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computer notes - Data Structures - 22
1. Class No.22 Data Structures http://ecomputernotes.com
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3. Deletion in AVL Tree Case 1a : the parent of the deleted node had a balance of 0 and the node was deleted in the parent’s left subtree. Action : change the balance of the parent node and stop. No further effect on balance of any higher node. Delete on this side http://ecomputernotes.com
4. Deletion in AVL Tree Here is why; the height of left tree does not change. 1 2 3 4 5 6 7 0 1 2 http://ecomputernotes.com
5. Deletion in AVL Tree Here is why; the height of left tree does not change. 1 2 3 4 5 6 7 2 3 4 5 6 7 0 1 2 remove(1) http://ecomputernotes.com
6. Deletion in AVL Tree Case 1b : the parent of the deleted node had a balance of 0 and the node was deleted in the parent’s right subtree. Action : (same as 1a ) change the balance of the parent node and stop. No further effect on balance of any higher node. Delete on this side http://ecomputernotes.com
7. Deletion in AVL Tree Case 2a : the parent of the deleted node had a balance of 1 and the node was deleted in the parent’s left subtree. Action : change the balance of the parent node. May have caused imbalance in higher nodes so continue up the tree. Delete on this side http://ecomputernotes.com
8. Deletion in AVL Tree Case 2b : the parent of the deleted node had a balance of -1 and the node was deleted in the parent’s right subtree. Action : same as 2a: change the balance of the parent node. May have caused imbalance in higher nodes so continue up the tree. Delete on this side http://ecomputernotes.com
9. Deletion in AVL Tree Case 3a : the parent had balance of -1 and the node was deleted in the parent’s left subtree, right subtree was balanced. http://ecomputernotes.com
10. Deletion in AVL Tree Case 3a : the parent had balance of -1 and the node was deleted in the parent’s left subtree, right subtree was balanced. Action : perform single rotation, adjust balance. No effect on balance of higher nodes so stop here. Single rotate http://ecomputernotes.com
11. Deletion in AVL Tree Case 4a : parent had balance of -1 and the node was deleted in the parent’s left subtree, right subtree was unbalanced. http://ecomputernotes.com
12. Deletion in AVL Tree Case 4a : parent had balance of -1 and the node was deleted in the parent’s left subtree, right subtree was unbalanced. Action : Double rotation at B. May have effected the balance of higher nodes, so continue up the tree. rotate double
13. Deletion in AVL Tree Case 5a : parent had balance of -1 and the node was deleted in the parent’s left subtree, right subtree was unbalanced. http://ecomputernotes.com
14. Deletion in AVL Tree Case 5a : parent had balance of -1 and the node was deleted in the parent’s left subtree, right subtree was unbalanced. Action : Single rotation at B. May have effected the balance of higher nodes, so continue up the tree. rotate single
15. Other Uses of Binary Trees Expression Trees http://ecomputernotes.com
19. Parse Tree for an SQL query Consider querying a movie database Find the titles for movies with stars born in 1960 The database has tables StarsIn(title, year, starName) MovieStar(name, address, gender, birthdate) SELECT title FROM StarsIn, MovieStar WHERE starName = name AND birthdate LIKE ‘%1960’ ; http://ecomputernotes.com
20. SQL Parse Tree < Query > SELECT <SelList> FROM <FromList> WHERE <Condition> <Attribute> <RelName> , <FromList> AND title StarsIn <RelName> <Condition> <Condition> <Attribute> = <Attribute> <Attribute> LIKE <Pattern> starName name birthdate ‘%1960’ MovieStar http://ecomputernotes.com
21. Compiler Optimization Common subexpression: (f+d*e)+((d*e+f)*g) f e + d g * + + d * * e f http://ecomputernotes.com
![Deletion in AVL Tree ,[object Object],[object Object],[object Object],http://ecomputernotes.com](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)