Question

The following algorithm checks if the array A is sorted in the ascending order.
   isSorted(A)
   n <- A.length
   i <- 2
   while i <= n
             if A[i - 1] >A[i]
                         return false
             i <- i + 1
   return true
a) Give its best-case and worst-case running time. Justify your answer.
b) Using a suitable loop invariant, prove the correctness of the algorithm.
c) Write an algorithm to check if a linked list is sorted in the ascending order.

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a) First of all, we notice that the algorithm can output “true” (sorted in ascending order) if and only if it is traversed the entire array. On the other hand, it can output “false” at any iteration of the “while” loop.
So the best case is achieved when the algorithm outputs “false” after a comparison (e.g. if a[1]>a[2]) or after a constant number of comparisons (by constant we consider a number c much less than input size n); in this case the algorithm requires O(1) (constant) effort...

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