module HittingSet HittingSetProblem{T} = Pair{Set{T}, Vector{Pair{T, Set{Set{T}}}}} # `subsets` should be a collection of Set objects function HittingSetProblem(subsets, chosen = Set()) wholeset = union(subsets...) T = eltype(wholeset) unsorted_moves = [ elt => Set(filter(s -> elt ∉ s, subsets)) for elt in wholeset ] moves = sort(unsorted_moves, by = pair -> length(pair.second)) Set{T}(chosen) => moves end function Base.display(problem::HittingSetProblem{T}) where T println("HittingSetProblem{$T}") chosen = problem.first println(" {", join(string.(chosen), ", "), "}") moves = problem.second for (choice, missed) in moves println(" | ", choice) for s in missed println(" | | {", join(string.(s), ", "), "}") end end println() end function solve(pblm::HittingSetProblem{T}, maxdepth = Inf) where T problems = Dict(pblm) println(typeof(problems)) while length(first(problems).first) < maxdepth subproblems = typeof(problems)() for (chosen, moves) in problems if isempty(moves) return chosen else for (choice, missed) in moves to_be_chosen = union(chosen, Set([choice])) if isempty(missed) return to_be_chosen elseif !haskey(subproblems, to_be_chosen) push!(subproblems, HittingSetProblem(missed, to_be_chosen)) end end end end problems = subproblems end problems end function test(n = 1) T = [Int64, Int64, Symbol, Symbol][n] subsets = Set{T}.([ [ [1, 3, 5], [2, 3, 4], [1, 4], [2, 3, 4, 5], [4, 5] ], # example from Amit Chakrabarti's graduate-level algorithms class (CS 105) # notes by Valika K. Wan and Khanh Do Ba, Winter 2005 # https://www.cs.dartmouth.edu/~ac/Teach/CS105-Winter05/ [ [1, 3], [1, 4], [1, 5], [1, 3], [1, 2, 4], [1, 2, 5], [4, 3], [ 2, 4], [ 2, 5], [6, 3], [6, 4], [ 5] ], [ [:w, :x, :y], [:x, :y, :z], [:w, :z], [:x, :y] ], # Wikipedia showcases this as an example of a problem where the greedy # algorithm performs especially poorly [ [:a, :x, :t1], [:a, :y, :t2], [:a, :y, :t3], [:a, :z, :t4], [:a, :z, :t5], [:a, :z, :t6], [:a, :z, :t7], [:b, :x, :t8], [:b, :y, :t9], [:b, :y, :t10], [:b, :z, :t11], [:b, :z, :t12], [:b, :z, :t13], [:b, :z, :t14] ] ][n]) problem = HittingSetProblem(subsets) if isa(problem, HittingSetProblem{T}) println("Correct type") else println("Wrong type: ", typeof(problem)) end problem end end