# 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.

## 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")


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)


View

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

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))


assert(computeForArrayClearKadane(SampleArray).array.toList == BestSolution)

def computeForArrayClearKadane(array: Array[Int]): MaximumSubArrayResult = ???