For each problem, provide an algorithm, demonstrate its correctness, and limit its execution time.

Correct solutions that are faster will receive higher scores.

A substring of a string $s$ is a sequence of consecutive characters from $s($for example, "aac" has

the following $6$ distinct substrings: $"$a$","$aa$","$ac$",$ "aac", $"$c$","").$ Provide an algorithm that, given two

strings $s$ and $t$ of the same length $n,$ returns the length of the longest string that is a substring of

both $s$ and $t.$

Example $1$: if $s=$ "abcdfe" and $t=$ "acdfet", then the longest common substring $("$cdfe$")$ has a

length of $4.$

Example $2$: if $s=$ "abc" and $t=$ "acd", then each longest common substring has a length of $1$

$($the longest substrings are $"a"$ and $"$c$").$