Language: C++ Write a Program with Comments for your code to improve quick sort. The quick sort algorithm presented in the ClassNotes-Sorting, it selects the first element in the list as the pivot. Revise it by selecting the median among the first, middle, and last elements in the list.Explain your Outputs or Answers for the following:(A) Analyze your algorithm, and give the results using order notation.(B) Give a list of n items (for example, an array of 10 integers) representing a scenario.(C) Give a list of n items (for example, an array of 10 integers) representing the worst-case scenario.(D) Give a list of n items (for example, an array of 10 integers) representing the best-case scenario.Please compile your answers in a file including all source code with comments, Explain your running Outputs or Answers in (A) ~(D).Examples of a quick sort from class slides is attached. ```cpp#include using namespace std;// Function prototypesvoid quickSort(int list[], int arraySize);void quickSort(int list[], int first, int last);int partition(int list[], int first, int last);void quickSort(int list[], int arraySize) { quickSort(list, 0, arraySize - 1);}void quickSort(int list[], int first, int last) { if (last > first) { int pivotIndex = partition(list, first, last); quickSort(list, first, pivotIndex - 1); quickSort(list, pivotIndex + 1, last); }}// Partition the array list[first..last]int partition(int list[], int first, int last) { int pivot = list[first]; // Choose the first element as the pivot int low = first + 1; // Index for forward search int high = last; // Index for backward search while (high > low) { // Search forward from left while (low <= high && list[low] <= pivot) low++; // Search backward from right while (low <= high && list[high] > pivot) high--; // Swap two elements in the list if (high > low) ```### ExplanationThis code snippet is an implementation of the QuickSort algorithm in C++. It consists of the following components:1. **Function Prototypes**: Declares the functions `quickSort` and `partition`.2. **Main QuickSort Function**: - The `quickSort` function is overloaded. The first version initializes the sorting process. - It calls the second `quickSort` function with starting and ending indices.3. **Recursive QuickSort Function**: - This function sorts an array recursively. - It checks if the sublist has more than one element (`last > first`). - The list is partitioned around a pivot, and the function is recursively called for subarrays.4. **Partition Function**: - Chooses a pivot element, usually the first element in this case. - Utilizes two indices `low` and `high` to traverse the list from both ends. - It swaps elements to ensure that numbers less than the pivot are on its left, and higher numbers are on its right. -

A. Analyze your algorithm, and give the results using order notation. Taking the analogical view in…

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Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

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Language: C++

Write a Program with Comments for your code to improve quick sort. The quick sort algorithm presented in the ClassNotes-Sorting, it selects the first element in the list as the pivot. Revise it by selecting the median among the first, middle, and last elements in the list.
Explain your Outputs or Answers for the following:

(A) Analyze your algorithm, and give the results using order notation.
(B) Give a list of n items (for example, an array of 10 integers) representing a scenario.
(C) Give a list of n items (for example, an array of 10 integers) representing the worst-case scenario.
(D) Give a list of n items (for example, an array of 10 integers) representing the best-case scenario.

Please compile your answers in a file including all source code with comments, Explain your running Outputs or Answers in (A) ~(D).

Examples of a quick sort from class slides is attached.

```cpp
#include <iostream>
using namespace std;

// Function prototypes
void quickSort(int list[], int arraySize);
void quickSort(int list[], int first, int last);
int partition(int list[], int first, int last);

void quickSort(int list[], int arraySize)
{
quickSort(list, 0, arraySize - 1);
}

void quickSort(int list[], int first, int last)
{
if (last > first)
{
int pivotIndex = partition(list, first, last);
quickSort(list, first, pivotIndex - 1);
quickSort(list, pivotIndex + 1, last);
}
}

// Partition the array list[first..last]
int partition(int list[], int first, int last)
{
int pivot = list[first]; // Choose the first element as the pivot
int low = first + 1; // Index for forward search
int high = last; // Index for backward search

while (high > low)
{
// Search forward from left
while (low <= high && list[low] <= pivot)
low++;

// Search backward from right
while (low <= high && list[high] > pivot)
high--;

// Swap two elements in the list
if (high > low)
```

### Explanation

This code snippet is an implementation of the QuickSort algorithm in C++. It consists of the following components:

1. **Function Prototypes**: Declares the functions `quickSort` and `partition`.

2. **Main QuickSort Function**:
- The `quickSort` function is overloaded. The first version initializes the sorting process.
- It calls the second `quickSort` function with starting and ending indices.

3. **Recursive QuickSort Function**:
- This function sorts an array recursively.
- It checks if the sublist has more than one element (`last > first`).
- The list is partitioned around a pivot, and the function is recursively called for subarrays.

4. **Partition Function**:
- Chooses a pivot element, usually the first element in this case.
- Utilizes two indices `low` and `high` to traverse the list from both ends.
- It swaps elements to ensure that numbers less than the pivot are on its left, and higher numbers are on its right.
-

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