A rare case where 1-based indexing is more convenient is complete binary trees laid out breadth-first (as in a standard binary heap): parent is i div 2 and children are 2i and 2i+1 when starting at one and who knows what when starting at zero. But that’s the only one I know.
Except 1-based indexing is what we use in normal language. We don't use "zeroeth" or "player (number) zero" etc. And the word "first" is shortened to 1st etc.
Personally I think we'd be better off if programming languages stuck to the same convention - off-by-1 errors aren't the hardest problems to deal with but they're still annoying.
That's confusing ordinal and cardinal numbers. The element with index 0 is the first number. The element with index 1 is the second number, and so on.
Using the term "zeroth" is basically some form of showing off (even though it's kinda fun), but will be utterly confusing when you get to the fifty-second element which is the last in a group of 53 elements.
I'm not confusing them, my point about abbreviating "first" as 1st was that in typical speech we start counting at 1. Nobody says "let's start with item zero on the list".
But programmers are stuck with having to say/think "item 0 in the array".
> With 0-based indexing the children are at 2i+1 and 2i+2. The parent is at (i-1) div 2.
> Not hard to figure out.
While that's true, "you just shift by 1" is equally good at all arguments for or against 0-based indexing, so deploying it here probably won't convince.
That said, the effort of one versus the other is so trivial that there is no point in ever using effort as an argument either way. Doubly so because what seems like effort to us is simple unfamiliarity.
What is important is which one leads to more careless errors in practice. As a trivial example, consistent indentation takes effort, but failing to do it leads to more careless errors. Therefore everyone indents code.
An incredibly unrare case happens all the time in my work: array[length - 1], or variations of this. Anything involving the last element of the array, and often iterating through the whole array will use something similar at some point.
