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Published at Aug 26 2019
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Instructions

Test suite

Solution

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 a piece of 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 --> 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

Resulting in:

- 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

Resulting in:

- 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.

The Scala exercises assume an SBT project scheme. The exercise solution source should be placed within the exercise directory/src/main/scala. The exercise unit tests can be found within the exercise directory/src/test/scala.

To run the tests simply run the command `sbt test`

in the exercise directory.

For more detailed info about the Scala track see the help page.

Inspired by the harry potter kata from Cyber-Dojo. http://cyber-dojo.org

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

```
import org.scalatest.{Matchers, FunSuite}
/** @version 1.4.0 */
class BookStoreTest extends FunSuite with Matchers {
test("Only a single book") {
BookStore.total(List(1)) should be (800)
}
test("Two of the same book") {
pending
BookStore.total(List(2, 2)) should be (1600)
}
test("Empty basket") {
pending
BookStore.total(List()) should be (0)
}
test("Two different books") {
pending
BookStore.total(List(1, 2)) should be (1520)
}
test("Three different books") {
pending
BookStore.total(List(1, 2, 3)) should be (2160)
}
test("Four different books") {
pending
BookStore.total(List(1, 2, 3, 4)) should be (2560)
}
test("Five different books") {
pending
BookStore.total(List(1, 2, 3, 4, 5)) should be (3000)
}
test("Two groups of four is cheaper than group of five plus group of three") {
pending
BookStore.total(List(1, 1, 2, 2, 3, 3, 4, 5)) should be (5120)
}
test("Two groups of four is cheaper than groups of five and three") {
pending
BookStore.total(List(1, 1, 2, 3, 4, 4, 5, 5)) should be (5120)
}
test("Group of four plus group of two is cheaper than two groups of three") {
pending
BookStore.total(List(1, 1, 2, 2, 3, 4)) should be (4080)
}
test("Two each of first 4 books and 1 copy each of rest") {
pending
BookStore.total(List(1, 1, 2, 2, 3, 3, 4, 4, 5)) should be (5560)
}
test("Two copies of each book") {
pending
BookStore.total(List(1, 1, 2, 2, 3, 3, 4, 4, 5, 5)) should be (6000)
}
test("Three copies of first book and 2 each of remaining") {
pending
BookStore.total(List(1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 1)) should be (6800)
}
test("Three each of first 2 books and 2 each of remaining books") {
pending
BookStore.total(List(1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 1, 2)) should be (7520)
}
test("Four groups of four are cheaper than two groups each of five and three") {
pending
BookStore.total(List(1, 1, 2, 2, 3, 3, 4, 5, 1, 1, 2, 2, 3, 3, 4, 5)) should be (10240)
}
}
```

```
import scala.collection.mutable
object BookStore {
private val cache = mutable.Map[List[Int], Int]()
private val discount: Map[Int, Double] = Map(1 -> 1, 2 -> 0.95, 3 -> 0.9, 4 -> 0.8, 5 -> 0.75)
private val corePrice: Int = 800
def total(books: List[Int]): Int = cache.getOrElseUpdate(books, getTotal(books))
private def getTotal(books: List[Int]): Int = books match {
case List() => 0
case _ => books.toSet.subsets.filter(_.nonEmpty)
.map(group => price(group) + total(books diff group.toList)).min
}
private def price(group: Set[Int]): Int = (corePrice * group.size * discount(group.size)).toInt
}
```

A huge amount can be learned from reading other peopleâ€™s code. This is why we wanted to give exercism users the option of making their solutions public.

Here are some questions to help you reflect on this solution and learn the most from it.

- What compromises have been made?
- Are there new concepts here that you could read more about to improve your understanding?

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