# Permutations, Combinations and Frustrations

# Permutations, Combinations and Frustrations

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The issue of permutations and combinations is sometimes funny.

Not funny weird. But funny "haha."

I received an email with 100's of words and 10 attachments. (10. Really.) The subject was how best to enumerate 6! permutations of something or other. With a goal of comparing some optimization algorithm with a brute force solution. (I don't know why. I didn't ask.)

Apparently, the programmer was not aware that permutation creation is a pretty standard algorithm with a standard solution. Most "real" programming languages have libraries which already solve this in a tidy, efficient, and well-documented way.

For example

https://docs.python.org/2/library/itertools.html#itertools.permutations

I suspect that this is true for every language in common use.

In Python, this doesn't even really involve programming. It's a first-class expression you enter at the Python >>> prompt.

>>> import itertools >>> list(itertools.permutations("ABC")) [('A', 'B', 'C'), ('A', 'C', 'B'), ('B', 'A', 'C'), ('B', 'C', 'A'), ('C', 'A', 'B'), ('C', 'B', 'A')]

What's really important about this question was the obstinate inability of the programmer to realize that their problem had a tidy, well understood solution. And has had a good solution for decades. Instead they did a lot of programming and sent 100's of words and 10 attachments (10. Really.)

The best I could do was provide this link:

Steven Skiena, The Algorithm Design Manual

It appears that too few programmers are aware of how much already exists. They plunge ahead creating a godawful mess when a few minutes of reading would have provided a very nice answer.

Eventually, they sent me this:

http://en.wikipedia.org/wiki/Heap's_algorithm

As a grudging acknowledgement that they had wasted hours failing to reinvent the wheel.

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