RL Rotation

RL rotations is to be performed if the new node is inserted into the left of right sub-tree of the critical node A. Let us consider, Node B is the root of the right sub-tree of the critical node, Node C is the root of the sub-tree in which the new node is inserted.

Let T1 be the left sub-tree of the critical node A, T2 and T3 be the left and right sub-tree of Node C respectively, sub-tree T4 be the right sub-tree of Node B.

Since, RL rotation is the mirror image of LR rotation. In this rotation, the node C becomes the root node of the tree with A and B as its left and right children respectively. Sub-trees T1 and T2 becomes the left and right sub-trees of A whereas, T3 and T4 becomes the left and right sub-trees of B.

The process of RL rotation is shown in the following image.

Example

Insert node with the value 92 into the tree shown in the following figure.

Solution :

inserting 92 disturbs the balance factor of the node 92 and it becomes the critical node A with 105 as the node B and 95 with

the node C. In RL rotation, C becomes the root of the tree (as shown in the figure) with node A (90) and B (105) as its left and right children respectively. The tree will be rotated as shown in the figure.