Given an array of size 2 * N integers. Divide the array into N pairs, such that the maximum pair sum is minimized. In other words, the optimal division of array into N pairs should result into a maximum pair sum which is minimum of other maximum pair sum of all possibilities.

Examples:

Input : N = 2

arr[] = { 5, 8, 3, 9 }

Output : (3, 9) (5, 8)

Explanation:

Possible pairs are :

1. (8, 9) (3, 5) Maximum Sum of a Pair = 17

2. (5, 9) (3, 8) Maximum Sum of a Pair = 14

3. (3, 9) (5, 8) Maximum Sum of a Pair = 13

Thus, in case 3, the maximum pair sum is minimum of all the other cases. Hence, the answer is(3, 9) (5, 8).Input : N = 2

arr[] = { 9, 6, 5, 1 }

Output : (1, 9) (5, 6)

**Approach:** The idea is to first sort the given array and then iterate over the loop to form pairs (i, j) where i would start from 0 and j would start from end of array correspondingly. Increment i and Decrement j to form the next pair and so on.

Below is the implementation of above approach.

## C++

// CPP Program to divide the array into // N pairs such that maximum pair is minimized #include <bits/stdc++.h> using namespace std; void findOptimalPairs(int arr[], int N) { sort(arr, arr + N); // After Sorting Maintain two variables i and j // pointing to start and end of array Such that // smallest element of array pairs with largest // element for (int i = 0, j = N - 1; i <= j; i++, j--) cout << "(" << arr[i] << ", " << arr[j] << ")" << " "; } // Driver Code int main() { int arr[] = { 9, 6, 5, 1 }; int N = sizeof(arr) / sizeof(arr[0]); findOptimalPairs(arr, N); return 0; }

## Java

// Java Program to divide the array into // N pairs such that maximum pair is minimized import java.io.*; import java.util.Arrays; class GFG { static void findOptimalPairs(int arr[], int N) { Arrays.sort(arr); // After Sorting Maintain two variables i and j // pointing to start and end of array Such that // smallest element of array pairs with largest // element for (int i = 0, j = N - 1; i <= j; i++, j--) System.out.print( "(" + arr[i] + ", " + arr[j] + ")" + " "); } // Driver Code public static void main (String[] args) { int arr[] = {9, 6, 5, 1}; int N = arr.length; findOptimalPairs(arr, N); } } // This code is contributed by anuj_67.

**Output:**

(1, 9) (5, 6)

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