Lecture 10 - Problems

  1. What is the precondition for performing a left rotation on a node? What about for a right rotation?

  2. Suppose you are implementing a TreeSet - an implementation of the Set ADT where each value is stored in a node of a binary search tree. If you want to make the TreeSet generic, what if any restrictions must be placed on the type parameter for this to work?

  3. Give a sequence of rotations that can be applied to the following tree such that 11 becomes the root. Each rotation should be specified as a direction with a node as its argument, such as left(10).

    image-20200826133847359

  4. I claimed that tree rotations do not violate the BST property, but I didn’t prove it. Based on the diagram below, explain why values in subtrees \alpha, \beta, and \gamma cannot violate the BST property after a left rotation if they did not violate it before.

    image-20200918153448364
    image-20200918153448364

  5. For each of the following trees, calculate the balance factor of every node, then find the shortest possible sequence of rotations (if any) needed to achieve a tree whose nodes all have balance factors no smaller than -1 and no larger than 1.

    image-20200826134407667

    image-20200826134441165

    image-20200826134522525