Question: (30 points) Let A[1...n] be an array of n distinct numbers (i.e., no two numbers are equal). If i A[j], then the pair (A[i], A[j])

(30 points) Let A[1...n] be an array of n distinct numbers (i.e., no two numbers are equal). If i A[j], then the pair

(30 points) Let A[1...n] be an array of n distinct numbers (i.e., no two numbers are equal). If i A[j], then the pair (A[i], A[j]) is called an inversion of A. (a) List all inversions of the array {4, 2,9,1, 7}. (5 points) (b) What array with elements from the set {1, 2, ...,n} has the most inversions? How many inversions does it have? (5 points) (c) Give a divide-and-conquer algorithm that computes the number of inversions in array A in O(n log n) time. (Hint: Modify merge sort.) (20 points)

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