Algorithm goal

Find combinations of an array that sum up to N. Numbers are not unique. Support large inputs. Represent the set of non-unique values as a multiset, ie Map[Int, Count], where type Count = Int. For the unique items version, see: FindCombinationsAddingUpToUnique.

Test cases in Scala

assert(combosList(Array.empty, target = 0).isEmpty)
assert(
  combosList(Array(1, 2, 3), target = 3).toSet ==
    Set(Map(1 -> 1, 2 -> 1), Map(3 -> 1))
)
assert(
  combosList(Array(1, 1, 1, 2), target = 3).toSet ==
    Set(Map(1 -> 3), Map(1 -> 1, 2 -> 1))
)
assert(
  combosList(Array(2, 1, 1, 1, 2), target = 3).toSet ==
    Set(Map(2 -> 1, 1 -> 1), Map(1 -> 3))
)

Algorithm in Scala

9 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.In generating the combination, we use a way to group items, and the extract the count of members in each group. (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').

3. View

   The .view syntax creates a structure that mirrors another structure, until "forced" by an eager operation like .toList, .foreach, .forall, .count.