1. Binary Search Tree (BST)

2. Binary Search Tree (BST)
Definition:
“A BINARY SEARCH TREE is a binary tree in symmetric order.”
A binary tree is either:
empty
a key-value pair and two binary trees
[neither of which contain that key]

3. Binary Search Tree (BST)
Symmetric order means that:
every node has a key
every node’s key is
larger than all keys in its left subtree
smaller than all keys in its right subtree

4. Difference between BT & BST
A binary tree is simply a tree in which each node can have at most two
children. Typically the first node is known as the parent and the child
nodes are called left and right.
A binary search tree is a binary tree in which the nodes are assigned
values, with the following restrictions ; 
No duplicate values
Left child node is smaller than its parent Node
Right child node is greater than its parent Node BT
BST

5. Binary Search Tree a b c d e g h i l f j k

6. Binary Search Tree Operations
Creating a binary search tree
Finding a node in a binary search tree
Inserting a node into a binary search tree
Deleting a node in a binary search tree
Traversing a binary search tree.

7. Creating a Binary (Search) Tree
We will use a simple class that implements a binary tree to store integer values
We create a class called IntBinaryTree

8. A Node of BST

9. Finding a node in a binary search tree
Find ( root, 2 )

10. Code

12. Inserting a node into a BST
If a tree or sub-tree does not exist, create a node and insert the value in it.
If the value we are inserting is less than the root of the tree we move to the left sub-tree and start at step 1 again.
If the value is greater than the root of the tree we move to the right sub-tree and start at step 1 again.
If the value is equal to the root of the tree or sub- tree we do nothing because the value is already there. In this case we return.

13. Example

14. Code

15. Deleting a Node in BST Algorithm Observation
Perform search for value X
If X is a leaf, delete X
Else // must delete internal node
Replace with largest value Y on left subtree
OR smallest value Z on right subtree
Delete replacement value (Y or Z) from subtree
Observation
Deletions may unbalance tree

16. Example Deletion (Leaf)

17. Example Deletion (Internal Node)

18. Traversal of Binary Trees
Inorder Traversal (symmetric traversal)
Preorder Traversal (depth first traversal)
Postorder Traversal

19. InOrder Traversal
Manner:
Left Root Right
Sorted

20. Code

21. InOrder ‘2’ ‘3’ ‘4’ ‘+’ ‘*’ What value does it have?
( ) * 3 = 18

22. PreOrder Traversal
Manner
Root Left Right

23. Code

24. PostOrder Traversal
Manner
Left Right Root

25. Code