Scala algorithm: 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.

Test cases in Scala

assert(computeForArrayClearKadane(SampleArray).array.toList == BestSolution)
assert(computeForArrayClearKadane(SampleArray).sumSoFar == 6)

Algorithm in Scala

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

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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

  1. 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")
    
  2. 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))
    
  3. 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)
    
  4. View

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


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

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Study our 94 Scala Algorithms: 6 fully free, 54 published & 40 upcoming

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

  1. Quick Sort sorting algorithm in pure immutable Scala
  2. Find minimum missing positive number in a sequence
  3. Longest increasing sub-sequence length
  4. Counting inversions of a sequence (array) using a Merge Sort
  5. Check if an array is a palindrome
  6. Monitor success rate of a process that may fail
  7. Find combinations adding up to N (non-unique)
  8. Find combinations adding up to N (unique)
  9. Find k closest elements to a value in a sorted Array
  10. Compute a Roman numeral for an Integer, and vice-versa
  11. Matching parentheses algorithm with foldLeft and a state machine
  12. Traverse a tree Breadth-First, immutably
  13. Read a matrix as a spiral
  14. Remove duplicates from a sorted list (state machine)
  15. Merge Sort: stack-safe, tail-recursive, in pure immutable Scala, N-way
  16. Binary search a generic Array
  17. Merge Sort: in pure immutable Scala
  18. Is an Array a permutation?
  19. Count number of contiguous countries by colors
  20. Add numbers without using addition (plus sign)
  21. Tic Tac Toe MinMax solve
  22. Run-length encoding (RLE) Encoder
  23. Print Alphabet Diamond
  24. Balanced parentheses algorithm with tail-call recursion optimisation
  25. Reverse a String's words efficiently
  26. Count number of changes (manipulations) needed to make an anagram with foldLeft and a MultiSet
  27. Compute nth row of Pascal's triangle
  28. Run-length encoding (RLE) Decoder
  29. Check if a number is a palindrome
  30. In a range of numbers, count the numbers divisible by a specific integer
  31. Find the index of a substring ('indexOf')
  32. Reshape a matrix
  33. Closest pair of coordinates in a 2D plane
  34. Find the contiguous slice with the minimum average
  35. Compute maximum sum of subarray (Kadane's algorithm)
  36. Binary search in a rotated sorted array
  37. Rotate Array right in pure-functional Scala - using an unusual immutable efficient approach
  38. Length of the longest common substring
  39. Tic Tac Toe board check
  40. Find an unpaired number in an array
  41. Check if a String is a palindrome
  42. Count binary gap size of a number using tail recursion
  43. Remove duplicates from a sorted list (Sliding)
  44. Find sub-array with the maximum sum
  45. Find the minimum absolute difference of two partitions
  46. Find maximum potential profit from an array of stock price
  47. Fibonacci in purely functional immutable Scala
  48. Fizz Buzz in purely functional immutable Scala
  49. Count factors/divisors of an integer
  50. Compute single-digit sum of digits
  51. Traverse a tree Depth-First
  52. Reverse bits of an integer
  53. QuickSelect Selection Algorithm (kth smallest item/order statistic)
  54. Rotate a matrix by 90 degrees clockwise

Explore the 21 most useful Scala concepts

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

  1. Class Inside Class
  2. Class Inside Def
  3. Collect
  4. Def Inside Def
  5. Drop, Take, dropRight, takeRight
  6. foldLeft and foldRight
  7. For-comprehension
  8. Lazy List
  9. Option Type
  10. Ordering
  11. Partial Function
  12. Pattern Matching
  13. Range
  14. scanLeft and scanRight
  15. Sliding / Sliding Window
  16. Stack Safety
  17. State machine
  18. Tail Recursion
  19. Type Class
  20. View
  21. Zip

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