1. Data Structures: Binary Search Trees
By: A. H. Abdul Hafez
DS, by Dr. A.H. Abdul Hafez, CE Dept. HKU
January 1, 2019

2. Outlines Dictionary Definition of a binary search tree
Operations on BST
Search
Insert
Delete
End
DS, by Dr. A.H. Abdul Hafez, CE Dept. HKU
January 1, 2019

3. Dictionary
An abstract data type that support operations insert, delete, and search is called a dictionary. It has applications in a numerous algorithms.
Comparison methods vs. direct access methods. Binary search tree is example of the former while hashing tables are example of the later.
Example: Application to search n a library.
DS, by Dr. A.H. Abdul Hafez, CE Dept. HKU
January 1, 2019

4. Definition of Binary Search Trees BSTs
DS, by Dr. A.H. Abdul Hafez, CE Dept. HKU
January 1, 2019

5. Operations on BSTs
BST support the operations search, insert, and delete; both by key value and by rank.
By key values: find en element with key = x. insert after key=x, and delete element with key=x.
By rank: find the fifth smallest element, delete …., insert and determine the rank.
Tree in (a) is not BST
DS, by Dr. A.H. Abdul Hafez, CE Dept. HKU
January 1, 2019

6. Searching a BST Recursive search of a binary search tree.
DS, by Dr. A.H. Abdul Hafez, CE Dept. HKU
January 1, 2019

7. Searching a BST Iterative search of a binary search tree.
DS, by Dr. A.H. Abdul Hafez, CE Dept. HKU
January 1, 2019

8. Searching a BST Searching a binary search tree by rank.
DS, by Dr. A.H. Abdul Hafez, CE Dept. HKU
January 1, 2019

9. Insertion into a BST
To insert an element x, we must first verify that its key is different from those of existing elements.
To do this, a search is carried out. If the search is unsuccessful, then the element is inserted at the point the search terminated.
DS, by Dr. A.H. Abdul Hafez, CE Dept. HKU
January 1, 2019

10. Insertion into a BST DS, by Dr. A.H. Abdul Hafez, CE Dept. HKU
January 1, 2019

11. Deletion from a BST
To delete a leaf node, set the left/right-child field of its parent to 0.
To delete non-leaf element that has only one child, change the pointer from the parent node to the single child node.
DS, by Dr. A.H. Abdul Hafez, CE Dept. HKU
January 1, 2019

12. The end of the Lecture Thanks for your time Questions are welcome
DS, by Dr. A.H. Abdul Hafez, CE Dept. HKU
January 1, 2019