Def find_minimum(arr, start_ix): """ find the value and index of the minimum elements in arr[start_ix: ] assumes that len(arr) > 0. """ start_value = arr[start_ix] if start_ix == len(arr) - 1: return start_value, start_ix tail_min_value, tail_min_ix = find_minimum(arr, start_ix+1) if tail_min_value < start_value: return tail_min_value, tail_min_ix else: return start_value, start_ix(a) in the above algorithm, let n = len(arr) - start_ix; that is, n is the size of the sub-array which is searched. let s(n) be the time taken by find_minimum when run on an input of size n. write a recurrence for relation for s(n). the right hand side should contain s along with something else (express the "something else" in θ-) when solving a recurrence relation we can typically get away with replacing θ(f(n)) by f(n) as long as we express our final answer asymptotically. in part a), you should have θ(1) in your recurrence. replace this θ(1) with 1 solve the resulting recurrence relation. your final answer should be in θ-notation .