say that pattern of length is circular substring of text of length if there is an index < msuch that [ [ ]that isif is (normalsubstring of or is equal to the concatenation of suffix of and prefix of give an ( )-time algorithm for determining whether is circular substring of - the kmp pattern matching algorithm can be modified to run faster on binary strings by redefining the failure function as where denotes the complement of the kth bit of describe how to modify the kmp algorithm to be able to take advantage of this new failure function and also give method for computing this failure function show that this method makes at most comparisons between the text and the pattern (as opposed to the comparisons needed by the standard kmp algorithm given in section - modify the simplified bm algorithm presented in this using ideas from the kmp algorithm so that it runs in ( mtime - given string of length and string of length mdescribe an ( )time algorithm for finding the longest prefix of that is suffix of - give an efficient algorithm for deleting string from standard trie and analyze its running time - give an efficient algorithm for deleting string from compressed trie and analyze its running time - describe an algorithm for constructing the compact representation of suffix triegiven its noncompact representationand analyze its running time - let be text string of length describe an ( )-time method for finding the longest prefix of that is substring of the reversal of