in reply to Re^2: mathematical proof
in thread mathematical proof

The result is that building either the hash or the array is O(n).

Ah yes, I see.

If the data structures are big enough that they live on disk

While there are other data structures available to him (such as disk-based structures and tries), I chose to only speak about the ones he mentioned (hashes and arrays) due to time constraints.

Contrary to your final comment, it is the array that benefits more from duplicates. That is because if you're slightly clever in your merge sort, then eliminating lots of duplicates will reduce the size of your large passes, speeding up the sort.

You'll reduce the size of large passes you never have to do with a hash.

You'll speed up the sort you don't have to do with a hash.

With a hash, you never have to deal with more than $num_duplicates items. With an array, you'll deal with at least $num_duplicates items. I don't understand how come you say the array benefits more.