Question

I have multiple ordered lists. Unfortunately, the order of the items isn’t a simple alpha or numeric comparison, otherwise this is trivial. So what I have is something like:

List #1        List #2       List #3 groundhog      groundhog     easter mothersday     mayday        mothersday midsummer      laborday      halloween christmas 

And from this I can gather than groundhog < mothersday, but the relationship of groundhog and easter is unknown. I am guaranteed that the order of the items from list-to-list is self consistent. (i.e. that no matter which list it occurs in, easter is always before halloween)

But what I need is a new ordered list that represents each item in the other lists only once, that preserves all of the known relationships above:

groundhog easter mayday mothersday midsummer laborday halloween christmas 

However, the following list is also perfectly valid:

easter groundhog mothersday mayday midsummer laborday halloween christmas 

I’m looking for a fairly quick, general-purpose algorithm I can use to order N lists in this way. (Working C# code a plus, for sure, but not necessary.)

I have solution that works, but its O(N^2) and a dog with even modest data sets.

Answer 1

You may want to have a look at topological sorting. I think it applies quite well to your case.