given collection of cost-performance pairs ( , )describe an algorithm for finding the maxima pairs of in ( logntime - the quadratic probing strategy has clustering problem related to the way it looks for open slots namelywhen collision occurs at bucket ( )it checks buckets [( (kj mod ]for , show that mod will assume at most ( )/ distinct valuesfor primeas ranges from to as part of this justificationnote that mod ( ) mod for all better strategy is to choose prime such that mod and then to check the bucketsa[( ( + mod nas ranges from to ( )/ alternating between plus and minus show that this alternate version is guaranteed to check every bucket in - show that the methods above(pand prev(pare not actually needed to efficiently implement dictionary using skip list that iswe can implement entry insertion and removal in skip list using strictly top-downscan-forward 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 implement successors(kin an ordered dictionary realized using an ordered search table what is its running timec- repeat the previous exercise using skip list what is the expected running time in this casec- 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