# 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++

 `// CPP Program to divide the array into` `// N pairs such that maximum pair is minimized` `#include `   `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.`

## Python3

 `# Python 3 Program to divide the array into` `# N pairs such that maximum pair is minimized`   `def` `findOptimalPairs(arr, N):` `    ``arr.sort(reverse ``=` `False``)`   `    ``# 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` `    ``i ``=` `0` `    ``j ``=` `N ``-` `1` `    ``while``(i <``=` `j):` `        ``print``(``"("``, arr[i], ``","``, ` `                   ``arr[j], ``")"``, end ``=` `" "``)` `        ``i ``+``=` `1` `        ``j ``-``=` `1`   `# Driver Code` `if` `__name__ ``=``=` `'__main__'``:` `    ``arr ``=` `[``9``, ``6``, ``5``, ``1``]` `    ``N ``=` `len``(arr)`   `    ``findOptimalPairs(arr, N) ` `    `  `# This code is contributed by` `# Sahil_Shelangia`

## C#

 `// C# Program to divide the array into` `// N pairs such that maximum pair is minimized`   `using` `System;`   `public` `class` `GFG{` `    ``static` `void` `findOptimalPairs(``int` `[]arr, ``int` `N)` `{` `    ``Array.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--)` `        ``Console.Write( ``"("` `+ arr[i] + ``", "` `+ arr[j] + ``")"` `+ ``" "``);` `}`   `    ``// Driver Code` `    ``static` `public` `void` `Main (){` `        `  `        ``int` `[]arr = {9, 6, 5, 1};` `        ``int` `N = arr.Length;` `        ``findOptimalPairs(arr, N);`     `// This code is contributed by ajit.`   `    ``}` `}`

## PHP

 ``

## Javascript

 ``

Output

`(1, 9) (5, 6) `

Complexity Analysis:

• Time Complexity: O(n*log n) where n is the size of the array.
• Auxiliary Space: O(1)

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