Inversions

October 31, 2017

In an array A, the term inversions refers to the number of items that are out of order; each i < j for which A[j] < A[i] counts as a single inversion. For instance, the array [1 4 3 2 5] has three inversions: (4,3), (4,2) and (3,2). Inversions are a measure of the disorder of an array: an ordered array has no inversions and a reversed array has the maximum n(n−1)/2 number of inversions.

Your task is to write programs that count the number of inversions in an array and make an enumeration of them. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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