Let H be a binary min-heap consisting of n elements implemented as an array. What is the worst case time complexity of an optimal algorithm to find the maximum element in H?

What is the worst-case number of arithmetic operations performed by recursive binary search on a sorted array of size n?

A binary search tree T contains n distinct elements. What is the time complexity of picking an element in T that is smaller than the maximum element in T?

Consider a sequence of 14 elements : A = [-5, -10, 6, 3, -1, -2, 13, 4, -9, -1, 4, 12, -3, 0]. The subsequence sum $$S\left( {i,j} \right) = \sum\limits_{k = 1}^j {A\left[ k \right]} $$. Determine the maximum of S(i, j), where 0 ≤ i ≤ j < 14. (Divide and conquer approach may be used)

Answer : ________.