Single Rotation


Consider inserting the values $3, 5, 7$ in that order.

We start by inserting $3$:

We have a BST with a single node; it is balanced!

Next, we insert $5$.

Now our BST has two nodes. Notice the height and balance factor of the root has changed (and it is still balanced).

Next, we insert $7$.

Our BST has three nodes now. Notice the heights and balance factors of the parent and grand parent of $7$ have changed. In particular, the grand parent (the root) is not balanced anymore!

However, if we were to push $3$ to the left of $5$, we would restore balance:

This is called a (single) left rotation:

Notice the violation of balance property occurred in the grand parent of the newly inserted node. From the perspective of the grand parent node, the problem was caused in right child’s right subtree. The solution is a (single) left rotation to bring the parent node (median value) above the grand parent (high value).