Question

Write a C++ class that has an array of integers as a member variable, a pure virtual member function bool compare(int \(x, \text { int } y)=0\) that compares its two parameters and returns a boolean value, and a member function void sort () that uses the comparison defined by the compare virtual function to sort the array. The sort function will swap a pair of array elements a \([\mathrm{k}]\) and a \([\text { j }]\) if \\[ \text { compare }(a[k], a[j]) \\] returns true. Explain how you can use this class to produce classes that sort arrays in ascending order and descending order.

Short answer

**Answer:** The purpose of the base class, `BaseSorter`, is to define the common functionalities and data members that will be used in both ascending and descending sorting. It provides the foundation for creating the derived classes by defining the member variable for storing the integer array, the constructor for initializing this array, and the pure virtual comparison function that must be implemented in each derived class. The base class implementation avoids code duplication and enforces consistent behavior across derived classes. The derived classes, `AscendingSorter` and `DescendingSorter`, inherit from the base class and specialize the sorting behavior by implementing the pure virtual comparison function (`compare()`) according to their respective sorting order. The `AscendingSorter` class implements the `compare()` function in a way that sorts the array in ascending order, while the `DescendingSorter` class implements it to sort the array in descending order. This allows us to create objects of these classes and sort arrays in the desired order by calling the `sort()` function provided by their base class.

Step-by-step solution

Create the base class with array and pure virtual function

Define a C++ class named 'BaseSorter'. Declare an array of integers as a member variable (let's call it 'arr') and a pure virtual function 'compare()' to compare two integers and return a boolean value. Also, declare a constructor to initialize 'arr' with a given array of integers. ``` #include class BaseSorter { protected: int* arr; int size; public: BaseSorter(int* inputArr, int inputSize) : size(inputSize) { arr = new int[size]; for (int i = 0; i < size; i++) { arr[i] = inputArr[i]; } } virtual bool compare(int x, int y) = 0; }; ```

Implement the sort function in the base class

Implement the 'sort()' member function in the base class 'BaseSorter'. The function should use the 'compare()' function to sort the 'arr' array. Please note that the compare function will be implemented in derived classes later. ```cpp void sort() { for (int i = 0; i < size - 1; i++) { for (int j = i + 1; j < size; j++) { if (compare(arr[i], arr[j])) { std::swap(arr[i], arr[j]); } } } } ```

Create derived classes for ascending and descending sorting

Create two derived classes 'AscendingSorter' and 'DescendingSorter' from the 'BaseSorter' class. Implement the 'compare()' function in each of them to suit the ascending and descending sorting, respectively. ```cpp class AscendingSorter : public BaseSorter { public: AscendingSorter(int* inputArr, int inputSize) : BaseSorter(inputArr, inputSize) {} bool compare(int x, int y) override { return x > y; } }; class DescendingSorter : public BaseSorter { public: DescendingSorter(int* inputArr, int inputSize) : BaseSorter(inputArr, inputSize) {} bool compare(int x, int y) override { return x < y; } }; ``` Now, we are able to create objects of 'AscendingSorter' and 'DescendingSorter' classes with given arrays and sort them in ascending and descending order, respectively, by calling the 'sort()' function. Both ascending and descending sorters are derived from the base class 'BaseSorter' that holds the common functionalities. The sort function uses 'compare()' to sort the array, and since the 'compare()' function is implemented differently in derived classes, it provides the desired functionality for ascending and descending sorting.

Key concepts

C++ Class Inheritance

Understanding C++ class inheritance is pivotal while learning object-oriented programming. Inheritance allows us to define a class in terms of another class, which makes it easier to create and maintain an application. It also provides a way to create a new class from an existing class - the new class is called the derived class, and the existing class is referred to as the base class.

For example, consider a base class BaseSorter in C++ which defines a general idea of a sorter that can sort an array of integers. You could then extend this class by creating derived classes, such as AscendingSorter and DescendingSorter, which inherit properties of the base class and also implement specific sorting behavior. The key benefits of inheritance include reusability of code (since the derived classes can reuse base class functionality) and the ability to implement polymorphic behavior. In polymorphism, derived classes can have different functionalities while sharing the same structure or interface of the base class.

C++ Sorting Algorithms

C++ sorting algorithms are a fundamental concept in both computer science education and in real-world applications like databases and search engines. Sorting algorithms arrange the elements in a list or array in a certain order, typically numerical or lexicographical. There are several different sorting algorithms, each with their own advantages in terms of speed, simplicity, memory usage, and efficiency.

Common sorting algorithms in C++ include Bubble Sort, Selection Sort, Insertion Sort, Merge Sort, and Quick Sort, among others. The choice of sorting algorithm depends on the size of the data set and the computational complexity we're willing to accommodate. For instance, Bubble Sort is a simple algorithm but inefficient for large datasets as it has a time complexity of \(O(n^2)\), whereas Quick Sort is much more efficient for larger datasets with an average time complexity of \(O(n \log n)\). When implementing a sort function in a class like BaseSorter, we can use any of these algorithms, leveraging the compare() function to determine the order of elements.

C++ Pure Virtual Functions

Pure virtual functions in C++ define the concept of an abstract base class, which is a class that cannot be instantiated on its own. These functions act as a placeholder that must be implemented by a derived class. Declaring a function as pure virtual in C++ is done using the syntax \(=0\) at the end of the function declaration.

In our example, the BaseSorter class declares a pure virtual function compare() using virtual bool compare(int x, int y) = 0;. This means that any class that derives from BaseSorter must provide a concrete implementation of the compare() function. The purpose is to allow different derived classes to implement different comparison logic, enabling polymorphism. This concept becomes crucial for designing a flexible sorter system where the sorting logic can be easily switched out without changing the sorting machinery itself—demonstrating a design that's both modular and extensible.