It is actually an application of divide-and-conquer algorithm, and if you are familiar with it you can come up with the solution quickly.
Take [1 3 8 5 7 2 4 6] as an example, assume we have sorted array as [1 3 5 8] and [2 4 6 7], and now we need to combine the two arrays and get the number of total inversions.
Since we already have number of inversions in each sub-array, we only need to find out the number of inversions caused by array merging. Each time an element is inserted, for example, 2 inserted into [1 # 3 5 8], you can know how many inversions there are between the first array and the element 2 (3 pairs in this example). Then you can add them up to get the number of inversions caused by merging.
