Follow the instruction under each function written in pseudo code to analyze its

Question

Follow the instruction under each function written in pseudo code to analyze its asymptotic running time. (a) Function f1 f1(A[1 to n]: Integer Array) sum 0 for i1 ton for j=1 to n-L return sum Instruction: The running time must be asymptotically proportional to 1+ 2i1Zjzi1. Calculate it exactly into a closed form. Also find the asymptotic running time in big O-notaion of n. Justify your answers in total 1-10 lines (b) Function f2 f2(A[1 to n]: Integer Array) sum 0 for i1 ton for j-1 to n-i, sum += maxi sk sj 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 irn big 0-notation of n. Justify your answers in total 1-10 lines

Explanation / Answer

1. n-1 + n-2 + n-3 + .... = (n-1)(n-2)/2= (n^2-3n+2)/2

the sequence is basically summation of first n-1 numbers.

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