Find sub-array with the maximum sum

Algorithm goal

The problem is a follow-up to the problem MaximumSubArraySum, to provide a result that also contains the sub-array of interest, not just the sum.

This sort of problem may come up in real-life optimisation tasks.

Explanation

Please read the MaximumSubArraySum problem explanation for the mathematics - for this problem here, we will focus on how to attach the source array and how to get it the most efficiently.

Here, we use a 'State Machine', which lets us group together various values. (this is © from www.scala-algorithms.com)

Once we have iterated through the whole array, we have a 'view' of a set of best results ending at each position. Then we pick the best one overall with `maxBy`, and from that, we extract the resulting array.

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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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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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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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Algorithm in Scala

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

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Test cases in Scala

assert(computeForArrayClearKadane(SampleArray).array.toList == BestSolution)
assert(computeForArrayClearKadane(SampleArray).sumSoFar == 6)
def computeForArrayClearKadane(array: Array[Int]): MaximumSubArrayResult = ???