total size of all the sequences - given sequence of elementson which total order relation is defineddescribe an efficient method for determining whether there are two equal elements in what is the running time of your methodc- let be sequence of elements on which total order relation is defined recall that an inversion in is pair of elements and such that appears before in but describe an algorithm running in (nlogntime for determining the number of inversions in - let be sequence of integers describe method for printing out all the pairs of inversions in in ( ktimewhere is the number of such inversions - let be random permutation of distinct integers argue that the expected running time of insertion-sort on is ( (hintnote that half of the elements ranked in the top half of sorted version of are expected to be in the first half of - let and be two sequences of integers each given an integer mdescribe an ( log -time algorithm for determining if there is an integer in and an integer in such that - given set of integersdescribe and analyze fast method for finding the logn integers closest to the median - bob has set of nuts and set of boltssuch that each nut in has unique matching bolt in unfortunatelythe nuts in all look the sameand the bolts in all look the same as well the only kind of comparison that bob can make is to take nut-bolt pair (ab)such that is in and is in band test it to see if the threads of are largersmalleror perfect match with the