Closest Pair Sum in an unsorted Array | 2-pointer algorithm | DSA

Question link:
https://www.geeksforgeeks.org/problem...

Given an array arr[] and an integer target. You have to find a pair in an array whose sum is closest to target.

Note: Return the pair in sorted order and if there are multiple such pairs return the pair with maximum absolute difference. If no such pair exists return an empty array.

Given an integer array and a target value, the task is to find a pair of elements whose sum is closest to the given target.

If multiple pairs have the same minimum absolute difference from the target:

Solution 1 (Tuple + PriorityQueue) selects the pair having the maximum difference between the two elements.

Steps:
Sort the array.
Use two pointers (i from start, j from end).
For each pair (a[i], a[j]), calculate:
Absolute difference from the target
Store (difference, a[i], a[j]) inside a PriorityQueue.
The PriorityQueue keeps pairs ordered by minimum difference.
If multiple pairs have the same closest sum:
Choose the pair with the maximum |a - b|.
Return the selected pair.
Why use this approach?
When the problem requires extra rules or tie-breaking logic.
Easy to extend for more conditions.
Time Complexity:
Sorting: O(n log n)
Two-pointer scan: O(n)
Overall: O(n log n)
Space Complexity: O(n) (PriorityQueue)

Solution 2 (Optimized Two Pointer) returns any one closest pair without extra tie-breaking.
Steps:
Sort the array.
Use two pointers.
Track the minimum absolute difference seen so far.
Update the answer whenever a better pair is found.
If exact target sum is found, return immediately.
Time Complexity: O(n log n)
Space Complexity: O(1)

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