Homework 5

Background: Ch. 13.1, 13.2, 13.3.

Due October 10th:

• 5.1: CLR Exercise 13.2-1 (pg. 249).
• 5.2: Show how to create a complete binary search tree. Prove it is complete (i.e., deepest level is ``left justified''.) [Extra credit!]
• 5.3: Show the binary tree resulting from inserting the letters of the word ``algorithm'' into a binary tree. What is the depth of the tree?
• 5.4: Consider the following sorting algorithm. Given a list of n elements, choose one uniformly at random. Make it the root of a binary search tree. Now create two sublists corresponding to numbers that will go to the left of the root and numbers that will go to the right of the root. Recursively create binary search trees for each of these lists, then attach them to the root. Finally, run SORT-TREE to output the elements in order. Ok, so what's the expected running time of this sorting algorithm? (Hint: The analysis here is trivial once you recognize what the algorithm is doing.)
• 5.5: Given a binary search tree T specified in terms of four arrays, , , , and , give pseudocode for performing a rotation at node i.