Max. number of rotations while inserting a new element into n-element red black tree

Question

What is the maximum number of rotations while inserting a new element into n-element Red Black Tree?

If I'm correct, insertion that does not violate rules of RBT requries maximum of 2 rotations (2 cases). Assuming that's it, is O(1) also a correct answer?

If that's right, confirm it and please tell me, what requires maximum of 3 rotations?

Answer 1

A maximum of 3 operations(or 2 rotations) are needed when implementing a Red-Black Tree correctly. For example the central BST shown in this image will need 3 operations to make it confirm to the Red Black BST's rules.

_{Image taken from Robert Sedgewick's slides from this MOOC.}.