Is the tree above an AVL tree Yesno Explain reasons If the t

Is the tree above an AVL tree? (Yes/no) Explain (reasons): If the tree above is an AVL tree, then leave it alone; otherwise, make it an AVL tree. Create a binary search tree, from an empty one, by adding the key values from a, b, c, ... j alphabetical work.

Solution

3. It is not an AVL tree

3a) If we calculate the Balace Factor of the Root of the tree T: height(T.left) - height(T.right)

0-2 = -2

for an AVL tree to be true the absolute value of Balace Factor should be always no more than 1.

  I.e. |BalanceFactor(T)| 1

3b) To make it AVL we need to perform rotations in this perticular case the RL rotation on the right branch of the tree

so, the tree becomes

5

4 14

10 17

so, the BF is -1 so it is the AVL tree.

thanks please comment below for any further clarification