Question: Given an integer array, find any 2 numbers which adds to a given integer. Return FALSE if no 2 such number exists.

Ex: array A[]= {3, 1, 8, 11, 5, 7}

given integer say N = 6
answer will be 1,5.

If N would be 5, answer will be FALSE.

Answer: A simple brute force approach may be to look for N-A[i] for every i from 0 to length of A. This will be an O(N^2) approach. If array is sorted, we can search N-A[i] in O(NlogN) time. Can we do better than this?

Not for unsorted array but for sorted array, we can certainly do better. It will add O(NlogN) time for sorting. (Time efficiency will be same as earlier binary search approach coz of sorting time but total number of comparison will be less.)


Sort array A[]
initialize 2 pointers. 
Start <= begining of the array A; 
end <= end of A 
while start < end 
  if A[start] + A[end] < N 
    increase start by 1 
  else if A[start] + A[end] == N 
    decrease end by 1 
end while 
return FALSE

bool sum_euqal_to_N(int A[], int N)
 int start = 0;
 int end = MAX-1;
 //check for boundary conditions
 if ((A[start]+A[start+1]) > N)
  return false;
 if ((A[end]+A[end+1]) < N)
  return false;
 while (end > start)
  if ((A[start] + A[end]) < N)
  else if ((A[start] + A[end]) == N)
   cout << A[start] << " " << A[end] << endl;
   return true;
 return false;

Efficiency: if input array A is sorted then O(N).
else O(NlogN) coz of sorting time NlogN.

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