This document discusses AVL trees, a self-balancing binary search tree. AVL trees were invented in 1962 by two Russian mathematicians, Adelson-Velskii and Landis. The heights of the left and right subtrees of any node in an AVL tree cannot differ by more than one. The document covers AVL tree rotations, including single, double, left and right rotations. It also discusses the algorithms for AVL tree insertion and balancing the tree during insertion to maintain the height difference property.

1. Advanced Data StructuresMphil AVL TreesJibrael Jos : Nov2009

2. AVLRotate Right / LeftSimple DoubleComplex RotateRotate AlgoDouble RotateAvoid Taking Printout : Use RTF Outline in case needed2Agenda

3. AVL Trees1962 – Two Russian MathematiciansAdelson-Velskii and LandisHeights of Subtree do not defer by more than oneAvoid Taking Printout : Use RTF Outline in case needed3

4. AVL Trees - WhyAvoid Taking Printout : Use RTF Outline in case needed41814Unbalanced BST Tree128812441418AVL

5. AVL – Rotate RightPlease Do Not Take Printout : Use RTF Outline in case needed51284

6. AVL – Rotate LeftPlease Do Not Take Printout : Use RTF Outline in case needed64812

7. Complex RightPlease Do Not Take Printout : Use RTF Outline in case needed71820128144

8. Complex LeftPlease Do Not Take Printout : Use RTF Outline in case needed88144181220

9. Complex Right - AlgoPlease Do Not Take Printout : Use RTF Outline in case needed918RootResult Should Be12tempPtr1218881414

10. Complex Right - AlgoPlease Do Not Take Printout : Use RTF Outline in case needed10tempPtr = root -> leftRoot -> left = tempPtr -> righttempPtr -> right = rootRoot = tempPtrreturn18Root12tempPtr814

11. Simple Double Rotate RightPlease Do Not Take Printout : Use RTF Outline in case needed11124Step 1 : 8

12. Simple Double Rotate RightPlease Do Not Take Printout : Use RTF Outline in case needed12128Step 2 : 4

13. AVL NodeNodeKeyDataleftRightBal (RH , LH , EH)End NodeAvoid Taking Printout : Use RTF Outline in case needed13

14. AVL Insert / TranscriptIn linked list we did search and then insertBut here we need to adjust balance and may have to adjust tree not only at the point of insertion but all the way upWe set taller flagLet prev module decide as we back out of recursionsAvoid Taking Printout : Use RTF Outline in case needed14

15. AVL InsertPlease Do Not Take Printout : Use RTF Outline in case needed156050EHOther Node already inserted13EH18LH1220EHEH814EHEHDifferent stages of a node visit ?

16. Flow ChartPlease Do Not Take Printout : Use RTF Outline in case needed16RecursionIf tree is tallerIf LH and we inserted on leftYesYesBalanceNoNoYesIf RH and we inserted on right

17. AVL INSERT ALGOIf root is null Taller = true Root = newPtrelse If insert on left “ < “ AVL Insert (root -> left) if taller if LH do left balance else if root is RH taller=false adjust balance factorAvoid Taking Printout : Use RTF Outline in case needed17When will it not be taller ?

18. AVL left BalanceleftTree= root - >leftIf leftTree is LH Case 1: left of left : single rotateElseCase 2: right of left : Double RotationrightTree=leftTree->rightAdjust balance for Right TreerotateLeft(leftTree)rotateRight(root)Taller = falsereturnAvoid Taking Printout : Use RTF Outline in case needed18

19. FlowPlease Do Not Take Printout : Use RTF Outline in case needed19

20. ReferenceMy CourseFurzonPlease Do Not Take Printout : Use RTF Outline in case needed20Action ItemSelf Learning