worksheet 32: Tree Sort (Skip List Version) Name:
An Active Learning Approach to Data Structures using C
1
Worksheet 32: Tree Sort
In Preparation: Read chapter 10 on the Tree data type.
Both the Skip List and the AVL tree provide a very fast O(log n) execution time for all
three of the fundamental Bag operations: addition, contains, and remove. They also
maintains values in sorted order. If we add an iterator then we can loop over all the
values, in order, in O(n) steps. This makes them a good general purpose container.
Here is an application you might not have immediately thought about: sorting. Recall
some of the sorting algorithms we have seen. Insertion sort and selection sort are O(n2),
although insertion sort can be linear if the input is already nearly sorted. Merge sort and
quick sort are faster at O(n log n), although quick sort can be O(n2) in its worst case if the
input distribution is particularly bad.
Consider the following sorting algorithm:
How to sort a array A
Step 1: copy each element from A into a skip list (or AVL tree)
Step 2: copy each element from the skip list back into the array
Assuming the array has n elements, what is the algorithmic execution time for step 1?
What is the algorithmic execution time for step 2? Recall that insertion sort and quick
sort are examples of algorithms that can have very different execution times depending
upon the distribution of input values. Is the execution time for this algorithm dependent
in any way on the input distribution?
A sorted dynamic array bag also maintained elements in order. Why would this algorithm
not work with that data structure? What would be the resulting algorithmic execution
time if you tried to do this?
Can you think of any disadvantages of this algorithm?
