\(getItemWithHighest\Pr iority\left(\right)\){

1.  if A.heap-size < 1

            error "heap underflow"

2.   max = A[1]

3.   A[1] = A[A.heap-size]

4.   A.heap-size = A.heap-size - 1

5.   Remove <item, index> from AVL for max.  //  O(log n)

6.   Max-Heapify(A, 1)     //  O(log n)

7.    return max

Time Complexity Analysis:  Worst case could take maximum of O(log n) time.

Space Complexity Analysis: Max heapify may take log n  space to save log n recursivecalls to itself. Thus O(log n)