Subject - Design & Anal algorithms

Please complete all the question together. Thank you in Advance.

I have two algorithms, A and B, that are used to change the ordering of an array of n elements. A uses n 2 operations, whereas B uses n log(n) operations. Which algorithm should one prefer and why? Problem 3. Bubblesort: [25pt] Consider the following pseudocode for bubblesort: bubblesort(A, n) for i from 1 to n − 1 for j from n to i + 1 if A[j] < A[j − 1] swap(A[j], A[j − 1]) (a) What is the loop invariant for bubblesort? (b) State briefly a proof of correctness. (c) Derive concisely the worst-case running time of bubblesort as a function of the input array size n? Show your work! (d) Derive concisely the best-case running time as a function of n. Show your work!