chap lower bounds single-elimination tournaments are notorious for their scheduling difficulties imagine that you are organizing tournament for basketball teams (you may assume that for some integer iwe will further simplify things by assuming that each game takes less than an hourand that each team can be scheduled for game every hour if necessary (note that everything said here about basketball courts is also true about processors in parallel algorithm to solve the maximum-finding problem(ahow many basketball courts do we need to insure that every team can play whenever we want to minimize the total tournament time(bhow long will the tournament be in this case(cwhat is the total number of "court-hoursavailablehow many total hours are courts being usedhow many total court-hours are unused(dmodify the algorithm in such way as to reduce the total number of courts neededby perhaps not letting every team play whenever possible this will increase the total hours of the tournamentbut try to keep the increase as low as possible for your new algorithmhow long is the tournamenthow many courts are neededhow many total court-hours are availablehow many court-hours are usedand how many unused explain why the cost of splitting list of six into two lists of three to find the minimum and maximum elements requires eight comparisonswhile splitting the list into list of two and list of four costs only seven comparisons write out table showing the number of comparisons required to find the minimum and maximum for all divisions for all values of < present an adversary argument as lower bounds proof to show that comparisons are necessary to find the maximum of values in the worst case present an adversary argument as lower bounds proof to show that comparisons are necessary in the worst case when searching for an element with value (if one existsfrom among elements section claims that by picking pivot that always discards at least fixed fraction of the remaining arraythe resulting algorithm will be linear explain why this is true hintthe master theorem (theorem might help you show that any comparison-based algorithm for finding the median must use at least comparisons show that any comparison-based algorithm for finding the second-smallest of values can be extended to find the smallest value alsowithout requiring any more comparisons to be performed