Give an efficient solution to determine if there exists an integer i such that A_i = i in an array of integers A₁ < A₂ < A₃ < .....< A_n .

The naive and basic approach is to do the sequential search. Sequentially look at every item in the array and find whether there is a match for A[i] = i for any index i. The worst-case runtime of this algorithm is O(N), N being the size of input.

Please Note that, the array is sorted in ascending order. Can you find a better (more efficient than O(N)) solution to this problem?

Write down the better algorithm (in Pseudocode) and show the worst case and best case run time (using big-oh notation) of the algorithm