2. (20pts) Follow the instruction under each function written in pseudo code to analyze its asymptotic running time. (a) Function f1 fl Al1 to n:Integer Array) sum 0 for i-1 to n for j-1 to n-i sumAl return sum Instruction: The running time must be asymptotically proportional to 1 + 212-11. Calculate it exactly into a closed form. Also find the asymptotic running time in big 0-notaion of n. Justify your answers in total 1-10 lines. (b) Function f2 f2(A[1 to n: Integer Array) sum-0 for i-1 to n forja 1 to n- sum+max1sksj A[k] return sum Instruction: Find an expression including a double sum describing the running time similarly to the one in (a). Calculate it exactly into a closed form. Also find the asymptotic running time in big 0-notation of n. Justify your answers in total 1-10 lines