Algorithm goal

Find combinations of an array that sum up to N, where numbers are unique. Support large inputs. For the non-unique version, see FindCombinationsAddingUpTo.

Test cases in Scala

assert(combosList(Set.empty, target = 0).isEmpty)
assert(combosList(Set(1, 2, 3), target = 3).toSet == Set(Set(1, 2), Set(3)))
assert(combosList(Set(1, 2, 3), target = 7).isEmpty)
assert(
  combosList(Set(1, 2, 3, 4, 5, 6), target = 5).toSet ==
    Set(Set(1, 4), Set(2, 3), Set(5))
)
assert(combosList(Set(2, 1), target = 3).toSet == Set(Set(2, 1)))

Algorithm in Scala

8 lines of Scala (compatible versions 2.13 & 3.0), showing how concise Scala can be!

Explanation

The Scala solution is quite elegant and expressive as well as stack-safe due to the fact that there is no recursion (many languages have a solution but the solution is often using recursion).

Scala provides a 'combinations' method on Array, given a selection length; then the only thing we need to vary is the selection length, which we can produce using a Lazy List. Then, using a for-comprehension and a guard we check if the target of what we are looking for is met, and return that combination if it is. (this is © from www.scala-algorithms.com)

Scala concepts & Hints

1. For-comprehension

   The for-comprehension is highly important syntatic enhancement in functional programming languages.

   val Multiplier = 10
   
   val result: List[Int] = for {
     num <- List(1, 2, 3)
     anotherNum <-
       List(num * Multiplier - 1, num * Multiplier, num * Multiplier + 1)
   } yield anotherNum + 1
   
   assert(result == List(10, 11, 12, 20, 21, 22, 30, 31, 32))
   

   ▶ Run code in the IDE

2. Lazy List

   The 'LazyList' type (previously known as 'Stream' in Scala) is used to describe a potentially infinite list that evaluates only when necessary ('lazily').