Maximum possible difference of two subsets of an array

30 May, 2022
Given an array of n-integers. The array may contain repetitive elements but the highest frequency of any elements must not exceed two. You have to make two subsets such that the difference of the sum of their elements is maximum and both of them jointly contain all elements of the 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 the difference of subset-sum. So, we can easily ignore them.
For making the difference of the sum of elements of both subset maximum we have to make subset in such a way that all positive elements belong to one subset and negative ones to other subsets.
Algorithm with time complexity O(n2): 
for i=0 to n-1
    isSingleOccurrence = 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
            isSingleOccurrence = false;
            break;
            
    if isSingleOccurrence == true
        if (arr[i] > 0)
            SubsetSum_1 += arr[i];
        else 
            SubsetSum_2 += arr[i];
return abs(SubsetSum_1 - SubsetSum2)
C++
Java
Python3
C#
PHP
Javascript
// CPP find maximum difference of subset sum#include <bits/stdc++.h>using namespace std; // function for maximum subset diffint maxDiff(int arr[], int n){    int SubsetSum_1 = 0, SubsetSum_2 = 0;    for (int i = 0; i <= n - 1; i++) {         bool isSingleOccurrence = 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]) {                isSingleOccurrence = false;                arr[i] = arr[j] = 0;                break;            }        }        if (isSingleOccurrence) {            if (arr[i] > 0)                SubsetSum_1 += arr[i];            else                SubsetSum_2 += arr[i];        }    }    return abs(SubsetSum_1 - SubsetSum_2);} // driver programint 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;}
// java find maximum difference// of subset sumimport 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 isSingleOccurrence = 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])                {                    isSingleOccurrence = false;                    arr[i] = arr[j] = 0;                    break;                }            }            if (isSingleOccurrence)            {                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.
# Python3 find maximum difference# of subset sum import math # function for maximum subset diffdef maxDiff(arr, n) :    SubsetSum_1 = 0    SubsetSum_2 = 0    for i in range(0, n) :         isSingleOccurrence = 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]) :                isSingleOccurrence = False                arr[i] = arr[j] = 0                break         if (isSingleOccurrence == True) :            if (arr[i] > 0) :                SubsetSum_1 += arr[i]            else :                SubsetSum_2 += arr[i]     return abs(SubsetSum_1 - SubsetSum_2) # Driver Codearr = [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)
// C# find maximum difference of// subset sumusing 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 isSingleOccurrence = 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])                {                    isSingleOccurrence = false;                    arr[i] = arr[j] = 0;                    break;                }            }            if (isSingleOccurrence)            {                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.
<?php// PHP find maximum difference// of subset sum // function for maximum subset difffunction maxDiff($arr, $n){    $SubsetSum_1 = 0;    $SubsetSum_2 = 0;    for ($i = 0; $i <= $n - 1; $i++)    {         $isSingleOccurrence = true;        for ($j = $i + 1; $j <= $n - 1; $j++)        {             // if frequency of any element is two            // make both equal to zero            if ($arr[$i] == $arr[$j])            {                $isSingleOccurrence = false;                $arr[$i] = $arr[$j] = 0;                break;            }        }        if ($isSingleOccurrence)        {            if ($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?>
<script> // JavaScript Program to find maximum difference// of subset sum     // function for maximum subset diff    function maxDiff(arr, n)    {        let SubsetSum_1 = 0, SubsetSum_2 = 0;        for (let i = 0; i <= n - 1; i++)        {            let isSingleOccurrence = true;            for (let j = i + 1; j <= n - 1; j++)            {                      // if frequency of any element                // is two make both equal to                // zero                if (arr[i] == arr[j])                {                    isSingleOccurrence = false;                    arr[i] = arr[j] = 0;                    break;                }            }            if (isSingleOccurrence)            {                if (arr[i] > 0)                    SubsetSum_1 += arr[i];                else                    SubsetSum_2 += arr[i];            }        }                  return Math.abs(SubsetSum_1 - SubsetSum_2);    }       // Driver program         let arr = [ 4, 2, -3, 3, -2, -2, 8 ];        let n = arr.length;                  document.write("Maximum Difference = "                               + maxDiff(arr, n));                 // This code is contributed by susmitakundugoaldanga.</script>
Maximum Difference = 20
 
Algorithm with time complexity O(n log n):  
-> sort the array
-> for i =0 to n-2
      // consecutive two elements are not equal
      // add absolute arr[i] to result
      if arr[i] != arr[i+1]
          result += abs(arr[i])
      // else skip next element too
      else
          i++;
          
