What is Pair – Sum Array?

A pair-sum array in JavaScript is an array that holds the total number of potential pairs of elements from the original array. The pair-sum array, designated as pairSumArr, will have a length of n*(n-1)/2 when an array arr of length n is given. This is because it contains the sum of all conceivable combinations of two entries from the original array.

Example 1:

Suppose we have the original array arr = [2, 5, 7]. The pair-sum array will be:
pairSumArr = [2+5, 2+7, 5+7] = [7, 9, 12]
Here, pairSumArr[0] contains the sum of the first two elements of arr, i.e., 2 + 5 = 7. 
Similarly, pairSumArr[1] contains the sum of the first and last elements of arr, i.e., 2 + 7 = 9, 
and pairSumArr[2] contains the sum of the last two elements of arr, i.e., 5 + 7 = 12

Example 2:

2. If we take another example Suppose we have the original array arr = [3, 6, 8, 2]. 
We will construct the pair-sum array for this array.
pairSumArr = [3+6, 3+8, 3+2, 6+8, 6+2, 8+2] 
pairSumArr = [9, 11, 5, 14, 8, 10]
Use of Pair - Sum Array

1. Array Reconstruction: If the pair-sum array is known, it can be used to rebuild the original array. In this procedure, the sum array is reverse-engineered to get the elements of the original array.
2. Combinatorics: Applications of the pair-sum array include combinatorial issues, particularly when array combinations are involved.
3. Optimization Problems: The pair-sum array can assist in identifying patterns and connections between items in some optimization problems, resulting in optimum solutions.
4. Finding Missing Elements: When some items of an array are lost but their pairwise sums are still available, the pair-sum array can be useful. We may determine the elements that are missing by using the pair-sum array.

The pair-sum array is a unique construction that holds the sum of all potential pairs of elements from the original array. At first glance, it might appear to be challenging, but in this article, we’ll Construct an array from its pair-sum array and discover some of its most intriguing uses.