# Problem 44

#### Description

This problem was asked by Google.

We can determine how "out of order" an array A is by counting the number of inversions it has. Two elements `A[i]`

and `A[j]`

form an inversion if `A[i] > A[j]`

but `i < j`

. That is, a smaller element appears after a larger element.

Given an array, count the number of inversions it has. Do this faster than `O(N^2)`

time.

You may assume each element in the array is distinct.

For example, a sorted list has zero inversions. The array `[2, 4, 1, 3, 5]`

has three inversions: `(2, 1)`

, `(4, 1)`

, and `(4, 3)`

. The array `[5, 4, 3, 2, 1]`

has ten inversions: every distinct pair forms an inversion.