Show how to use an order-statistic tree to count the number of inversions (see Problem 2-4) in an array of size n in time O(n lg n).

1)建立order-statistic tree 需要O(nlgn)

2)求每个元素的rank需要O(nlgn)

3)元素i的逆序数等于 |i - rank(i)|需要O(1)

4)将所有元素逆序数求和,需要O(n)

综上,需要O(nlgn)的时间复杂度.