Suppose we are using the Rabin$-$Karp algorithm to search for the first four letters

of your last name $(\text{'}$barn$\text{'})$ in a text consisting of lowercase letters.

$($a$)$ Determine the hash value for the first four letters of your last name using the alphabet $\{$a$,$b$,$c$,...,$z$\}$ where a $=0,$ b $=1,$ etc., using a modulus of $23.$ Example calcuation $(26^3($a$)+26^2($n$)+26($m$)+$n$)$ mod $23.$

$($b$)$ Find an $8$ character string starting with abc which leads to the maximum number of false hits when searching for the first four letters of your last name.

$($c$)$ Find an $8$ character string that has $4$ false hits before successfully finding the pattern consisting of the first four letters of your last name.