String Functions

We consider a string of n characters, indexed 1,2,\dots,n. Your task is to calculate all values of the following functions: - z(i) denotes the maximum length of a substring that begins at position i and is a prefix of the string. In addition, z(1)=0. - \pi(i) denotes the maximum length of a substring that ends at position i, is a prefix of the string, and whose length is at most i-1. Note that