage;}
      void outputMessage() {cout << message << endl;}
   private:
      string message;
};

// queue is empty
class queueEmpty
{
   public:
      queueEmpty(string theMessage = 
                   "Invalid operation on empty queue")
            {message = theMessage;}
      void outputMessage() {cout << message << endl;}
   private:
      string message;
};

// hash table is full
class hashTableFull
{
   public:
      hashTableFull(string theMessage = 
                   "The hash table is full")
            {message = theMessage;}
      void outputMessage() {cout << message << endl;}
   private:
      string message;
};

// edge weight undefined
class undefinedEdgeWeight
{
   public:
      undefinedEdgeWeight(string theMessage = 
                   "No edge weights defined")
            {message = theMessage;}
      void outputMessage() {cout << message << endl;}
   private:
      string message;
};

// method undefined
class undefinedMethod
{
   public:
      undefinedMethod(string theMessage = 
                   "This method is undefined")
            {message = theMessage;}
      void outputMessage() {cout << message << endl;}
   private:
      string message;
};
#endif