a$)$ Create the failure function $($P$[$j$],$ f$[$j$])$ according to the Knuth$-$Morris$-$Pratt $($KMP$)$ algorithm for the pattern $$aabaabb$$ and

provide your result in the following table. In the blank space below the table insert your calculations step by step as

presented in the exercise.

j $0123456$

P$[$j$]$

f$[$j$]$ b$)$ Apply the KMP algorithm with the pattern $$aabaabb$($from example $1$a$)$ to the following text sequence $$baaabbaabaabaabb$,$

and determine the number of required comparisons. For this, write down the characters of the pattern that you currently

compare to the character in the text $($one character per cell$)$ and add in parantheses $()$ the number of comparisons

$($continuously increasing counter$)$ as illustrated in the $2$nd line of the table.

b a a a b b a a b a a b a a b b

a$(1)$