Scala algorithm: Length of the longest common substring

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

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

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 \(0\).

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")
   

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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))
   

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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)
   

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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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