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 (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 Â© 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').

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

How our 100 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.

Study our 100 Scala Algorithms: 6 fully free, 100 published & 0 upcoming

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

Explore the 22 most useful Scala concepts

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

Subscribe to Scala Algorithms

Maximize your Scala with disciplined and consistently unit-tested solutions to 100+ algorithms.

Use it from improving your day-to-day data structures and Scala; all the way to interviewing.