harry potter

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 EUR.

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 EUR.

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?

2 copies of the first book 2 copies of the second book 2 copies of the third book 1 copy of the fourth book 1 copy of the fifth book

One way of group these 8 books is: 1 group of 5 --> 25% discount (1st,2nd,3rd,4th,5th) +1 group of 3 --> 10% discount (1st,2nd,3rd) This would give a total of 5 books at a 25% discount +3 books at a 10% discount Giving 5 x (8 - 2.00) == 5 x 6.00 == 30.00 +3 x (8 - 0.80) == 3 x 7.20 == 21.60 For a total of 51.60

However, a different way to group these 8 books is: 1 group of 4 books --> 20% discount (1st,2nd,3rd,4th) +1 group of 4 books --> 20% discount (1st,2nd,3rd,5th) This would give a total of 4 books at a 20% discount +4 books at a 20% discount Giving 4 x (8-1.60) == 4 x 6.40 == 25.60 +4 x (8-1.60) == 4 x 6.40 == 25.60 For a total of 51.20

And 51.20 is the price with the biggest discount.