## Exercise II

Consider the following BST:

Exercise Remove the value $13$ and apply a structural rotation to balance the BST if needed.

## Solution

Let’s observe the original BST is balanced:

Here is the BST after removal:

Notice the violation of balance property occurs in the parent of node which was removed. From the perspective of the parent node, __the problem is caused in left child’s right subtree. (the highlighted nodes)__ This is the pattern which requires (double) left-right rotation to rebalance.

So we perform a left rotation to bring $10$ above $9$ (to bring the median value on a level between the low and high values):

And then a right rotation to bring $10$ above $12$ (to bring the median value on a level above the low and high values):