Please answer all parts and explain each and every steps. Thanks

2. (20pts) Follow the instruction under each function written in pseudo code to analyze its asymptotic running time. (a) Function f1 f1(Al1 to n: Integer Array) sum-0 for i-1 to n for j-1 ton-i sum+ Ali return sum Instruction: The running time must be asymptotically proportional to 1 + ?-E:1. 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(A1 to n]: Integer Array) sum-0 for i-1 to n for j-1 ton-i sum +maxiskSJ 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. (c) Function f3 f3(Al1 to n: integer array) na return A[1] else return f3A1 to to n Instruction: Write its running time recurrence. Then solve it to find the asymptotic running time of f3 in big e-notaion. Justify your answers in total 1-10 lines. (d) Function f4 f4(A1 to n: integer array) return Al1] else return f4(A1 to n-1]) f4(A[2 to n]) Instruction: Write its running time recurrence. Then solve it to find the asymptotic running time of f4 in big e-notaion, assuming T(1)-1. Justify your answers in total 1-10 lines. 2. (20pts) Follow the instruction under each function written in pseudo code to analyze its asymptotic running time. (a) Function f1 f1(Al1 to n: Integer Array) sum-0 for i-1 to n for j-1 ton-i sum+ Ali return sum Instruction: The running time must be asymptotically proportional to 1 + ?-E:1. 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(A1 to n]: Integer Array) sum-0 for i-1 to n for j-1 ton-i sum +maxiskSJ 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. (c) Function f3 f3(Al1 to n: integer array) na return A[1] else return f3A1 to to n Instruction: Write its running time recurrence. Then solve it to find the asymptotic running time of f3 in big e-notaion. Justify your answers in total 1-10 lines. (d) Function f4 f4(A1 to n: integer array) return Al1] else return f4(A1 to n-1]) f4(A[2 to n]) Instruction: Write its running time recurrence. Then solve it to find the asymptotic running time of f4 in big e-notaion, assuming T(1)-1. Justify your answers in total 1-10 lines