Right Rotation

Exercise III

Consider the following BST:

Exercise Insert the value $3$ and apply a structural rotation to balance the BST if needed.


Let’s observe the original BST is balanced:

Here is the BST after insertion:

Notice the violation of balance property occurs in the great grand parent of the inserted node. From the perspective of the great grand parent node, the problem is caused in left child’s left subtree. This is the pattern which requires a (single) right rotation. However, this case is a bit tricky:

When you bring $7$ to be the parent of $14$, the latter needs to go to the right of $7$. However, $11$ is already to the right of $7$. So we need to attach $11$ to the left of $14$ (where $7$ used to be).