Write an efficient algorithm for the problem below, describe why it is a correct algorithm, and analyze the time complexity If you cannot find any polynomial time algorithm, then give a backtracking algorithm Problem Find Array Core Input An array A 1 n of positive integers, and an integer k where k n No integer is repeated in A Output Two numbers p and q of A such that there are exactly k other elements in A which are neither smaller than p and nor larger than q Example Input A 4,7,5,3,9,1 , k 2 Output p 4, q 9 (because there are exactly two numbers 7 and 5 (other than 4 and 9) which are neither smaller than 4 nor larger than 9 )

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Question: Write an efficient algorithm for the problem below, describe why it is a correct algorithm, and analyze the time complexity. If you cannot find any

Write an efficient algorithm for the problem below, describe why it is a correct algorithm, and analyze the time complexity. If you cannot find any polynomial-time algorithm, then give a backtracking algorithm.

Problem: Find Array Core
Input: An array A[1...n] of positive integers, and an integer k where k < n. No integer is repeated in A.
Output: Two numbers p and q of A such that there are exactly k other elements in A which are neither smaller than p and nor larger than q.
Example: Input: A = [4,7,5,3,9,1], k = 2. Output: p = 4, q = 9 (because there are exactly two numbers 7 and 5 (other than 4 and 9) which are neither smaller than 4 nor larger than 9.)

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