To try and encourage more sales of the 5 different Harry Potter books they sell, a bookshop has decided to offer discounts of multiple-book purchases.
One copy of any of the five books costs $8.
If, however, you buy two different books, you get a 5% discount on those two books.
If you buy 3 different books, you get a 10% discount.
If you buy 4 different books, you get a 20% discount.
If you go the whole hog, and buy all 5, you get a huge 25% discount.
Note that if you buy, say, four books, of which 3 are different titles, you get a 10% discount on the 3 that form part of a set, but the fourth book still costs $8.
Your mission is to write a piece of code to calculate the price of any conceivable shopping basket (containing only Harry Potter books), giving as big a discount as possible.
For example, how much does this basket of books cost?
Input
(2c-1b)2 copies of the first book
(2c-2b)2 copies of the second book
(2c-3b)2 copies of the third book
(1c-4b)1 copy of the fourth book
(1c-5b)1 copy of the fifth book
Answer: $51.60