Engine prototype #13

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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