> so, does 135,000,000 distinct integers work for any size of input?

Always (notice my stipulation of 32 bit). However, regardless of the
size of an integer (in bits) there is _always_ a fixed number of bits
that can represent it in the manner I explained.

> (Nowhere in the original problem did it say we were 1. working with 32
> bit numbers,

Which is why I gave several examples that lead to how the solution
scales.

> or, for that matter, 2. working with a bounded set --

Integers are bounded.

> where did the initial problem say anything about there being a maximum
> value -- this is a theoretical question) Whenever you are working with
> problems like this -- if you are going to put bounds on the set of
> numbers you are using, you state that you are working in a RAM (or

[snip]

The initial post stated:
"I'm interested in the following problem: there is an array of
integers..."

Notice the use of the word integers, _not_ values or numbers

And then, later on...
" there is no additional info on the input data beyond what is stated
in the original post. "

And further to that,
"if you hold to _exactly_ what is mentioned in your post"

So, based on that thread of thought and foundation, the answer is
perfectly valid.



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