Question

Let A be an array of n positive integers, and k a given integer.

I’m looking for algorithm to find if there is a pair of elements in the array such that
A[i] * A[j] == k and A[i] == A[j] + k. If there is such a pair, the algorithm should return their index.

This is a homework exercise, and we’re told that there is an O(n*log(n)) solution.

Answer 1

Here is somewhat clarified Graphics Noob’s solution.

Also, it is more like O(N) (assuming hashing won’t fail us), not O(N*log(N)).

Result findMultiplicationIndices(int[] A, int[] B, int k)
{
    HashMap<Integer,Integer> aDivisors = new HashMap<Integer,Integer>();
    for(int i=0;i<A.length;i++)
    {
        int a = A[i];
        if(a!=0)
        {
            int d = k/a;
            if(d*a == k) 
                aDivisors.put(d, i);
        }
    }
    for(int i=0;i<B.length;i++)
    {
        Integer ai = aDivisors.get(B[i]);
        if(ai != null)
            return new Result(ai, i);
    }
    return null;
}