Part $1$: Circular Array Implementation of Deque $(15$ points$)$

Implement the Deque Class:

Create a DequeArray class that implements a deque using a circular array.

Attributes:

arr: The array to store elements.

front: Index of the front element.

rear: Index of the rear element.

size: Current number of elements in the deque.

capacity: Maximum number of elements the deque can hold.

Methods:

is$\_$empty$()$: Check if the deque is empty.

is$\_$full$()$: Check if the deque is full.

add$\_$front$($item$)$: Add an element at the front.

add$\_$rear$($item$)$: Add an element at the rear.

remove$\_$front$()$: Remove and return the front element.

remove$\_$rear$()$: Remove and return the rear element.

get$\_$front$()$: Return the front element without removing it$.$

get$\_$rear$()$: Return the rear element without removing it$.$

Test the Implementation:

Write test cases to validate your deque implementation.

Test edge cases like adding$/$removing from an empty deque, or adding to a full deque.

Part $2$: Extended Operations $(15$ points$)$

Extend the Functionality:

Implement the following additional operations in DequeArray:

size$()$: Return the number of elements in the deque.

clear$()$: Remove all elements from the deque.

rotate$($k$)$: Rotate the deque by k elements. Positive k rotates to the right, negative k rotates to the left.

peek$\_$nth$($n$)$: Return the nth element from the front without removing it$.$ The first element has index $0.$

Analyze the Performance:

Analyze the time complexity of each operation in the DequeArray implementation.