Consider the pseudocode below that computes the index of the maxium value in array:

Max(A, n) // A is an array of integers

max = A[1]

for i=2 to n

if A[i] > max

max = A[i]

return max

1. Write a loop invariant that can be used to prove the correctness of the loop above.

2. Show the invariant you wrote on part 1 is true at initialization, maintenance and termination of the loop. Then use that fact to prove the correctness of the algorithm.