Instructions
To try and encourage more sales of different books from a popular 5 book series, a bookshop has decided to offer discounts on 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 buy all 5, you get a 25% discount.
Note that if you buy 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 code to calculate the price of any conceivable shopping basket (containing only books of the same series), 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 grouping these 8 books is:
- 1 group of 5 (1st, 2nd,3rd, 4th, 5th)
- 1 group of 3 (1st, 2nd, 3rd)
This would give a total of:
- 5 books at a 25% discount
- 3 books at a 10% discount
Resulting in:
- 5 × (100% - 25%) × $8 = 5 × $6.00 = $30.00, plus
- 3 × (100% - 10%) × $8 = 3 × $7.20 = $21.60
Which equals $51.60.
However, a different way to group these 8 books is:
- 1 group of 4 books (1st, 2nd, 3rd, 4th)
- 1 group of 4 books (1st, 2nd, 3rd, 5th)
This would give a total of:
- 4 books at a 20% discount
- 4 books at a 20% discount
Resulting in:
- 4 × (100% - 20%) × $8 = 4 × $6.40 = $25.60, plus
- 4 × (100% - 20%) × $8 = 4 × $6.40 = $25.60
Which equals $51.20.
And $51.20 is the price with the biggest discount.
Subtypes
This exercise defines a Subtype called Book, for natural numbers 1 through 5.
A Subtype can be thought of as a pair ⟨x, h⟩, where x is the value and h is the proof of its validity.
The value inside a Subtype (x, in this case) can be accessed by using .val, for example, x.val.
Its proof can be accessed by using .property, for example, x.property.
Both can also be accessed by pattern matching, as usual.
