Note: All programs must use the appropriate C$++$ features.

Objective:

Enhance the provided Treap class to incorporate additional functionalities that will help in

understanding the use of augmented data structures in tree$-$based algorithms and OOP

principles.

Tasks:

You are provided with a basic implementation of a Treap class that includes methods for

insertion, deletion, search, etc. Your task is to modify the Treap class so that

each node can keep track of the sum of keys of nodes under this node, including

itself. Then, print the sum for each node.

For example, nodes under node $20$ include node $10,22,5$ and $12.$

each node can keep track of the count of all nodes under this node, including itself.

Then, print the count for each node.

Add a new function to the Treap class to return the count of nodes without children

$($leaf nodes$).$ Then, print this count.

Add a new function to the Treap class to return the count of nodes with only one

child. Then, print this count.

Add a new function to the Treap class to return the count of nodes with two

children. Then, print this count.

Input & Output:

You need to provide test cases in the main function to test each additional functionality.

Submit:

$1,$ all C$++$ source code

$2,$ week$10.$txt: a txt file contains all the source code.

$3,$ week$10.$docx or week$10.$pdf$,$ this document should include

the screenshot of printing the treap, with key and priority

the screenshots for each of these five tasks.