Question

Build an AVL tree for the following collection of numbers in the given order. Show the balance factor for each node. 20, 40, 80, 60, 55, 11, 99, 77,33

Answer 1

• Insertion an element into AVL tree is similar to that of BST. The balance factor (= height of left subtree - height of right subtree of the node) are calculated and if any of the nodes have a balance factor greater than 1, we need to perform rotation to restore the AVL tree.
• To perform rotation, it is necessary to identify a specific node A, whose Balance factor (BF) is neither -1 , 0 or 1 and which is nearest ancestor to the inserted node on the path from the inserted node to the root of the tree.
• There are 4 types of rotation:
  • LL - Inserted node is in the left subtree of the left subtree of the root
  • RR - Inserted node is in the right subtree of the right subtree of the root
  • LR - Inserted node is in the right subtree of the left subtree of the root
  • RL - Inserted node is in the left subtree of the right subtree of the root
• LL and RR rotations are called single rotation whereas RL and LR are known as double rotations. LR comprises of RR followed by LL and RL comprises of LL followed by RR.

AVL tree after inserting : 20, 40, 80, 60, 55, 11, 99, 77 , 33:

Step 1: Insert 20 Since AVL Tree in empty, make 20 as the root Tree (20) Step 2: Insert 40 Since 40720, it is inserted subtree of zo. in the right Step 3: Insest so since so > 40, it in Subtree of 40. inserted in the right

since balance factor (BF) of 20 =-2 because so has been insested cuchich is in the right subtree of right subtree of 200, t balance we will do RR rotations, Step 4: Insest 60 SO Steps: Insert ss

Since Br of so = 2 because 55 has been inserted (which is in the left subtree of left subtree of sol. So to balance we will do L L' rotation Step 6: Insert L Step 7: Insert 99

Step 8: Insert 77 + Step 9: Insest 33 Final AVL free! 10300