[julia-users] Re: Iterating over all possible subsets

[harven]

I use the following to get the (untyped) powerset of an array:

function powerset (x)
  result = {{}}
  for i in x, j = 1:length(result)
    push!(result, [result[j],i])
  end
  result
end

julia> show(powerset(1:3))
{{},{1},{2},{1,2},{3},{1,3},{2,3},{1,2,3}}

Then sdifsums can be written as

sdifsums(a) = sum(a).-[2sum([a[i] for i=s]) for s=powerset([1:length(a)])]

If performance matters, one should type everything and deal with the sums 
in powerset itself when the subsets are computed. Probably slower than your 
approach. At least the powerset function seems to have an interest on its 
own.