Essay on Algorithm. Paper must be at least 1750 words. The time taken for reversing the array would be linear to the length of the subsequence at each round. The time taken for palindromic check would also be linear to half of the length of the subsequence returned at each round. Hence, the total time for the algorithm would be O (n2).For the subsequence x [i…j] to be palindromic, the element x[i] should be equal to x[j], the element x [i+1] should be equal to x [j-1] and so on. Hence, to compute L (i, j), the elements x [i] and the element x [j] are first checked for equality. If equal, then we can say that L (i, j) holds at least a minimum value of 2 and the equality check is repeated for the next element x [i+1] and x [j-1]. If not equal, it is concluded that at least one of the element is not included in the palindrome. In that case, we are interested in repeating the check for elements x[i] and x [j-1] as well as x [i+1] and x [j] as we are not sure which element is not included in the palindrome. In the worst case, if none of the elements match, then L (i, j) is equal to 1 as every element is a palindrome of itself.Complexity analysis: As the computation involves two for loops, one running n-1 times which is O (n) and the other running n-s times which is also O (n), the total running time for the algorithm would be O (n2).Let be the median of x1, x2, x3.