Pair formation such that maximum pair sum is minimized

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++

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// 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;
}

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Java

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// 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.

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Output:

(1, 9) (5, 6)


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