Need answer for question 3. Do not post codes plz .

INSTRUCTIONS: In the following problems you are asked to design and analyze efficient iterative or recursive algorithms. Follow the Loop-Invariant design-&-verification method for iterative algorithms, and the strong induction method for recursive algorithms. You should clearly state and explain the proof steps as learned in the course. 1. Double Vision in Sorted Array: Design and analyze an O(n) time in-place algorithm for the following problem. Input: An array A[1..n] of n positive real numbers sorted in increasing order. Output: True if there is a pair of indices i and j such that A[i] = 2A[j] ; false otherwise. 2. The Longest All-Positive Sub-Array Problem: Input: An array A[1..n] of arbitrary integers. Output: The longest contiguous sub-array of A[1..n] with positive entries only. 3. The Maximum-Sum Monotone Sub-Array Problem: Input: An array A[1..n] of arbitrary positive integers. Output: The maximum-element-sum contiguous sub-array of A[1..n] whose entries form a monotone sequence (either ascending or descending)