Coding challenge

Technical Question: Powerset

Suppose you're given a file with a single string of comma separated numbers like the following

$ cat input
123,456,789

Your program must print to STDOUT the powerset of the given set, like follows (actual order is not relevant)

$ cat input | <your program> > output
$ cat output

123
456
789
123,456
123,789
456,789
123,456,789

Your solution must print to STDOUT and any extraneous output will be considered an error (but you may print to STDERR at your convenience). Your program will be tested against inputs of growing size, the more they can take, the better!

The solution must contain documentation explaining time and space complexity of your implementation.

You should use only stuff other than the standard library of your language of choice, any additional requirement should be documented and motivated. Java, Python, Scala or Rust are preferred.

Technical answer

The code has been written in Python 3.7, and no external libraries or dependencies were used for this solution.

$ $(echo 123,456,789) | powerset_generator.py > output
$ cat output

123
456
789
123,456
123,789
456,789
123,456,789

Requirements and assumptions

Accepts and process only the input composed of, comma separated, strings of elements.
Raise an exception and gracefully exit the code if input does not match the first condition.
The results are printed to STDOUT.
The order of the result does not matter.
The void set is ignored.

Design

for each elem in elements:
    i is position(elem, elements)
    recur([elem], i)

recur(res, pos):
    result.append(res)
    for each elem in elements:
        i is position(elem, elements)
        res = res.append(elem)
        recur(res, i)

Time and space complexity analysis

Space complexity is O(n*2^n)
Time complexity is O(n*2^n)

Performance measurement

The benchmark was performed with the following setup:

CPU: Intel Core i5-6300 @ 2.40 GHz, 2 Cores, 4 Logical Processors
RAM: 8GB
OS: Microsoft Windows 10 Enterprise Build 17763

The best performing algorithm is powerset_pythonic. Note that all algorithms fail with MemoryError from length subset of 25. The error is caused by the inherent space complexity of the algorithm which is very demanding in term of space allocation.

License

DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE
                    Version 2, December 2004

 Copyright (C) 2004 Sam Hocevar <sam@hocevar.net>

 Everyone is permitted to copy and distribute verbatim or modified
 copies of this license document, and changing it is allowed as long
 as the name is changed.

            DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE
   TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION

  0. You just DO WHAT THE FUCK YOU WANT TO.

References

[1] https://en.wikipedia.org/wiki/Power_set
[2] https://rosettacode.org/wiki/Power_set
[3] https://cs.stackexchange.com/questions/121230/explanation-of-on2n-time-complexity-for-powerset-generation
[4] https://www.geeksforgeeks.org/power-set/
[5] https://docs.python.org/3/library/itertools.html#itertools.combinations
[6] https://docs.python.org/3/library/itertools.html#itertools-recipes
[7] https://stackoverflow.com/questions/24365954/how-to-generate-a-power-set-of-a-given-set

mhackampari / powerset