computer notes - Data Structures - 22
- 1. Class No.22 Data Structures http://ecomputernotes.com
- 2. Deletion in AVL Tree There are 5 cases to consider. Let us go through the cases graphically and determine what action to take. We will not develop the C++ code for deleteNode in AVL tree. This will be left as an exercise. http://ecomputernotes.com
- 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
- 16. Expression Trees Expression trees , and the more general parse trees and abstract syntax trees are significant components of compilers. Let us consider the expression tree. http://ecomputernotes.com
- 17. Expression Tree (a+b*c)+((d*e+f)*g) a c + b g * + + d * * e f http://ecomputernotes.com
- 18. Parse Tree in Compiler Expression grammar <assign> <id> := <expr> <id> A | B | C <expr> <expr> + <term> | <term> <term> <term> * <factor> | <factor> <factor> ( <expr> ) | <id> <assign> <id> <expr> <expr> <term> <term> <term> <factor> C B * + <id> <id> A := A <id> <factor> <factor> A := A + B * C
- 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
- 22. Compiler Optimization (Common subexpression: (f+d*e)+((d*e+f)*g) f e + d g * + * Graph! http://ecomputernotes.com