Question: Let [1. . ] be an array of distinct numbers (i.e., no two numbers are equal). If < and [] > [], then the pair

Let [1. . ] be an array of distinct numbers (i.e., no two numbers are equal). If < and [] > [], then the pair ([], []) is called an inversion of .

[5a]. List all inversions of the array {4, 2, 9, 1, 7}. (2.5 points)

[5b]. What array with elements from the set {1, 2, . . . , } has the most inversions? How many inversions does it have? (2.5 points)

[5c]. Give a divide-and-conquer algorithm that computes the number of inversions in array in ( log ) time. Show that your algorithm takes ( log ). (Hint: Modify merge sort.)

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