You wish to find duplicates in an unsorted n-element array A. 1,..., 2n integers. Give this solution's worst-case running time asymptotically T(n). Find the best algorithm

There’s a length n (n ≥ 3) array and we’d like to fill in each element of the array with an integer.The integers should be in {1, 2, . . . , k} and any 3 adjacency entries cannot have the same number. Given nand k , design a polynomial time algorithm to compute the number of ways to fill this array. Please alsojustify the correctness and the time complexity of your answers.

Algorthim of how to find the largest element missing in an unsorted array of n positive  integers and the running time of the algorthim is in O(n).  Example of this is that the n=6 array C= [5,90,8,6,26,9] The largest element missing in the array is 7

Give a MPI program segment to convert a n-by-n matrix distributed on a n-by-n 2D mesh such that allits rows and columns get sorted in ascending order. Show only the iterative loop. Only communicationsallowed are to the four direct neighbors. (Hint: You may employ a variant of odd-even transpositionsort, but the whole matrix does not need to be sorted.)