Homework #4

Problem 1:

Implement heap sort by using the bottom-up insertion 
method. Add this sort to your sorting framework. Evaluate
its performance in terms of the numbers of comparisons and
exchanges, and compare it to the performance of the two
advanced sorting methods that you have previously implemented.
Submit your report with detailed empirical results and a
thorough explanation of these results. Which of the three
advanced sorting method is the best choice for a) ordered
data, b) data in reverse order, and c) average data for the data sets
you have experimented with.

Problem 2: (This is not a programming project) Assume that
keys arrive for insertion in an initially empty AVL tree in 
the following order: 10, 20, 30, 25, 27, 7, 4, 23, 26, 21.  
Build the resulting tree showing each step of the insertion
process. Next, delete 30, 27 and 26. Show the resulting tree 
after every step. Discuss its fullness and compare it to the
binary tree with an ordering property resulting from exactly 
the same tree operations.