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That won't be efficient memorywise since the size of the result array is dependant on the largest value in the array of values.

Consider sorting an array of 2 large integers {65000,30000}. To sort this array, the result array will be initialized with 65000 elements. Very inefficient.

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Yeah, well, now you get an exception. Not much better...

You should look into bucketsort. That allows you to sort in finite universes in Theta(n+k) without allocating huge arrays for large integers.

I will read more about bucketsort and update the article as necessary.

I have a simple Python implementation of Countingsort, Bucketsort and Radixsort, if it helps: https://github.com/MauriceGit/Advanced_Algorithms

Thanks a bunch for the link.

Wouldn't using a sparse bit-array be equivalent to using Bucketsort in space-complexity, but more efficient in time-complexity, or am I missing something here.

Using a sparse bit-array will reduce the memory space of the problem.

Yes, but do you have an implementation of a sparse array with constant time lookups?

I can work up one. Choosing the right bucket will be O(1) as the index is integer. We can store the buckets for lookup in a hash-table or an array-of-arrays, which again will be O(1). Reaching to the actual index should again be O(1) - unless am messing something here.

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