How to get shortest representation of an enum flags value?

Question

I want to produce the shortest (or one of the shortest) possible combination(s) of the enum fields that would result in a particular enum value. What would be the best algorithm to accomplish this?

For example, say I have the enum:

enum MyEnum
{
    One = 1, 
    Two = 2,
    Three = One | Two,
    Four = 4,
    Six = Two | Four,
    Eight = 8,
    All = One | Two | Four | Eight
 }

Now for example for the value 7 I would like my function to output either "One | Six" or "Three | Six" .

Edit: Of course Three | Four Three | Four would be a valid output as well.

Answer 1

What you are basically asking for is minimum set cover, a problem known to be NP Complete. Fortunately, that doesn't mean that you can't solve it for small cases such as this. You can also get a O(logn) approximation via the greedy algorithm.

If there is no particular structure to your enum values, then you won't be able to do much better than brute force for a general exact solution. If you know that your enums have a particular structure, then you can often due much better via things like graph partitioning or CSP + backtracking.