Maximum difference between groups of size two

Difficulty Level : Easy
Last Updated : 26 Dec, 2018

Given an array of even number of elements, form groups of 2 using these array elements such that the difference between the group with highest sum and the one with lowest sum is maximum.

Note: An element can be a part of one group only and it has to be a part of at least 1 group.

Examples:

Input : arr[] = {1, 4, 9, 6}
Output : 10
Groups formed will be (1, 4) and (6, 9), 
the difference between highest sum group
(6, 9) i.e 15 and lowest sum group (1, 4)
i.e 5 is 10.


Input : arr[] = {6, 7, 1, 11}
Output : 11
Groups formed will be (1, 6) and (7, 11), 
the difference between highest sum group
(7, 11) i.e 18 and lowest sum group (1, 6)
i.e 7 is 11.

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Simple Approach: We can solve this problem by making all possible combinations and checking each set of combination difference between the group with highest sum and with the lowest sum. A total of n*(n-1)/2 such groups would be formed (nC2).
Time Complexity: O(n^3), because it will take O(n^2) to generate groups and to check against each group n iterations will be needed thus overall it takes O(n^3) time.

Efficient Approach: We can use the greedy approach. Sort the whole array and our result is sum of last two elements minus sum of first two elements.

C++

// CPP program to find minimum difference 
// between groups of highest and lowest 
// sums. 
#include <bits/stdc++.h> 
#define ll long long int 
using namespace std; 
  
ll CalculateMax(ll arr[], int n) 
{ 
    // Sorting the whole array. 
    sort(arr, arr + n); 
     
    int min_sum = arr[0] + arr[1]; 
    int max_sum = arr[n-1] + arr[n-2]; 
  
    return abs(max_sum - min_sum); 
} 
  
// Driver code 
int main() 
{ 
    ll arr[] = { 6, 7, 1, 11 }; 
    int n = sizeof(arr) / sizeof(arr[0]); 
    cout << CalculateMax(arr, n) << endl; 
    return 0; 
} 

Java

// Java program to find minimum difference  
// between groups of highest and lowest  
// sums.  
import java.util.Arrays;  
import java.io.*; 
  
class GFG { 
static int  CalculateMax(int  arr[], int n)  
{  
    // Sorting the whole array.  
    Arrays.sort(arr);  
      
    int min_sum = arr[0] + arr[1];  
    int max_sum = arr[n-1] + arr[n-2];  
  
    return (Math.abs(max_sum - min_sum));  
}  
  
// Driver code 
      
    public static void main (String[] args) { 
  
    int arr[] = { 6, 7, 1, 11 };  
    int n = arr.length;  
    System.out.println (CalculateMax(arr, n));  
    } 
} 

Python3

# Python 3 program to find minimum difference  
# between groups of highest and lowest  
def CalculateMax(arr, n): 
  
    # Sorting the whole array. 
    arr.sort() 
    min_sum = arr[0] + arr[1] 
    max_sum = arr[n - 1] + arr[n - 2] 
    return abs(max_sum - min_sum) 
  
# Driver code 
arr = [6, 7, 1, 11] 
n = len(arr) 
print(CalculateMax(arr, n)) 
  
# This code is contributed 
# by Shrikant13 

C#

// C# program to find minimum difference  
// between groups of highest and lowest  
// sums. 
using System; 
  
public class GFG{ 
  
static int CalculateMax(int []arr, int n)  
{  
    // Sorting the whole array.  
    Array.Sort(arr);  
      
    int min_sum = arr[0] + arr[1];  
    int max_sum = arr[n-1] + arr[n-2];  
  
    return (Math.Abs(max_sum - min_sum));  
}  
  
// Driver code 
      
    static public void Main (){ 
    int []arr = { 6, 7, 1, 11 };  
    int n = arr.Length;  
    Console.WriteLine(CalculateMax(arr, n));  
    } 
//This code is contributed by Sachin.     
} 

PHP

<?php 
// PHP program to find minimum  
// difference between groups of  
// highest and lowest sums. 
function CalculateMax($arr, $n) 
{ 
    // Sorting the whole array. 
    sort($arr); 
      
    $min_sum = $arr[0] +  
               $arr[1]; 
    $max_sum = $arr[$n - 1] +  
               $arr[$n - 2]; 
  
    return abs($max_sum - 
               $min_sum); 
} 
  
// Driver code 
$arr = array (6, 7, 1, 11 ); 
$n = sizeof($arr); 
echo CalculateMax($arr, $n), "\n" ; 
  
// This code is contributed by ajit 
?> 