Set covering problem using easy visuals and friendly variable names

set-covering-problem.py

colors_needed = set(["blue", "yellow", "green", "orange", "purple", "white", "black", "pink"])

boxes = {}
boxes["box_1"] = set(["orange", "purple", "white"])
boxes["box_2"] = set(["yellow", "orange", "blue"])
boxes["box_3"] = set(["green", "purple", "black"])
boxes["box_4"] = set(["purple", "white"])
boxes["box_5"] = set(["black", "pink"])

final_boxes = set()

while colors_needed:
  best_box = None
  best_coverage_so_far = set()
  
  for box, colors in boxes.items():
    colors_covered_by_box = colors_needed & colors 
    
    if len(colors_covered_by_box) > len(best_coverage_so_far): 
      best_box = box
      print(best_box)
      best_coverage_so_far = colors_covered_by_box 
      
  colors_needed -= best_coverage_so_far 
  final_boxes.add(best_box)

print(final_boxes)