Question 4 Tutorial 8
Tutorial 8
Dec 30, 2015
Tutorial 8. Question 4. Part A. Insert 20, 10, 15, 5 ,7, 30, 25, 18, 37, 12 and 40 in sequence into an empty binary tree. 20. 10. 30. 25. 37. 5. 15. 40. 7. 12. 18. Part B. Part B requires us to determine the new BST after each delete operation. - PowerPoint PPT Presentation
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Question 4
Tutorial 8
Part AInsert 20, 10, 15, 5 ,7, 30, 25, 18, 37, 12 and 40 in
sequence into an empty binary tree.
20
15
12
18
25
10
37
5
7
30
40
Part BPart B requires us to determine the new BST
after each delete operation.3 cases to consider when deleting a node
from a BSTCase 1: Leaf node (no children)Case 2: Node has 2 childrenCase 3: Node has only one child
Delete 30 from the BST30 has 2 childrenReplace node with inorder successor of 30, which is 37.
20
15
12
18
25
10
37
5
7
30
40
20
15
12
18
25
10
37
5
7
40
Delete 10 from BST10 has two children.Replace with inorder successor, which is 12
20
15
12
18
25
10
37
5
7
40
20
15
12
18
25
37
5
7
40
Delete 15 from BST15 currently has one child, 18.So just replace 15 with 18.
20
15
12
18
25
37
5
7
40
20
12
18
25
37
5
7
40
Part C :Is the binary tree full ???
A full binary tree is a tree where all nodes other than leaves have 2 children, and all leaves are at the same height.
Tree is not full.
20
12
18
25
37
5
7
40
Part C :Is the Binary Tree Complete ???
A binary tree is complete when all levels except POSSIBLY the last is completely filled, and the nodes are filled from left to right.
This tree is not complete.
20
12
18
25
37
5
7
40
If we delete 7
The resultant tree is both full and complete.
20
12
18
25
37
5
7
40
After deleting 7, if We add 4
Resulting tree is not full.However, the tree is complete.
20
12
18
25
37
5
40
4
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