find pair of numbers in array that add to given su

Question

Question: Given an unsorted array of positive integers, is it possible to find a pair of integers from that array that sum up to a given sum?

Constraints: This should be done in O(n) and in-place (without any external storage like arrays, hash-maps) (you can use extra variables/pointers)

If this is not possible, can there be a proof given for the same?

Answer 1

Naïve double loop printout with O(n x n) performance can be improved to linear O(n) performance using O(n) memory for Hash Table as follows:

void TwoIntegersSum(int[] given, int sum)
{
    Hashtable ht = new Hashtable();
    for (int i = 0; i < given.Length; i++)
        if (ht.Contains(sum - given[i]))
            Console.WriteLine("{0} + {1}", given[i], sum - given[i]);
        else
            ht.Add(given[i], sum - given[i]);
    Console.Read();
}