efficient method for computing each of partial sums what is the running time of this methodfor , - draw visual justification of proposition analogous to that of figure (bfor the case when is odd - an array contains unique integers in the range [ , that isthere is one number from this range that is not in design an ( )-time algorithm for finding that number you are only allowed to use ( additional space besides the array itself - let be set of lines in the plane such that no two are parallel and no three meet in the same point showby inductionthat the lines in determine th( intersection points - show that the summation is (nlognc- an evil king has bottles of wineand spy has just poisoned one of them unfortunatelythey don' know which one it is the poison is very deadlyjust one drop diluted even billion to one will still kill even soit takes full month for the poison to take effect design scheme for determining exactly which one of the wine bottles was poisoned in just one month' time while expending (logntaste testers - suppose that each row of an array consists of ' and ' such thatin any row of all the ' come before any ' in that row assuming is already in memorydescribe method running in (ntime (not ( timefor finding the row of that contains the most ' -