Find an unpaired number in an array

Algorithm goal

If you were to group each number of an array with another one of itself, would there be any that cannot be grouped?


This problem firstly does not specifically have to be on numbers - it applies in fact to any type, which is why we use generic types of Scala to implement the solution.

The solution approach is to create a Set, and as soon as an item is encountered, remove it from the set if it is there, and append to the set if it is not -- then any item remaining in the set is basically the unpaired item. (this is © from

This provides us with the ability to be more precise because a type T cannot be accidentally mixed up with an Int.

The Scala approach we use is to run a 'foldLeft' - a 'foldLeft' is basically an iteration over all the values with a function, and a final result. See 'Concepts' below for explanation.

Scala Concepts & Hints

Pattern Matching

Pattern matching in Scala lets you quickly identify what you are looking for in a data, and also extract it.

assert("Hello World".collect {
  case character if Character.isUpperCase(character) => character.toLower
} == "hw")

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foldLeft and foldRight

A 'fold' allows you to perform the equivalent of a for-loop, but with a lot less code.

def foldMutable[I, O](initialState: O)(items: List[I])(f: (O, I) => O): O =

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Stack Safety

Stack safety is present where a function cannot crash due to overflowing the limit of number of recursive calls.

This function will work for n = 5, but will not work for n = 2000 (crash with java.lang.StackOverflowError) - however there is a way to fix it :-)

In Scala Algorithms, we try to write the algorithms in a stack-safe way, where possible, so that when you use the algorithms, they will not crash on large inputs. However, stack-safe implementations are often more complex, and in some cases, overly complex, for the task at hand.

def sum(from: Int, until: Int): Int =
  if (from == until) until else from + sum(from + 1, until)

def thisWillSucceed: Int = sum(1, 5)

def thisWillFail: Int = sum(1, 300)

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Option Type

The 'Option' type is used to describe a computation that either has a result or does not. In Scala, you can 'chain' Option processing, combine with lists and other data structures. For example, you can also turn a pattern-match into a function that return an Option, and vice-versa!

assert(Option(1).flatMap(x => Option(x + 2)) == Option(3))

assert(Option(1).flatMap(x => None) == None)

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Algorithm in Scala

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

def findUnpairedItem[T](a: Array[T]): Option[T] = {
      case (set, n) if set.contains(n) =>
        set - n
      case (set, n) =>
        set + n

Test cases in Scala

assert(findUnpairedItem(Array(1, 2, 1)).contains(2))
assert(findUnpairedItem(Array(1, 2, 1, 1, 1)).contains(2))
assert(findUnpairedItem(Array(1, 1, 1, 1, 1)).contains(1))
assert(findUnpairedItem(Array(1, 1, 1, 1)).isEmpty)
assert(findUnpairedItem(Array(1, 2, 3, 1, 2)).contains(3))
assert(findUnpairedItem(Array(1, 2, 3, 3, 1, 2)).isEmpty)
def findUnpairedItem[T](a: Array[T]): Option[T] = ???