Question

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Given two arrays a and b .Find all pairs of elements (a1,b1) such that a1 belongs to Array A and b1 belongs to Array B whose sum a1+b1 = k .

Given : An unsorted array A of integers
Input : An integer k

Output : All the two element set with sum of elements in each set equal to k in O(n).

Example:

A = {3,4,5,1,4,2}

Input : 6
Output : {3,3}, {5,1}, {4,2}

Note : I know an O(n logn) solution but that would require to have the array sorted. Is there any way by which this problem can be solved in O(n). An non-trivial C++ data structure can be used i.e there’s no bound on space

Answer 1

Make a constant-time lookup table (hash) so you can see if a particular integer is included in your array (O(n)). Then, for each element in the array, see if k-A[i] is included. This takes constant time for each element, so a total of O(n) time. This assumes the elements are distinct; it is not difficult to make it work with repeating elements.