Tree Operations
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The document discusses algorithms for inserting and deleting nodes from binary search trees. It covers three cases for node deletion: (1) when the node to be deleted is a leaf, (2) when the node has one child, and (3) when the node has two children. For case 1, the leaf node is simply removed. For case 2, the child of the node replaces it. For case 3, the node is replaced with its inorder successor. The document also discusses inserting nodes by comparing values and placing new nodes in the appropriate position to maintain the binary search tree structure.
Tree Operations
- 1. TREE-OPERATIONS ASADULLAH TAREEN asadullah.tareen@gmail.com Ghazni University Computer Science Department ©Sem-II-2017 ALGORITHM & DATA- STRUCTURE
- 2. Outline This Topic Will Cover Tree Operations: 1. Insertion of a Node into a tree 2. Deletion of a Node from a tree Cases: 2.1 Case: The node to be deleted is a leaf 2.2 Case: The node to be deleted has 1 child 2.3 Case: The node to be deleted has 2 children Tree Operations 27-Sep-2017 2Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 3. Insert Node Given a Sorted List 5 8 9 13 21 44 45 46 1.1 Tree Operations 27-Sep-2017 3Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 4. Insert Node Given a Sorted List 5 8 9 13 21 44 45 46 If 14 is inserted, the list become: 5 8 9 13 14 21 44 45 46 1.1 Tree Operations 27-Sep-2017 4Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 5. Insert Node Given a Sorted List 5 8 9 13 21 44 45 46 If 14 is inserted, the list become: 5 8 9 13 14 21 44 45 46 1.1 Tree Operations 27-Sep-2017 5Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 6. Insert Node Given a Sorted List 5 8 9 13 21 44 45 46 If 14 is inserted, the list become: 5 8 9 13 14 21 44 45 46 FEATURES OF A SORTED LIST IS PRESERVED 1.1 Tree Operations 27-Sep-2017 6Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 7. Insert Node Given a Sorted List 5 8 9 13 21 44 45 46 If 14 is inserted, the list become: 5 8 9 13 14 21 44 45 46 Features of a Sorted List is Preserved So WHAT ARE THE FEATURES OF A SORTED LIST ???? 1.1 Tree Operations 27-Sep-2017 7Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 8. Insert Node Given a BST 1.1 Tree Operations 27-Sep-2017 8Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 9. Insert Node Given a BST 1.1 Tree Operations 64 33 88 7 99 10 27-Sep-2017 9Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 10. Insert Node Given a BST If 14 to be inserted 1.1 Tree Operations 64 33 88 7 99 10 27-Sep-2017 10Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 11. Insert Node Given a BST If 14 to be inserted 1.1 Tree Operations 64 33 88 7 99 10 How does the new BST look like ? 27-Sep-2017 11Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 12. Insert Node Given a BST If 14 to be inserted, 1.1 Tree Operations 64 33 88 7 99 10 How does the new BST look like ? How do you do it? 27-Sep-2017 12Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 13. Insert Node Given a BST Are the features of a BST preserved??? 1.1 Tree Operations 64 33 88 7 99 10 14 27-Sep-2017 13Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 14. Insert Node Algorithm to Insert 14 1.1 Tree Operations 64 33 88 7 99 10 27-Sep-2017 14Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 15. Insert Node Algorithm to Insert 14 1.1 Tree Operations 64 33 88 7 99 10 14 < 64? 27-Sep-2017 15Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 16. Insert Node Algorithm to Insert 14 1.1 Tree Operations 64 33 88 7 99 10 14 < 10? 27-Sep-2017 16Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 17. Insert Node Algorithm to Insert 14 1.1 Tree Operations 64 33 88 7 99 10 14 < 33? 27-Sep-2017 17Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 18. Insert Node Algorithm to Insert 14 1.1 Tree Operations 64 33 88 7 99 10 NULL 27-Sep-2017 18Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 19. Insert Node Algorithm to Insert 14 1.1 Tree Operations 64 33 88 7 99 10 Insert here 14 27-Sep-2017 19Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 20. Insert Node Algorithm to Insert 14 1.1 Tree Operations 64 33 88 7 99 10 14 27-Sep-2017 20Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 21. Insert Node Now try to Insert 99 1.1 Tree Operations 64 33 88 7 99 10 14 99 < 64 ? 27-Sep-2017 21Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 22. Insert Node Now try to Insert 99 1.1 Tree Operations 64 33 88 7 99 10 14 99 < 88? 27-Sep-2017 22Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 23. Insert Node Now try to Insert 99 1.1 Tree Operations 64 33 88 7 99 10 14 99 < 99 ? 