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## Programming Assignment 8 Removing in a Binary Search Tree

### Due: Saturday, Nov. 3, 11:59pm

Please see the general programming webpage for details about the programming environment for this course, guidelines for programming style, and details on electronic submission of assignments.

The files you may need for this assignment can be downloaded from the schedule page. A makefile is available here.

### Collaboration Policy

For this assignment, you must work alone.

### Contents:

For this assignment, you must implement the remove method for the Binary Search Tree class. The general idea was covered in class, and you may refer to lecture notes or the text book for assistance.

To implement remove, you will first use the find function to see if the value is in the list. If it is, there are several cases to consider.

Say that your value is in node x. If x is a leaf, you can simply delete it (using helper functions from BinaryTree.h). If x has only 1 child, you can delete it and promote that child while maintaining a binary search tree property. However, if it has two children, you need to find the next node in an inorder traveral. Call this node y. If y is a leaf, you swap the value into x's position and then delete the leaf node that contained y. If it is not a leaf, it must have only a right child (since the left child would come first in an inorder traversal), so you can delete y, promote its right child, and still put y's value into x's node.

For this assignment, you are welcome to implement any helper functions you need - just be careful to put them in a protected or private setting if they are not something an end user should have access to. More likely, you will want to use the functions provided in BinaryTree.h, both for the tree and for iterators.

Note: For simplicity, we are assuming that your trees will only store distinct elements. So if a value is inserted twice, you do not need to have it represented twice in your tree. You DO need to handle this case without crashing, however!

Write a function called TestBST.cpp which creates a binary search tree and performs inserts and removes on the tree. You are welcome to use the draw function (inherited from BinaryTree.h) to draw your tree at each step and debug your code.

Again, feel free to write other test functions - such as a function that prints the height of a node, or an inorder traversal of the tree - if that is helpful for your debugging process.

# Files We Are Providing

• BinaryTree.h and BinarySearchTree.h
These are the implementations of the Binary Tree and Binary Search Tree, from our work in class.

Note: For the sake of simplicity, we did not bother to separate out the function bodies for the class into a separate cpp files. All the function bodies are embeded directly into the header. You should make your changes directly to the .h file as well.

• makefile
This makefile should allow you to rebuild your project by simply typing 'make' rather than in invoking the compiler directly.

# Files to Submit

• Source Code
Submit your revised BinarySearchTree.h files. Note that you should not need to alter BinaryTree.h, so please let me know if you make any changes there (and explain why they are needed)!

• TestBST.cpp
A sample program that creates a binary search tree and walks through a set operations, checking that inserting and removing elements works.