Answer the following question using a step-by-step procedure. Include all necessary steps and comments, showing all your work throughout the solution. The material is based of zybooks and what was lectured during class time. Thank you and will rate afterwards!

3. (20 pts) Consider the following pseudocode of an algorithm, assuming that the input is an Integer array A[1..n], where n is a power of 2. SomeAlgo(A) n 0 return A[n/2] else return A[n] (a) (10 pts) Analyze running time of the above algorithm Some Algo and give the best bounds as you can on the running time of the algorithm. (b) (5 pts) Now assuming that lines 7 and 9 are replaced with 7 9 return SOMEALGO(A[1..n/2]) return SOMEALGO(A[(n/2 + 1)..n]) Give the recurrence that represents the running time of the algorithm. (c) (5 pts) Determine the running time of the algorithm SOMEALGO by solving the recurrence you gave in (b)