CSSE 230
Data Structures and Algorithm Analysis

Homework 6  -  45 points

Don't forget that you should be making notes about your team and team members, for eventual use in the EditorTrees team evaluation.

To Be Turned In

Questions 1 and 2 should be submitted to the drop box and the coding question(s) should be committed to your SVN repository.  You may earn a late day by submitting all parts early, or use a late day if you submit any part late.

  1. (10 points) Exercise 19.2 included finding the probability (based on equally likely insertion orders of each of the 24 permutations) of each of the 14 different trees that can result when inserting the numbers 1, 2, 3, and 4 into an initially empty BST (with no re-balancing).

    1. With the same assumption (that all permutations of the four numbers are equally likely), what is the (weighted) average height of the BSTs?
    2. With the same assumptions, do the same exercise for inserting the four numbers into an AVL tree. In other words, what is the average height of the AVL trees?
  2. (15 points) On paper, start with this red-black tree:

    (If it is hard to see, the two children of the root are red.) Insert the following nodes using the top-down insertion algorithm and show what happens (both rotations and re-colorings): 20, 10, 25, 27, 40. Please denote the red nodes very clearly, using red (best) or a key (acceptable). Work carefully - it will be hard to give partial credit if your answer is incorrect.

  3. (20 points) Checkout the PreorderBuildTree project from your SVN repository. In this problem, you'll create another Binary Tree constructor, one that constructs a Tree with Character data from two pre-order lists: a string of data and a string of children. For example, t = BinaryTree("abc", "200") would create a full tree of height 1 with root = a and two children b and c, and t = BinaryTree("cbad", "2L00") would create the minimum height-balanced tree of height 2, with an in-order traversal of "abcd".

    As a larger example, this tree was built from the strings, "ARGEDFKJHWS" and "R22200LL0L0":

    This format should sound familiar - see HW3 and its solution for more details. Note that this can construct any binary tree of characters, not just BSTs. I am posting two hints here, but I strongly suggest that you try to develop an algorithm first before referring to them.

Other problems for your consideration

6.31[6.17], 6.37[6.22], 7.3[7.3], 7.4[7.4], 7.23[7.19], 7.29