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Professor Combine has proposed a new convex hull algorithm that combines the divide and conquer algorithm and the Graham Scan algorithm. The pseudo code of the al gorithm is presented below: CombinedConvexHull(S)// finding the convex hull for the set of points (S) 1 if jSIk9// the set has less than 9 points retum Graham Scan(S) //return convex hull of S constructed using Graham scan 3 else //divide and conquer approach 4 5 S1 lessMym S) I find all the points whose y-coordsym 6 Yn = median(S) // return the median of y-coords of points in S. It can be done in OasD S2 greaterMym S)I find all the points whose y-coords>y CH1 CombinedConvexHull (SI) CH2-CombinedConvexHull (S2) convex hull of S1 convex hull of S2 9 return Combine(CH1, CH2)// merges the 2 convex hulls. //assume the complexity of merge is0(CHll-CH2 ).CHII=#ofpoints on CHI | a. Give a recurrence for the worst-case running time of CombinedConvexHull for a set of n points. b. Solve the recurrence obtained in (a) using the master theorem Give one reason you think Professor Combine's algorithm might be better than the standard divide-conquer convex hull? Justify your answer c