Find the number of unordered pair in an array

Question

I ran into an interesting algorithm problem:

Given an array of integer, find the number of un-ordered pairs in that array, say given {1, 3, 2}, the answer is 1 becau

Answer 1

It is possible to solve this problem in O(n log n) time using a balanced binary search tree. Here is a pseudo-code of this algorithm:

tree = an empty balanced binary search tree
answer = 0
for each element in the array:
     answer += number of the elements in the tree greater then this element
     add this element to the tree