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Yes, the boolean group operations make many otherwise non-trivial problems remarkably easy. That's why I consider sets such a crucial feature.



Could you give some examples please?


Sure, let's get a really simple one.

You have N groups of something (persons, sales units, cars, tools, whatever). Find the values that are present in all of them. This problem comes up, all the time, in some form.

With sets it's trivial. Take the first set, and calculate a cascading intersection with every other set. At the end you're left with only the values that appeared in every one. In very clear python the code might look like this:

    common = ALL_SETS[0]
    for _set in ALL_SETS[1:]:
      common = common.intersection(_set)
    return common
Now, you can argue that underneath the hood that's still going to do N expensive iterations and you'd be right. This is where proper optimisations come in - when provided by a robust stdlib, we expect the set operations to be implemented with bitmaps.[0, 1] These are not something you'd see in a casual implementation.

Btw, in the above code example I have deliberately omitted a trivial optimisation. Let's leave that as an exercise for the reader. :)

0: http://roaringbitmap.org/about/

1: https://en.wikipedia.org/wiki/Bit_array


Examples like this really make me miss fold.

    return functools.reduce(lambda x,y: x&y, ALL_SETS)




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