1. Non-Linear Structures
Trees

2. A Tree Structure - Each node may have multiple child nodes.
President
VP - Mktg
VP - Oper
VP - Sales
CIO
Sales Mgr.
A Tree Structure - Each node may have multiple child nodes.
Show parent/child relationship

3. data
data
data
data
data
data
data
data
data
data
data
data
The height of this tree is 4.
Balanced Tree – The depth of all nodes differs by no more than one.
Full Tree – Every node (except leaves) has two children.
Complete Tree – All levels, except the last one, are full.
data
data
data
data

4. Building a Binary Search Tree
Incoming values: 70, 23, 90, 47, 88, 52, 17, 99, 35, 28, 65, 55, 1, 41, 87 70 23 90 17 47 88 99 1 35 52 87 28 41 65 55

5. BTNode
- data : Object
- left : BTNode
- right : BTNode
+ createBTNode()
+ getData() : Object
+ setData() : void
+ getLeft() : BTNode
+ setLeft() : void
+ getRight(): BTNode
+ setRight(): void

6. Generally, the procedure is the same as for adding a node to the tree.
Follow the path until you run into a node with the value you're searching for.
If you reach a null pointer, the value doesn't exist in the tree.
Searching a BST

7. 70 23 90 47 88 52 17 99 35 28 65 55 1 41 87
Searching a BST

8. Deleting a Node from a BST
After deletion, the tree still must qualify as a BST.
Three different cases:
The node to be removed is a leaf.
The node to be removed has one child.
The node to be removed has two children.
Deleting a Node from a BST

9. Deleting – Case 1 70 23 90 47 88 52 17 99 35 28 65 55 1 41 87
Delete node containing 1

10. Deleting – Case 2 70 23 90 17 47 88 99 35 52 87
Delete node containing 88. 28 41 65 55

11. Deleting – Case 3 70 23 90 17 47 87 99 35 52 Delete node containing 4728 41 65 55

12. Deleting – Case 3 (Step 1) 70 23 90 17 41 87 99 35 52 28 47 65 55

13. Deleting – Case 3 (Step 2) 70 23 90 17 41 87 99 35 52 28 65 55

14. BST Deletion Algorithm
Find the node with the value to be deleted (n1).
If it's a leaf Delete the node.
If it has one child Assign a reference to n1's child to n1's parent.
If it has 2 children Find the node with the highest value in the left sub-branch (n2). Swap the values of n1 and n Call delete recursively to remove the original value.
BST Deletion Algorithm

15. BST Methods insert – Inserts a node at the proper location.
delete – Deletes a node based on a key. Returns true if the node deleted, and false if the key not found.
find – Finds a node based on a key, and returns the data object found in the node. Returns null if the key is not found.
clear – Empties the tree of all nodes.
BST Methods