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Tutorial 8

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.

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Tutorial 8

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  1. Tutorial 8 Question 4

  2. 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

  3. Part B • Part B requires us to determine the new BST after each delete operation. • 3 cases to consider when deleting a node from a BST • Case 1: Leaf node (no children) • Case 2: Node has 2 children • Case 3: Node has only one child

  4. Delete 30 from the BST • 30 has 2 children • Replace node with inorder successor of 30, which is 37. 20 20 10 10 37 30 25 25 37 5 5 15 15 40 40 7 7 12 12 18 18

  5. Delete 10 from BST • 10 has two children. • Replace with inorder successor, which is 12 20 20 10 12 37 37 25 25 5 5 15 15 40 40 7 7 12 18 18

  6. Delete 15 from BST • 15 currently has one child, 18. • So just replace 15 with 18. 20 20 12 12 37 37 25 25 5 5 15 40 40 18 7 7 18

  7. 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 37 25 5 40 18 7

  8. 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 37 25 5 40 18 7

  9. If we delete 7 • The resultant tree is both full and complete. 20 12 37 25 5 40 18 7

  10. After deleting 7, if We add 4 • Resulting tree is not full. • However, the tree is complete. 20 12 37 25 40 18 5 4

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