Scala algorithm: Find combinations adding up to N (unique)

Published

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 (version 2.13), showing how concise Scala can be!

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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))
    
  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').


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  5. Check if an array is a palindrome
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  8. Find combinations adding up to N (unique)
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Explore the 21 most useful Scala concepts

To save you going through various tutorials, we cherry-picked the most useful Scala concepts in a consistent form.

  1. Class Inside Class
  2. Class Inside Def
  3. Collect
  4. Def Inside Def
  5. Drop, Take, dropRight, takeRight
  6. foldLeft and foldRight
  7. For-comprehension
  8. Lazy List
  9. Option Type
  10. Ordering
  11. Partial Function
  12. Pattern Matching
  13. Range
  14. scanLeft and scanRight
  15. Sliding / Sliding Window
  16. Stack Safety
  17. State machine
  18. Tail Recursion
  19. Type Class
  20. View
  21. Zip

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