3. The algorihtm 2a is a standard find-min operation: it is supposed to return the element of minimum value in A. Use a loop invariant proof to show the algorithm 2a from the preceding question is correct. Here is a scaffold of the proof to get you started. We will use the following as our loop invariant: [your loop invariant here] Initialization: [your proof of initialization here] Maintenance: [state the maintenance condition you are proving here, then prove it] Termination: [your proof of what happens when the loop terminates here] [Remember to finish up the proof of correctness of the algorithmproving that the algorithm returns the correct valuewhich is at least one small step beyond the termination of the for loop.]

2. Identify and state a useful loop invariant in the following algorithms. You do not need to prove anything about it. (a) FindMinElement(A) : //array A is not empty A[length(A)] for i = 1 to length(A)-1 { if A[length(A)-i]