Question 3. (30 points) Let P=p1p2pm be a string and let f be the function (as defined in the slides on KMP) such that f(i) is the length of the longest proper prefix of p1p2pi that is also a suffix of p1p2pi. For example, if P=abracadabra then f(4)=1 and f(11)=4. Suppose that m is a power of 2 , i.e., it is 2q for some integer q (assume q8 ). Answer each of the following questions. 1. Assuming f(m)=m2, write down a simple equation for f(j) as a function of j for 2j