# 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

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 Â© 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.

### scanLeft and scanRight

Scala's `scan` functions enable you to do folds like foldLeft and foldRight, while collecting the intermediate results

### 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.

### 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.