CSci 3501 Algorithms and Computability - Lab 1.

August 27th. Due Wednesday, September 2nd at 11:59pm.

What to submit and when:

Lab assignment

30 points.

Work in pairs.

Design and implement an algorithm for finding all combinations of the first n integers.
Input: n.
Output: all possible combinations of numbers from 1 to n written one combination per line without repetitions (in any order).
Example: input: n = 3. Output:


1 2 3
1 3 2
2 1 3
2 3 1
3 1 2 
3 2 1

Time your program using Java time function (time in milliseconds):


long time = System.currentTimeMillis();

gives you the current time in milliseconds. Measure it before and after printing the output, subtract the two numbers, and print the result.

If you are using another programming language, please time your program with the time function provided by the language or by the system time command.

Your solution should not store all possible combinations of n-1 numbers in memory in order to generate all combinations of n. Think of ways to avoid large amounts of storage. Recursion may be a good direction to explore.
Keep in mind that your program should work correctly no matter what n is.

Make sure to test your program thoroughly, in particular make sure that all the combinations are printed with no duplicates. Figure out on paper how many lines you would have for n=4 and n=5, then check that you are getting the right number of lines (a counter may be useful here so that you don't need to count by hand). Make sure to submit your computation for the number of lines.

What is the efficiency of your algorithm in the number of printed lines as a function of n? Give your answer as Big-O, explain how you computed it.

Based on your timing results and on the Big-O approximation please estimate how long your program would run for n = 15 and for n = 20. Show how you have computed the estimate.


CSci 3501 course web site.

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