Scala algorithm: Find maximum potential profit from an array of stock price

Algorithm goal

Find the maximum potential profit given an array of stock prices, based on a buy followed by a sell. Where not possible to profit, return None.- Here we look for an efficient solution (\(O(n)\)). This problem is known as:

  • On Codility: MaxProfit - Given a log of stock prices compute the maximum possible earning. (100% pass)

Algorithm in Scala

20 lines of Scala (compatible versions 2.13 & 3.0), showing how concise Scala can be!

def findMaximumProfit(stockPrices: Array[Int]): Option[Int] = {
  val maximumSellPricesFromIonward = stockPrices.view
    .scanRight(0)({ case (maximumPriceSoFar, dayPrice) =>
      Math.max(maximumPriceSoFar, dayPrice)
  val maximumSellPricesAfterI = maximumSellPricesFromIonward.drop(1)
  if (stockPrices.length < 2) None
      .map({ case (buyPrice, sellPrice) =>
        getPotentialProfit(buyPrice = buyPrice, sellPrice = sellPrice)

def getPotentialProfit(buyPrice: Int, sellPrice: Int): Option[Int] = {
  if (sellPrice > buyPrice) Some(sellPrice - buyPrice) else None

Test cases in Scala

assert(findMaximumProfit(Array(163, 112, 105, 100, 151)).contains(51))
assert(findMaximumProfit(Array(1, 2)).contains(1))
assert(findMaximumProfit(Array(2, 1)).isEmpty)


We will derive the solution mathematically, so that we are certain that we are right (I will not even name the algorithm in this explanation because the mathematics is quite important so you can derive the solution for variations of this problem - knowing the algorithm is mostly not enough).

Our final goal is to find out \(\$_{\max} = \max\{\$_1, \$_2, ..., \$_{n-1}\}\), where \(\$_d\) is the maximum profit that that can be gained by can be achieved at buying a stock on day \(d\) at price \(p_d\) and selling it any day after \(d\). \(n-1\) is because cannot buy-and-sell on the same day. (this is © from

The price at which we sell stock after day \(d\) is simply the maximum price after day \(d\) (as to maximise the profit). If we name that \(S_d\) then it will be \(S_d = \max\{p_{d+1}, p_{d+2}, ..., p_{n}\}\). Then, \(\$_d = S_d - p_d\).

Notice that \(\max\{a, b, c\} = \max\{\max\{a, b\}, c\}\) (this is very important in this sort of problems), meaning that \(S_d = \max\{p_{d+1},S_{d+1}\}\).

Computing \(\$_{max} = \max\{S_1-p_1,S_2-p_2, ..., S_{n-1} - p_{n-1}\}\) directly is \(O(n^2)\) but because of our earlier relation, we can pre-compute the value of \(S_d\) from the value of \(S_{d+1}\) - it just means we have compute from right to left - in fact we can compute the whole array of \(S\) like that.

After computing \(S_d\), we already have \(p_d\) from the original price array, and then we can compute \(\$_d\) from all pairings of \(S_d\) and \(p_d\) to eventually find \(\$_{max}\).

In Scala, however, we needn't iterate and mutate - we can utilise functional programming and Scala's powerful collections. Please see the 'Scala concepts' below.

We plug in the relation for \(S_d\) into a `scanRight`, then we `zip` the prices \(p_d\) with \(S_d\) to find maximum potential profit at day \(d\), and then we find the maximum value across all values of \(d\).

How can you do `.max` on a `Array[Option[Int]]`?!!!

Scala is powerful. It has something called an `Ordering` which is automatically generated for eg `Option` so long as there is an `Ordering` for an `Int`.

Scala concepts & Hints

  1. 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))
  2. 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)
  3. 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")
  4. 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))
  5. 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)
  6. View

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

  7. Zip

    'zip' allows you to combine two lists pair-wise (meaning turn a pair of lists, into a list of pairs)

    It can be used over Arrays, Lists, Views, Iterators and other collections.

    assert(List(1, 2, 3).zip(List(5, 6, 7)) == List(1 -> 5, 2 -> 6, 3 -> 7))
    assert(List(1, 2).zip(List(5, 6, 7)) == List(1 -> 5, 2 -> 6))
    assert(List(5, 6).zipWithIndex == List(5 -> 0, 6 -> 1))
    assert(List(5, 6).zipAll(List('A'), 9, 'Z') == List(5 -> 'A', 6 -> 'Z'))
    assert(List(5).zipAll(List('A', 'B'), 1, 'Z') == List(5 -> 'A', 1 -> 'B'))

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

Think in Scala & master the highest paid programming language in the US

Scala is used at many places, such as AirBnB, Apple, Bank of America, BBC, Barclays, Capital One, Citibank, Coursera, eBay, JP Morgan, LinkedIn, Morgan Stanley, Netflix, Singapore Exchange, Twitter.

