A vector is an Abstract Data Type $($ADT$)$ that offers the following functions: $$ size $()$

$$ empty $()$

$$ at $($i$)$ returns the element at index i $$ set $($i$,$ e$)$ replaces the element at index with value e $$ insert $($i$,$ e$)$ inserts value e at index i $$ erase $($i$)$ removes the element at index i

Other C$++$ STL containers are the following: $$ list $$ stack $$ queue $$ priority$\_$queue $$ deque $$ set $$ map

STL vector $$ is a C$++$ container, which is a collection of elements.

#include

using std::vector

vector myVector $(100)$;

STL vector is similar to a C$++$ array with the following additions:

$1.$ uses indexing $([])$ to access vector elements but checks if index is within the array

index range.

$2.$ STL vectors can be dynamically resized to add or remove elements.

$3.$ STL destruction automatically invokes the destructor for each of the elements.

$4.$ Offers functions that operate on the entire vector $($not just elements$),$ like copying

and comparing entire vectors, or inserting and erasing multiple elements.

Methods: $$ vector $($n$)$ : constructor. Creates a vector of n elements. An empty vector is

created if no argument is present. $$ size $()$ : returns the number of elements in the vector.

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$$ empty $()$ : true if the vector is empty.

$$ resize $($n$)$ : resizes the vector so that it can hold n elements.

$$ reserve $($n$)$ : allocated storage space should be able to hold n elements.

$$ at $($i$)$ : returns a reference to the element at index i but also checks if index i is

within the correct bounds of the vector.

$$ front $()$ : returns a reference to the first element of the vector.

$$ back $()$ : returns a reference to the last element of the vector.

$$ push$\_$back $($e$)$ : adds a copy of element e at the end of the vector.

$$ pop$\_$back $()$ : removes the last element of the vector.

Use the C$++$ STL vector to solve the following two exercises:

$1.$ Devise a C$++$ program that uses each of the above methods for a vector of

integers. Display the results after every method call.

$2.$ Implement bubble sort to sort the vector of integers.

$3.$ Given N decimal numbers, find the mean, maximum, minimum. Your program

will first ask for N$,$ the number of integers in the list, which the user will input.

Then the user will input N more numbers. Use vector to store the numbers.

Submit the main program with comprehensive tests.