Scala algorithm: Length of the longest common substring

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Algorithm goal

The longest common substring is shared between two Strings. For example: 'XYZzz' and 'ddXYZdd' has common substring 'XYZ', which is of length 3.

Test cases in Scala

assert(longestCommonSubstringLength("XYZ", "XYZ") == 3)
assert(longestCommonSubstringLength("XYZd", "XYZ") == 3)
assert(longestCommonSubstringLength("XYZdd", "XYZ") == 3)
assert(longestCommonSubstringLength("ddXYZdd", "XYZ") == 3)
assert(longestCommonSubstringLength("zzXYZzz", "ddXYZ") == 3)
assert(longestCommonSubstringLength("zzXYZzz", "ddXYZdd") == 3)
assert(longestCommonSubstringLength("XYZzz", "ddXYZdd") == 3)
assert(longestCommonSubstringLength("XYZ", "ddXYZdd") == 3)
assert(longestCommonSubstringLength("zzXYZdd", "ddXYZ") == 3)

Algorithm in Scala

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Explanation

The type of mathematical deduction or proof we can deduce here is similar to LongestIncreasingSubSequenceLength:

Consider \(l(f, s)\) being the length of common sub-string ending at position \(f\) of the first string, and position \(s\) of the second string. (this is © from www.scala-algorithms.com)

Then, the next longest sub-string is \(l(f + 1, s + 1)\), which has a 1 added to it if the characters \(f+1\) of the first string and \(s+1\) of the second are equal.

If they are not equal, then \(l(f + 1, s + 1)\) is \(0\).

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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.

  5. 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'))
    

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