func part(_,    {.is_empty}) { [[]] }
func partitions({.is_empty}) { [[]] }

func part(s, args) {
  gather {
    s.combinations(args[0], { |*c|
      part(s - c, args.ft(1)).each{|r| take([c] + r) }
    })
  }
}

func partitions(args) {
  part(@(1..args.sum), args)
}

[[],[0,0,0],[1,1,1],[2,0,2]].each { |test_case|
  say "partitions #{test_case}:"
  partitions(test_case).each{|part| say part }
  print "\n"
}