Study our 92 Scala Algorithms: 6 fully free, 74 published & 18 upcoming

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

  1. Compute the length of longest valid parentheses
  2. Check a binary tree is balanced
  3. Make a queue using stacks (Lists in Scala)
  4. Find height of binary tree
  5. Single-elimination tournament tree
  6. Quick Sort sorting algorithm in pure immutable Scala
  7. Find minimum missing positive number in a sequence
  8. Least-recently used cache (LRU)
  9. Count pairs of a given expected sum
  10. Compute a Roman numeral for an Integer, and vice-versa
  11. Compute keypad possibilities
  12. Matching parentheses algorithm with foldLeft and a state machine
  13. Traverse a tree Breadth-First, immutably
  14. Read a matrix as a spiral
  15. Remove duplicates from a sorted list (state machine)
  16. Merge Sort: stack-safe, tail-recursive, in pure immutable Scala, N-way
  17. Longest increasing sub-sequence length
  18. Reverse first n elements of a queue
  19. Binary search a generic Array
  20. Merge Sort: in pure immutable Scala
  21. Make a queue using Maps
  22. Is an Array a permutation?
  23. Count number of contiguous countries by colors
  24. Add numbers without using addition (plus sign)
  25. Tic Tac Toe MinMax solve
  26. Run-length encoding (RLE) Encoder
  27. Print Alphabet Diamond
  28. Balanced parentheses algorithm with tail-call recursion optimisation
  29. Reverse a String's words efficiently
  30. Count number of changes (manipulations) needed to make an anagram with foldLeft and a MultiSet
  31. Count passing cars
  32. Establish execution order from dependencies
  33. Counting inversions of a sequence (array) using a Merge Sort
  34. Longest common prefix of strings
  35. Check if an array is a palindrome
  36. Check a directed graph has a routing between two nodes (depth-first search)
  37. Compute nth row of Pascal's triangle
  38. Run-length encoding (RLE) Decoder
  39. Check if a number is a palindrome
  40. In a range of numbers, count the numbers divisible by a specific integer
  41. Find the index of a substring ('indexOf')
  42. Reshape a matrix
  43. Compute modulo of an exponent without exponentiation
  44. Closest pair of coordinates in a 2D plane
  45. Find the contiguous slice with the minimum average
  46. Compute maximum sum of subarray (Kadane's algorithm)
  47. Pure-functional double linked list
  48. Binary search in a rotated sorted array
  49. Check if a directed graph has cycles
  50. Rotate Array right in pure-functional Scala - using an unusual immutable efficient approach
  51. Check a binary tree is a search tree
  52. Length of the longest common substring
  53. Tic Tac Toe board check
  54. Find an unpaired number in an array
  55. Check if a String is a palindrome
  56. Count binary gap size of a number using tail recursion
  57. Remove duplicates from a sorted list (Sliding)
  58. Monitor success rate of a process that may fail
  59. Find sub-array with the maximum sum
  60. Find the minimum absolute difference of two partitions
  61. Find maximum potential profit from an array of stock price
  62. Fibonacci in purely functional immutable Scala
  63. Fizz Buzz in purely functional immutable Scala
  64. Find combinations adding up to N (non-unique)
  65. Make a binary search tree (Red-Black tree)
  66. Remove duplicates from an unsorted List
  67. Find combinations adding up to N (unique)
  68. Count factors/divisors of an integer
  69. Compute single-digit sum of digits
  70. Traverse a tree Depth-First
  71. Reverse bits of an integer
  72. Find k closest elements to a value in a sorted Array
  73. QuickSelect Selection Algorithm (kth smallest item/order statistic)
  74. 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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