This is unlikely something you'll use in practice, but I just read about it so it came to mind. A Braun tree is a binary tree that represents a flexible array

This is unlikely something you'll use in practice, but I just read about it so it came to mind. A Braun tree is a binary tree that represents a flexible array (indexable everywhere and extendable at both ends). The gist of it is that you take your array index and read it as a binary string that tells you how to go down the tree. If your index is 1, then you're at the right place and you stop. Then you go left/right depending on whether the remainder is 0/1. That is the 1-based interpretation, and it works because 1 is in the first digit while 2 and 3 need the next digit as well. If you want to use 0-based indices, it doesn't work out as cleanly, because 0 and 1 share the same digit, while 1 and 2 use different digits. So now you have to branch on whether your index is odd or even, and then either (i-1)/2, or (i/2)-1. It's not a big deal either way, but it turns a simple to visualize data structure into one where you have to think about the indices.