mapshash tablesand skip lists - although keys in map are distinctthe binary search algorithm can be applied in more general setting in which an array stores possibly duplicative elements in nondecreasing order consider the goal of identifying the index of the leftmost element with key greater than or equal to given does the find index method as given in code fragment guarantee such resultdoes the find index method as given in exercise - guarantee such resultjustify your answers - suppose we are given two sorted search tables and each with entries (with and being implemented with arraysdescribe an (log )time algorithm for finding the kth smallest key in the union of the keys from and (assuming no duplicatesc- give an (log )-time solution for the previous problem - suppose that each row of an array consists of ' and ' such thatin any row of aall the ' come before any ' in that row assuming is already in memorydescribe method running in ( log ntime (not ( time!for counting the number of ' in - given collection of cost-performance pairs (cp)describe an algorithm for finding the maxima pairs of in ( log ntime - show that the methods above(pand prev(pare not actually needed to efficiently implement map using skip list that iswe can implement insertions and deletions in skip list using strictly top-downscanforward approachwithout ever using the above or prev methods (hintin the insertion algorithmfirst repeatedly flip the coin to determine the level where you should start inserting the new entry - describe how to modify skip-list representation so that index-based operationssuch as retrieving the item at index jcan be performed in (log nexpected time - for sets and the syntax returns new set that is the symmetric differencethat isa set of elements that are in precisely one of or this syntax is supported by the special xor method provide an implementation of that method in the context of the mutableset abstract base classrelying only on the five primary abstract methods of that class - in the context of the mutableset abstract base classdescribe concrete implementation of the and methodwhich supports the syntax for computing the intersection of two existing sets - an inverted file is critical data structure for implementing search engine or the index of book given document dwhich can be viewed as an unorderednumbered list of wordsan inverted file is an ordered list of wordslsuch thatfor each word in lwe store the indices of the places in where appears design an efficient algorithm for constructing from