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

Published , last updated

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)
  combosList(Array(1, 2, 3), target = 3).toSet ==
    Set(Map(1 -> 1, 2 -> 1), Map(3 -> 1))
  combosList(Array(1, 1, 1, 2), target = 3).toSet ==
    Set(Map(1 -> 3), Map(1 -> 1, 2 -> 1))
  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!

Get the full algorithm Scala algorithms logo, maze part, which looks quirky!


'Unlimited Scala Algorithms' gives you access to all the 81 published & 11 upcoming Scala Algorithms (92 total)! Plenty to master your Scala algos skills!

Upon purchase, you will be able to Register an account to access all the algorithms on multiple devices.

Stripe logo


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

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').

  3. View

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

Scala Algorithms: The most comprehensive library of algorithms in standard pure-functional Scala

Study our 92 Scala Algorithms: 6 fully free, 81 published & 11 upcoming

Fully unit-tested, with explanations and relevant concepts; new algorithms published about once a week.

  1. Compute the length of longest valid parentheses
  2. Check a binary tree is balanced
  3. Make a queue using stacks (Lists in Scala)
  4. Find height of binary tree
  5. Single-elimination tournament tree
  6. Reverse Polish Notation calculator
  7. Quick Sort sorting algorithm in pure immutable Scala
  8. Find minimum missing positive number in a sequence
  9. Least-recently used cache (LRU)
  10. Count pairs of a given expected sum
  11. Compute a Roman numeral for an Integer, and vice-versa
  12. Compute keypad possibilities
  13. Matching parentheses algorithm with foldLeft and a state machine
  14. Traverse a tree Breadth-First, immutably
  15. Read a matrix as a spiral
  16. Remove duplicates from a sorted list (state machine)
  17. Merge Sort: stack-safe, tail-recursive, in pure immutable Scala, N-way
  18. Longest increasing sub-sequence length
  19. Reverse first n elements of a queue
  20. Binary search a generic Array
  21. Game of Life
  22. Merge Sort: in pure immutable Scala
  23. Make a queue using Maps
  24. Is an Array a permutation?
  25. Count number of contiguous countries by colors
  26. Add numbers without using addition (plus sign)
  27. Tic Tac Toe MinMax solve
  28. Run-length encoding (RLE) Encoder
  29. Print Alphabet Diamond
  30. Balanced parentheses algorithm with tail-call recursion optimisation
  31. Reverse a String's words efficiently
  32. Count number of changes (manipulations) needed to make an anagram with foldLeft and a MultiSet
  33. Count passing cars
  34. Establish execution order from dependencies
  35. Counting inversions of a sequence (array) using a Merge Sort
  36. Longest common prefix of strings
  37. Check if an array is a palindrome
  38. Check a directed graph has a routing between two nodes (depth-first search)
  39. Compute nth row of Pascal's triangle
  40. Run-length encoding (RLE) Decoder
  41. Check if a number is a palindrome
  42. In a range of numbers, count the numbers divisible by a specific integer
  43. Find the index of a substring ('indexOf')
  44. Reshape a matrix
  45. Compute modulo of an exponent without exponentiation
  46. Closest pair of coordinates in a 2D plane
  47. Find the contiguous slice with the minimum average
  48. Compute maximum sum of subarray (Kadane's algorithm)
  49. Pure-functional double linked list
  50. Binary search in a rotated sorted array
  51. Check if a directed graph has cycles
  52. Rotate Array right in pure-functional Scala - using an unusual immutable efficient approach
  53. Check a binary tree is a search tree
  54. Length of the longest common substring
  55. Sliding Window Rate Limiter
  56. Tic Tac Toe board check
  57. Find an unpaired number in an array
  58. Check if a String is a palindrome
  59. Count binary gap size of a number using tail recursion
  60. Remove duplicates from a sorted list (Sliding)
  61. Monitor success rate of a process that may fail
  62. Least-recently used cache (MRU)
  63. Find sub-array with the maximum sum
  64. Find the minimum absolute difference of two partitions
  65. Find maximum potential profit from an array of stock price
  66. Fibonacci in purely functional immutable Scala
  67. Fizz Buzz in purely functional immutable Scala
  68. Find triplets that sum to a target ('3Sum')
  69. Find combinations adding up to N (non-unique)
  70. Make a binary search tree (Red-Black tree)
  71. Remove duplicates from an unsorted List
  72. Mars Rover
  73. Find combinations adding up to N (unique)
  74. Find indices of tuples that sum to a target (Two Sum)
  75. Count factors/divisors of an integer
  76. Compute single-digit sum of digits
  77. Traverse a tree Depth-First
  78. Reverse bits of an integer
  79. Find k closest elements to a value in a sorted Array
  80. QuickSelect Selection Algorithm (kth smallest item/order statistic)
  81. Rotate a matrix by 90 degrees clockwise

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

Register now (free)

 Register with GitHub    

How the algorithms look

  1. A description/goal of the algorithm.
  2. An explanation with both Scala and logical parts.
  3. A proof or a derivation, where appropriate.
  4. Links to Scala concepts used in this specific algorithm, also unit-tested.
  5. An implementation in pure-functional immutable Scala, with efficiency in mind (for most algorithms, this is for paid subscribers only).
  6. Unit tests, with a button to run them immediately in our in-browser IDE.
Screenshot of an example algorithm demonstrating the listed features