Title: “Program Assignment 2: Analyzing Sorting Algorithm Performance”
Points: 100 points – 60pts for coded portion, 40 points for written analysis
Due Date: Wednesday October 23, 2002
Objectives: (1) To reinforce the concepts underlying the asymptotic behavior of several sorting
algorithms. (2) Further develop Java programming skills.
Description: Create a Java program that produces the necessary data to analyze the asymptotic
behavior of three sorting algorithms. Do this according to the steps shown below:
1. You will need to generate 3 random permutations of the first N integers for values of N
equal to 100, 500, 1000, 5000, and 10,000 (you may need to adjust the sizes of N) as well as
fixed permutations 1..N and N..1 when N = 500. Thus for each value of N you will have
five arrays: 3 permuted and 2 fixed sequences.
2. Once the arrays are generated use a copy of each of them as input to the following sorting
algorithms: (a) insertion sort, (b) selection sort, and (c) Shell sort with the initial gap and a
decrement of N/2.
3. Determine the execution time required by each of the sorting algorithms on all five of the
arrays (for each size of N) (be sure to get non-zero times).
4. Analyze the data for each of the sorts on the five different array sizes to determine the
following:
a. Using the T(N)/F(N) technique determine the Big-Oh run-time for each of the three
sorting algorithms. For insertion and selection sorts produce T(N)/F(N) tables for
F(N) = N, N2, and N3. For Shell sort produce T(N)/F(N) tables for F(N) = N, N1.5,
and N2..
b. Separate the data to determine if the sorting algorithm performance is affected by the
order of the data. In other words, can you tell a difference in the running time of the
sort if the data is already sorted (1..N fixed permutation) or is reverse sorted (N..1
fixed permutation).
5. Additional analysis for Shell sort. As we indicated in class; the Shell sort is a “tunable” sort
since the initial gap and decrement parameters can be altered to produce changes in the
performance of the algorithm. In this part of the project you will alter these parameters to
determine their effect on the sort. Use just two different sized arrays, say 1000 and 10,000
for this part of the project. Run several different experiments to obtain data for analysis of
this sorting algorithm. Try initial gap sizes of 1.8, 2.0, 2.2, and 2.4. Try decrements of
straight division by 2, straight division by 2.2 (using floor function), and only odd gaps.
Also test for random permutations as well as the fixed permutations.
6. Although you may want to actually print out the sorted arrays while you are working on
your program, to make sure it works – it will necessary to print the sorted output arrays only
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COP 3503H – Programming Assignment #2 – Fall 2002
