[Python][CheckiO] How much gold

In order to solve this problem, we need to calculate the following proportion

(a1) gold-tin

(a2) gold-copper

(a3) gold-iron

Once we got (a1), (a2), and (a3), we can calculate the proportion of gold applying the following equation:

gold = ( (a1)+(a2)+(a3) - 1 ) / 2

Therefore we can divide this question into three sub-questions (a1) (a2) (a3).

Firstly, we can categorize the given proportion into two classes.

(b1) proportion consists of "gold"

       Ex. gold-tin proportion

(b2) proportion doesn't consist of "gold"

       Ex. copper-iron proportion

If the given proportion belongs to (b1), we just return it

However, when it belongs to (b2), we return (1 - given_proportion)

And following is the source code

 from fractions import Fraction  

 METALS = ('gold', 'tin', 'iron', 'copper')  

 def get_proportion(ele1, ele2, ele3, ele4, alloys):  
   #print(ele1+','+ele2+','+ele3+','+ele4)  
   if ele1+'-'+ele2 in alloys:  
     return alloys[ele1+'-'+ele2]  
   elif ele2+'-'+ele1 in alloys:  
     return alloys[ele2+'-'+ele1]  
   elif ele3+'-'+ele4 in alloys:  
     return 1 - alloys[ele3+'-'+ele4]  
   elif ele4+'-'+ele3 in alloys:  
     return 1 - alloys[ele4+'-'+ele3]  
   else:  
     assert(0)  

 def checkio(alloys):  
   #step 1. find proportion of gold-tin, gold-iron, and gold-copper  
   gold_tin = get_proportion('gold', 'tin', 'iron', 'copper', alloys)  
   gold_iron = get_proportion('gold', 'iron', 'tin', 'copper', alloys)  
   gold_copper = get_proportion('gold', 'copper', 'tin', 'iron', alloys)  
   #step 2.   
   return Fraction(gold_tin + gold_iron + gold_copper - 1, 2)