Maximum possible difference of two subsets of an array

Given an array of n-integers. Array may contain repetitive elements but the highest frequency of any elements must not exceed two. You have to make two subsets such that difference of their elements sum is maximum and both of them jointly contains all of elements of given array along with the most important condition, no subset should contain repetitive elements.

Examples:

Input : arr[] = {5, 8, -1, 4}
Output : Maximum Difference = 18
Explanation : 
Let Subset A = {5, 8, 4} & Subset B = {-1}
Sum of elements of subset A = 17, of subset B = -1
Difference of Sum of Both subsets = 17 - (-1) = 18

Input : arr[] = {5, 8, 5, 4}
Output : Maximum Difference = 12
Explanation : 
Let Subset A = {5, 8, 4} & Subset B = {5}
Sum of elements of subset A = 17, of subset B = 5
Difference of Sum of Both subsets = 17 - 5 = 12

Before solving this question we have to take care of some given conditions and they are listed as:

  • While building up the subsets, take care that no subset should contain repetitive elements. And for this we can conclude that all such elements whose frequency are 2, going to be part of both subsets and hence overall they don’t have any impact on difference of subset sum. So, we can easily ignore them.
  • For making the difference of sum of elements of both subset maximum we have to make subset in such a way that all positive elements belongs to one subset and negative ones to other subset.

Algorithm with time complexity O(n2):

for i=0 to n-1
    isSingleOccurance = true;
    for  j= i+1 to n-1

        // if frequency of any element is two
        // make both equal to zero
        if arr[i] equals arr[j]
            arr[i] = arr[j] = 0
            isSingleOccurance = false;
            break;
            
    if isSingleOccurance == true
        if (arr[i] > 0)
            SubsetSum_1 += arr[i];
        else 
            SubsetSum_2 += arr[i];
return abs(SubsetSum_1 - SubsetSum2)            

C++

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// CPP find maximum difference of subset sum
#include <bits/stdc++.h>
using namespace std;
  
// function for maximum subset diff
int maxDiff(int arr[], int n)
{
    int SubsetSum_1 = 0, SubsetSum_2 = 0;
    for (int i = 0; i <= n - 1; i++) {
  
        bool isSingleOccurance = true;
        for (int j = i + 1; j <= n - 1; j++) {
  
            // if frequency of any element is two
            // make both equal to zero
            if (arr[i] == arr[j]) {
                isSingleOccurance = false;
                arr[i] = arr[j] = 0;
                break;
            }
        }
        if (isSingleOccurance) {
            if (arr[i] > 0)
                SubsetSum_1 += arr[i];
            else
                SubsetSum_2 += arr[i];
        }
    }
    return abs(SubsetSum_1 - SubsetSum_2);
}
  
// driver program
int main()
{
    int arr[] = { 4, 2, -3, 3, -2, -2, 8 };
    int n = sizeof(arr) / sizeof(arr[0]);
    cout << "Maximum Difference = " << maxDiff(arr, n);
    return 0;
}

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Java

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// java find maximum difference
// of subset sum
import java .io.*;
  
public class GFG {
      
    // function for maximum subset diff
    static int maxDiff(int []arr, int n)
    {
        int SubsetSum_1 = 0, SubsetSum_2 = 0;
        for (int i = 0; i <= n - 1; i++)
        {
            boolean isSingleOccurance = true;
            for (int j = i + 1; j <= n - 1; j++)
            {
      
                // if frequency of any element
                // is two make both equal to
                // zero
                if (arr[i] == arr[j])
                {
                    isSingleOccurance = false;
                    arr[i] = arr[j] = 0;
                    break;
                }
            }
            if (isSingleOccurance)
            {
                if (arr[i] > 0)
                    SubsetSum_1 += arr[i];
                else
                    SubsetSum_2 += arr[i];
            }
        }
          
        return Math.abs(SubsetSum_1 - SubsetSum_2);
    }
      
    // driver program
    static public void main (String[] args)
    {
        int []arr = { 4, 2, -3, 3, -2, -2, 8 };
        int n = arr.length;
          
        System.out.println("Maximum Difference = "
                               + maxDiff(arr, n));
    }
}
  
// This code is contributed by vt_m.

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Python3

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# Python3 find maximum difference
# of subset sum
  
import math
  
# function for maximum subset diff
def maxDiff(arr, n) :
    SubsetSum_1 = 0
    SubsetSum_2 = 0
    for i in range(0, n) :
  
        isSingleOccurance = True
        for j in range(i + 1, n) :
  
            # if frequency of any element
            # is two make both equal to 
            # zero
            if (arr[i] == arr[j]) : 
                isSingleOccurance = False
                arr[i] = arr[j] = 0
                break
  
        if (isSingleOccurance == True) :
            if (arr[i] > 0) :
                SubsetSum_1 += arr[i]
            else :
                SubsetSum_2 += arr[i]
  
    return abs(SubsetSum_1 - SubsetSum_2)
  
# Driver Code
arr = [4, 2, -3, 3, -2, -2, 8]
n = len(arr)
print ("Maximum Difference = {}"
               . format(maxDiff(arr, n)))
  
# This code is contributed by Manish Shaw
# (manishshaw1)

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C#

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// C# find maximum difference of
// subset sum
using System;
  
public class GFG {
      
    // function for maximum subset diff
    static int maxDiff(int []arr, int n)
    {
        int SubsetSum_1 = 0, SubsetSum_2 = 0;
        for (int i = 0; i <= n - 1; i++)
        {
      
            bool isSingleOccurance = true;
            for (int j = i + 1; j <= n - 1; j++)
            {
      
                // if frequency of any element
                // is two make both equal to
                // zero
                if (arr[i] == arr[j])
                {
                    isSingleOccurance = false;
                    arr[i] = arr[j] = 0;
                    break;
                }
            }
            if (isSingleOccurance)
            {
                if (arr[i] > 0)
                    SubsetSum_1 += arr[i];
                else
                    SubsetSum_2 += arr[i];
            }
        }
          
        return Math.Abs(SubsetSum_1 - SubsetSum_2);
    }
      
    // driver program
    static public void Main ()
    {
        int []arr = { 4, 2, -3, 3, -2, -2, 8 };
        int n = arr.Length;
          
        Console.WriteLine("Maximum Difference = "
                              + maxDiff(arr, n));
    }
}
  
// This code is contributed by vt_m.

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PHP

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<?php
// PHP find maximum difference
// of subset sum
  
// function for maximum subset diff
function maxDiff($arr, $n)
{
    $SubsetSum_1 = 0;
    $SubsetSum_2 = 0;
    for ($i = 0; $i <= $n - 1; $i++)
    {
  
        $isSingleOccurance = true;
        for ($j = $i + 1; $j <= $n - 1; $j++)
        {
  
            // if frequency of any element is two
            // make both equal to zero
            if ($arr[$i] == $arr[$j]) 
            {
                $isSingleOccurance = false;
                $arr[$i] = $arr[$j] = 0;
                break;
            }
        }
        if ($isSingleOccurance
        {
            if ($arr[$i] > 0)
                $SubsetSum_1 += $arr[$i];
            else
                $SubsetSum_2 += $arr[$i];
        }
    }
    return abs($SubsetSum_1 - $SubsetSum_2);
}
  
    // Driver Code
    $arr = array(4, 2, -3, 3, -2, -2, 8);
    $n = sizeof($arr);
    echo "Maximum Difference = " , maxDiff($arr, $n);
  
// This code is contributed by nitin mittal
?>

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