You're probably right, the heap isn't necessary, but it's certainly the "natural" way of implementing the repeated "take the two smallest elements, combine them, and put them back in the pool" operations. I can change the module to not require Heap
(which I'm not that fond of anyways). Especially for < 256 elements, it shouldn't make a difference. So, did you sort the elements initially, then splice the results in at the right places in the list or something?
As for the brain-teaser, I imagine it's the same as telling whether two binary trees are isomorphic. I remember doing that on a problem set by putting them both in a canonical form (e.g. longest bits on one side). IIRC you had to assign a "weight" to each node based on the number and depth of its children, then always put the heaviest child on the left. I don't remember the exact details, but is it something like this?
Update: Heap dependency removed, and if anything it's faster.