gistfile1.rb

module Enumerable
  def sum
    self.inject(0) {|acc, i| acc+i}
  end
end

module Harry
  class << self
    def price(books)
      nslots = 5
      raise ArgumentError, "books must contain count of each volume in 5 slots" unless books.size == nslots

      if books.sum == 0
        return 0
      else
        # simulate picking topmost book from each slot where there it at least one book
        mask = slot_mask(books)
        selections = bitmasks(nslots).
          map { |m| mask_to_array(nslots, m) }.
          select {|s| legal_selections(s, books) }
        
        selections.map do |s|
          discounted_price_for_selection(s) + price(extract_selection(books, s))
        end.min
      end
    end

    def legal_selections(s, books)
      extract_selection(books, s).all? {|i| i >= 0}
    end

    def mask_to_array(size, mask)
      (0...size).map {|i| 1 & (mask >> i)}.reverse
    end

    # pick at least one book from all books with the constraint that all
    # picked books are still unique
    def extract_selection(books, selection)
      books.zip(selection).map { |orig_count, i| orig_count - i }
    end

    def slot_mask(books)
      m = 0
      indexes_with_books(books).each_with_index do |i, idx|
        m = m | (2**idx) if i == 1
      end
      m 
    end

    def indexes_with_books(books)
      books.map { |i| i > 0 ? 1 : 0 }
    end
    
    def bitmasks(length)
      (1..(2**length)-1).to_a
    end

    def discounted_price_for_selection(selection)
      unit_price = 8
      discounts = [0, 0, 0.05, 0.10, 0.20, 0.25]
      
      uniq_books = selection.sum
      (1-discounts[uniq_books]) * unit_price * uniq_books
    end
  end
end