27-Sep-2017 23Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 24. Insert Node This algorithm is not so effective Try building a BST using the Same algorithm for the following Sequence: K N G I C U K U C I N G C G I K N U 1.1 Tree Operations 27-Sep-2017 24Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 25. Insert Node ALKHWARIZMI: • Inserting Node in such algorithm is less effective (insert algorithms described above to the following sequence:) K N G I C U K U C I N G C G I K N U 1.1 Tree Operations 27-Sep-2017 25Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 26. Insert Node This algorithm is not so effective Try building a BST using the Same algorithm for the following Sequence: K N G I C U K U C I N G C G I K N U It is difficult to produce a balanced Tree One way is using the AVL Tree algorithm 1.1 Tree Operations 27-Sep-2017 26Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 27. Insert Node • Try to develop PGD ( Proper Generalized Decompositions) use insert algorithms described above to the following sequence: K N G I C U K U C I N G C G I K N U • It is difficult to produce a balanced Tree • one way is using the AVL Tree algorithm 1.1 Tree Operations 27-Sep-2017 27Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 28. Delete Node 3 Cases: I. The node to be deleted is a leaf II. The node to be deleted has 1 child III. The node to be deleted has 2 children 2 Tree Operations 27-Sep-2017 28Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 29. Delete Node (1st Case) To delete D: 2.1 Tree Operations M E D P B VN T ZA 27-Sep-2017 29Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 30. Delete Node (1st Case) To delete D: 2.1 Tree Operations M E D P B VN T ZA 27-Sep-2017 30Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 31. Delete Node (1st Case) To delete D: 2.1 Tree Operations M E D P B VN T ZA Parent 27-Sep-2017 31Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 32. Delete Node (1st Case) To delete D: 2.1 Tree Operations M E D P B VN T ZA Parent x 27-Sep-2017 32Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 33. Delete Node (1st Case) To delete D: 2.1 Tree Operations M E D P B VN T ZA Parent x Set the right child of Parent as null 27-Sep-2017 33Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 34. Delete Node (1st Case) To delete D: 2.1 Tree Operations M E D P B VN T ZA Parent x Set the right child of Parent as null Free X 27-Sep-2017 34Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 35. Delete Node (1st Case) To delete D: 2.1 Tree Operations M E P B VN T ZA Parent x Set the right child of Parent as null Free X 27-Sep-2017 35Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 36. Delete Node (2nd Case) To delete E: 2.2 Tree Operations M E D P B VN T ZA 27-Sep-2017 36Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 37. Delete Node (2nd Case) To delete E: 2.2 Tree Operations M E D P B VN T ZA 27-Sep-2017 37Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 38. Delete Node (2nd Case) To delete E: 2.2 Tree Operations M E D P B VN T ZA x Parent Set the Lchild (@ Rchild) of x as the Lchild (@ Rchild) of parent 27-Sep-2017 38Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 39. Delete Node (2nd Case) To delete E: 2.2 Tree Operations M E D P B VN T ZA x Parent Set the Lchild (@ Rchild) of x as the Lchild (@ Rchild) of parent 27-Sep-2017 39Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 40. Delete Node (2nd Case) To delete E: 2.2 Tree Operations M E D P B VN T ZA x Parent Set the Lchild (@ Rchild) of x as the Lchild (@ Rchild) of parent Free x 27-Sep-2017 40Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 41. Delete Node (2nd Case) To delete E: 2.2 Tree Operations M D P B VN T ZA Parent Set the Lchild (@ Rchild) of x as the Lchild (@ Rchild) of parent Free x 27-Sep-2017 41Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 42. Delete Node (2nd Case) To delete E: 2.2 Tree Operations M D PB VN T Z A Parent Set the Lchild (@ Rchild) of x as the Lchild (@ Rchild) of parent Free x 27-Sep-2017 42Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 43. Delete Node (3rd Case) To delete P: 2.3 Tree Operations M E D P B VN T ZA 27-Sep-2017 43Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 44. Delete Node (3rd Case) To delete P: 2.3 Tree Operations M E D P B VN T ZA Parent x 27-Sep-2017 44Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 45. Delete Node (3rd Case) To delete P: 2.3 Tree Operations M E D P B VN T ZA Parent xDetermine the next node based on Inorder(LNR) *Usually, the Inorder node has only one child or no children at all 27-Sep-2017 45Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 46. Delete Node (3rd Case) To delete P: 2.3 Tree Operations M E D P B VN T ZA Parent xDetermine the next node based on Inorder(LNR) y Parent of y 27-Sep-2017 46Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 47. Delete Node (3rd Case) To delete P: 2.3 Tree Operations M E D P B VN T ZA Parent x y Parent of y Copy x->data = y->data 27-Sep-2017 47Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 48. Delete Node (3rd Case) To delete P: 2.3 Tree Operations M E D P B VN T ZA Parent x y Parent of y Copy x->data = y->data x = y 27-Sep-2017 48Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 49. Delete Node (3rd Case) To delete P: 2.3 Tree Operations M E D P B VN T ZA Parent x y Parent of y Delete T 27-Sep-2017 49Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 50. Delete Node (3rd Case) To delete P: 2.3 Tree Operations M E D P B VN T ZA Parent x y Parent of y Delete T (as in case 1) parent_y->Lchild = NULL 27-Sep-2017 50Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 51. Delete Node (3rd Case) To delete P: 2.3 Tree Operations M E D P B VN T ZA Parent y Parent of y Delete T (as in case 1) parent_y->Lchild = NULL 27-Sep-2017 51Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 52. Delete Node (3rd Case) To delete P: 2.3 Tree Operations M E D T B VN ZA Parent Parent of y Delete T (as in case 1) parent_y->Lchild = NULL 27-Sep-2017 52Lecturer: Asadullah Tareen Ghazni University Computer Science Department
- 53. Your ? 27-Sep-2017 53Lecturer: Asadullah Tareen Ghazni University Computer Science Department