a$)$ Suppose that all characters in the pattern $P$ are different. Show how to accelerate NAIVE$-$

STRING$-$MATCHER to run in $O(n)$ time on an n$-$character text T$.$

b$)$ You are supposed to find out how many spurious hits does the Rabin$-$Karp matcher encounter

in the text $T=3141592653589793$ when looking for the pattern $P=26$ working with modulo $q$

calculated by using the given formula.

$q=($Last four digits of your roll number$)$ modulus $11$

For example, if your roll number is $23i-2159$ then $q=2159$ modulus $11=3.$