Category: [DRAFT]

It’s probably the case that all math is trivial. So the statement that “[some particular mathematical result] is trivial” would, then, be trivially true — and useless! It might be better to say that “all math is trivial — if you have the intuition for it”. And this problem was not at all trivial (for me) to figure out, however inevitable and even obvious it looks (to me) in …

To take a multiset and reversibly transform it into a set of the same cardinality … start with the multiset's smallest element, add 0 to it; then go to the next element (which might be a duplicate), and add 1 to it (which will guarantee it's no longer a duplicate); then go to the next element (which might still be a duplicate of the first), and add 2 to it (which will guarantee it's no longer a duplicate of the first or second elements), and so on. After this transformation is applied, you'll have a set with no duplicates, from a k−1-elements-larger universe, that can easily be transformed back by just subtracting instead of adding!

I saw an online resource that claimed “The collections.Counter class in the Python standard library implements a multiset (or bag) type that allows elements in the set to have more than one occurrence.” However, (and despite the fact that he is quoting comments in the CPython source code,) this is misleading. While the collections.Counter class does allow you to have more than 1 occurrence of elements in a set, …

Just found out about this cool feature in the Python standard library that allows you to merge two iterables based on a comparison: from heapq import merge as merge_heapwise some_numbers = (1, 5, 10, 15) other_numbers = (2, 4, 6, 8, 10, 12, 14, 16) merged_numbers = tuple(merge_heapwise(some_numbers, other_numbers)) # Using a tuple so comparisons work, for didactic demo reasons assert merged_numbers == (1, 2, 4, 5, 6, 8, …