Find the minimum absolute difference of two partitions

Algorithm goal

Find the minimum absolute difference of partitions in an Array:

For example, array \([7,12,21]\) has partitions \(([7],[12,21])\) and \(([7,12],[21])\) with sums \((7, 12 + 21 = 33)\) and \((7 + 12 = 19,21)\), thus absolute differences of \(33 - 7 = 26\) and \(21-19=2\), thus minimum absolute difference of \(2\).

Empty partitions (sum \(0\)) are not considered.

This algorithm is similar to 'TapeEquilibrium' on Codility.

Explanation

In a more declarative Scala fashion, we should produce for ourselves a collection which contains a type (Int, Int) to describe the sum of the left partition and the sum of the right partition.

Once we have this collection, we can run the 'absolute' operation on it, and then 'minOption' to find the minimal value of that. (this is © from www.scala-algorithms.com)

To produce this collection, we start from (0, TotalSum), and then for each element, we add it to the first int, and subtract it from the second int. The result then becomes our collection - this sort of result is achieved with scanLeft and scanRight, and the optimisation with a View.

Scala Concepts & Hints

Drop, Take, dropRight, takeRight

Scala's `drop` and `take` methods typically remove or select `n` items from a collection.

assert(List(1, 2, 3).drop(2) == List(3))

assert(List(1, 2, 3).take(2) == List(1, 2))

assert(List(1, 2, 3).dropRight(2) == List(1))

assert(List(1, 2, 3).takeRight(2) == List(2, 3))

assert((1 to 5).take(2) == (1 to 2))

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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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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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scanLeft and scanRight

Scala's `scan` functions enable you to do folds like foldLeft and foldRight, while collecting the intermediate results

assert(List(1, 2, 3, 4, 5).scanLeft(0)(_ + _) == List(0, 1, 3, 6, 10, 15))

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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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View

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

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Algorithm in Scala

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

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Test cases in Scala

assert(solution(Array.empty) == None)
assert(solution(Array(7)) == None)
assert(solution(Array(7, 12)) == Some(5))
assert(solution(Array(7, 12, 21)) == Some(2))
assert(solution(Array(4, 5, 1, 3, 2)) == Some(3))
def solution(a: Array[Int]): Option[Int] = ???