@dsimcha wrote:
Counting sort: When you are sorting integers with a limited range
I would change that to:
Counting sort: When you sort positive integers (0 - Integer.MAX_VALUE-2 due to the pigeonhole).
You can always get the max and min values as an efficiency heuristic in linear time as well.
Also you need at least n extra space for the intermediate array and it is stable obviously.
/**
* Some VMs reserve some header words in an array.
* Attempts to allocate larger arrays may result in
* OutOfMemoryError: Requested array size exceeds VM limit
*/
private static final int MAX_ARRAY_SIZE = Integer.MAX_VALUE - 8;
(even though it actually will allow to MAX_VALUE-2)
see:
Do Java arrays have a maximum size?
Also I would explain that radix sort complexity is O(wn) for n keys which are integers of word size w. Sometimes w is presented as a constant, which would make radix sort better (for sufficiently large n) than the best comparison-based sorting algorithms, which all perform O(n log n) comparisons to sort n keys. However, in general w cannot be considered a constant: if all n keys are distinct, then w has to be at least log n for a random-access machine to be able to store them in memory, which gives at best a time complexity O(n log n). (from wikipedia)
