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 (version 2.13), showing how concise Scala can be!
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
The for-comprehension is highly important syntatic enhancement in functional programming languages.
The 'LazyList' type (previously known as 'Stream' in Scala) is used to describe a potentially infinite list that evaluates only when necessary ('lazily').
.viewsyntax creates a structure that mirrors another structure, until "forced" by an eager operation like .toList, .foreach, .forall, .count.