Add powerset function (#63)

Fixes #11.

src/combinations.jl

@@ -1,7 +1,8 @@
 export combinations,
        CoolLexCombinations,
        multiset_combinations,
-       with_replacement_combinations
+       with_replacement_combinations,
+       powerset
 
 #The Combinations iterator
 
@@ -261,3 +262,19 @@ function Base.next(c::WithReplacementCombinations, s)
     (comb, s)
 end
 Base.done(c::WithReplacementCombinations, s) = !isempty(s) && s[1] > length(c.a) || c.t < 0
+
+## Power set
+
+"""
+    powerset(a, min=0, max=length(a))
+
+Generate all subsets of an indexable object `a` including the empty set, with cardinality
+bounded by `min` and `max`. Because the number of subsets can be very large, this function
+returns an iterator object. Use `collect(powerset(a, min, max))` to get an array of all
+subsets.
+"""
+function powerset(a, min::Integer=0, max::Integer=length(a))
+    itrs = [combinations(a, k) for k = min:max]
+    min < 1 && append!(itrs, eltype(a)[])
+    IterTools.chain(itrs...)
+end

test/combinations.jl

@@ -39,3 +39,9 @@ using Compat.Test
 @test_throws DomainError [CoolLexCombinations(5, 0)...]
 @test [CoolLexCombinations(4,2)...] == Vector[[1,2], [2,3], [1,3], [2,4], [3,4], [1,4]]
 @test isa(start(CoolLexCombinations(1000, 20)), Combinatorics.CoolLexIterState{BigInt})
+
+# Power set
+@test collect(powerset([])) == Any[[]]
+@test collect(powerset(['a', 'b', 'c'])) == Any[[],['a'],['b'],['c'],['a','b'],['a','c'],['b','c'],['a','b','c']]
+@test collect(powerset(['a', 'b', 'c'], 1)) == Any[['a'],['b'],['c'],['a','b'],['a','c'],['b','c'],['a','b','c']]
+@test collect(powerset(['a', 'b', 'c'], 1, 2)) == Any[['a'],['b'],['c'],['a','b'],['a','c'],['b','c']]