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

You can use a modified merge-sort algorithm. Merging would look something like this.

merge(a, b):
    i = 0
    j = 0
    c = new int[a.length+b.length]
    inversions = 0
    for(k = 0 ; k < Math.min(a.length, b.length); k++)
        if(a[i] > b[j]):
            inversions++
            c[k] = b[j]
            j++
        else:
            c[k] = a[i]
            i++
    //dump the rest of the longer array in c
    return inversions

Merging is done in O(n) time. Time complexity of the whole merge sort is O(n log n)