tree-rotation

Given a set of values, it's possible for there to be many different possible binary search trees that can be formed from those values. For example, for the values 1, 2, and 3, there are five BSTs we can make from those values: 1 1 2 3 3 \ \ / \ / / 2 3 1 3 1 2 \ / \ / 3 2 2 1 Many data structures that are based on balanced binary search trees use tree rotations as a primitive for reshaping a BST without breaking the required binary search tree invariants. Tree rotations can be used to pull a node up above its parent, as shown here: rotate u right v / \ -----> / \ v C A u / \ <----- / \ A B

While i was studying for midterm about binary trees, i found a statement that any arbitrary n-node binary tree can be transformed into any other n-node binary tree with at most 2*n-2 rotations. Is there any proof for that? I found some kind of proof with asymptotic notations but it was not that clear. I mean could someone explain/show why it is true? And if it says that n-node binary tree, does it include the root? This answer is from CLRS 3rd Edition textbook question 13.2-4. Let LEFT = an entire left linked list binary tree RIGHT = an entire right linked list binary tree. You can easily