Implementing Merge Sort with Vectors and Exception Handling

Introduction to Merge Sort:

Merge Sort is a divide$-$and$-$conquer sorting algorithm that divides an array $($or vector$)$ into two

halves, recursively sorts each half, and then merges the sorted halves to produce a fully sorted

array. This algorithm is efficient for large datasets.

In this exercise, you will implement the Merge Sort algorithm while working with vectors and

handling exceptions. The exercise includes several functions to manage vector operations and

the implementation of Merge Sort for sorting a vector of integers.

Your Tasks:

$1)$ Create a function populateVector$($std::vector& vec, int n$)$:

This function should take a reference to a std::vector and an integer n$.$

Populate the vector with n random integers between $1$ and $100.$

$2)$ Create a function printVector$($const std::vector& vec$)$:

Takes a constant reference to a std::vector.

Prints its elements.

$3)$ Create a function int getElement$($const std::vector& vec, int index$)$:

Tries to access the element at the specified index in the vector.

Throws an std::out$\_$of$\_$range exception with a suitable error message if the index is out

of bounds.

$4)$ Write a function mergeSort$($std::vector& vec, char direction$)$:

Implement the Merge Sort method to sort the vector in the specified direction $(\text{'}$a$\text{'}$ for

ascending, $\text{'}$d$\text{'}$ for descending$).$ Use the at$()$ function to access elements and include try$-$

catch blocks to handle exceptions. Then, display the result.

$5)$ In your main$()$ function:

a$)$ Read numbers from a file, ask the user how they would like to sort the numbers $($in

ascending or descending order$),$ sort them, and display the result.

b$)$ Prompt the user to enter the size for creating a new vector and display it$.$

c$)$ Ask the user to enter an index to retrieve an element value from this new vector. Use

try$-$catch blocks to handle any potential exceptions thrown when accessing the vector

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