# Length of the longest common substring

## Algorithm goal

The longest common substring is what is shared between two Strings, eg: 'XYZzz' and 'ddXYZdd' (as per test cases) has common substring 'XYZ', which is of length 3.

## 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

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")


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))


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.

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))


## Algorithm in Scala

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

## 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)

def longestCommonSubstringLength(first: String, second: String): Int = ???