C++ programming – Given a sorted array and a number x, find the pair in array whose sum is closest to x

Given a sorted array and a number x, find a pair in array whose sum is closest to x.

Examples:

Input: arr[] = {10, 22, 28, 29, 30, 40}, x = 54
Output: 22 and 30

Input: arr[] = {1, 3, 4, 7, 10}, x = 15
Output: 4 and 10

A simple solution is to consider every pair and keep track of closest pair (absolute difference between pair sum and x is minimum). Finally print the closest pair. Time complexity of this solution is O(n²)

An efficient solution can find the pair in O(n) time. The idea is similar to method 2 of this post. Following is detailed algorithm.

1) Initialize a variable diff as infinite (Diff is used to store the 
   difference between pair and x).  We need to find the minimum diff.
2) Initialize two index variables l and r in the given sorted array.
       (a) Initialize first to the leftmost index:  l = 0
       (b) Initialize second  the rightmost index:  r = n-1
3) Loop while l < r.
       (a) If  abs(arr[l] + arr[r] - sum) < diff  then 
           update diff and result 
       (b) Else if(arr[l] + arr[r] <  sum )  then l++
       (c) Else r--