Problem 3 : Given an array of integers, A, we define the inversion value, i(A), of array A as follows. Let i and j be indices into the array A such that i A[j] then the pair (i, j) is an inversion. The inversion value is the total number of inversion pairs in the array. (a) Construct a brute-force algorithm that executes in O(na) time that calculate the inversion value for any array. (b) Improve the solution from part (a) by employing a Merge Sort that operates in O(n log n) time complexity. Problem 3 : Given an array of integers, A, we define the inversion value, i(A), of array A as follows. Let i and j be indices into the array A such that i A[j] then the pair (i, j) is an inversion. The inversion value is the total number of inversion pairs in the array. (a) Construct a brute-force algorithm that executes in O(na) time that calculate the inversion value for any array. (b) Improve the solution from part (a) by employing a Merge Sort that operates in O(n log n) time complexity