## CSci 3501 Algorithms and Computability - Lab 1.

#### August 25th. Due Wednesday, August 31st at 11:59pm.

What to submit and when:

- All submissions are electronic: by e-mail to elenam at morris.umn.edu and CC to all lab
partners. Please do not delete your e-mail from "Sent mail" or your
mailbox until the end of the semester.
- When working on the lab, please comment your work so that it is
clear what contributions of each person are.
- At the end of the lab each group should send me the results of their
in-class work. Please indicate if this is your final submission. Don't
forget to answer all the questions below.
- If your submission at the end of the lab time was not final,
please send me(CC to the lab partner(s)) a final copy before the due
time. Please use the subject "3501 Lab N", where N is the lab
number.

#### 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.

Make sure to test your program thoroughly, in particular make sure
that all the combinations are printed. Figure out 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).

What is the efficiency of your algorithm in the number of printed
lines? 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 computed the estimate.

CSci 3501
course web site.

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