// special check for last two elements
-> if (arr[n-2] != arr[n-1])
    result += arr[n-1]

-> return result;
C++
Java
Python 3
C#
PHP
Javascript
// CPP find maximum difference of subset sum#include <bits/stdc++.h>using namespace std; // function for maximum subset diffint maxDiff(int arr[], int n){    int result = 0;     // sort the array    sort(arr, arr + n);     // calculate the result    for (int i = 0; i < n - 1; i++) {        if (arr[i] != arr[i + 1])            result += abs(arr[i]);        else            i++;    }     // check for last element    if (arr[n - 2] != arr[n - 1])        result += abs(arr[n - 1]);     // return result    return result;} // driver programint 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;}
// java find maximum difference of// subset sumimport java. io.*;import java .util.*; public class GFG {     // function for maximum subset diff    static int maxDiff(int []arr, int n)    {        int result = 0;             // sort the array        Arrays.sort(arr);             // calculate the result        for (int i = 0; i < n - 1; i++)        {            if (arr[i] != arr[i + 1])                result += Math.abs(arr[i]);            else                i++;        }             // check for last element        if (arr[n - 2] != arr[n - 1])            result += Math.abs(arr[n - 1]);             // return result        return result;    }         // 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.
# Python 3 find maximum difference# of subset sum # function for maximum subset diffdef maxDiff(arr, n):     result = 0     # sort the array    arr.sort()     # calculate the result    for i in range(n - 1):        if (abs(arr[i]) != abs(arr[i + 1])):            result += abs(arr[i])         else:            pass     # check for last element    if (arr[n - 2] != arr[n - 1]):        result += abs(arr[n - 1])     # return result    return result # Driver Codeif __name__ == "__main__":         arr = [ 4, 2, -3, 3, -2, -2, 8 ]    n = len(arr)    print("Maximum Difference = " ,                   maxDiff(arr, n)) # This code is contributed by ita_c
// C# find maximum difference// of subset sumusing System; public class GFG {     // function for maximum subset diff    static int maxDiff(int []arr, int n)    {        int result = 0;             // sort the array        Array.Sort(arr);             // calculate the result        for (int i = 0; i < n - 1; i++)        {            if (arr[i] != arr[i + 1])                result += Math.Abs(arr[i]);            else                i++;        }             // check for last element        if (arr[n - 2] != arr[n - 1])            result += Math.Abs(arr[n - 1]);             // return result        return result;    }         // 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.
<?php// PHP find maximum difference of subset sum // function for maximum subset difffunction maxDiff( $arr, $n){    $result = 0;     // sort the array    sort($arr);     // calculate the result    for ( $i = 0; $i < $n - 1; $i++)    {        if ($arr[$i] != $arr[$i + 1])            $result += abs($arr[$i]);        else            $i++;    }     // check for last element    if ($arr[$n - 2] != $arr[$n - 1])        $result += abs($arr[$n - 1]);     // return result    return $result;}     // Driver Code    $arr = array( 4, 2, -3, 3, -2, -2, 8 );    $n = count($arr);    echo "Maximum Difference = "        , maxDiff($arr, $n);         // This code is contributed by anuj_67.?>
<script> // Javascript find maximum difference of subset sum // function for maximum subset difffunction maxDiff(arr, n){    var result = 0;     // sort the array    arr.sort((a,b)=> a-b)     // calculate the result    for (var i = 0; i < n - 1; i++) {        if (arr[i] != arr[i + 1])            result += Math.abs(arr[i]);        else            i++;    }     // check for last element    if (arr[n - 2] != arr[n - 1])        result += Math.abs(arr[n - 1]);     // return result    return result;} // driver programvar arr = [ 4, 2, -3, 3, -2, -2, 8 ];var n = arr.length;document.write( "Maximum Difference = " + maxDiff(arr, n)); </script>
Maximum Difference = 20
 
Algorithm with time complexity O(n):  
make hash table for positive elements:
    for all positive elements(arr[i])
        if frequency == 1
            SubsetSum_1 += arr[i];
make hash table for negative elements:
    for all negative elements
        if frequency == 1
            SubsetSum_2 += arr[i];
return abs(SubsetSum_1 - SubsetSum2)
C++
Java
Python3
C#
Javascript
// CPP find maximum difference of subset sum#include <bits/stdc++.h>using namespace std; // function for maximum subset diffint maxDiff(int arr[], int n){    unordered_map<int, int> hashPositive;    unordered_map<int, int> hashNegative;     int SubsetSum_1 = 0, SubsetSum_2 = 0;     // construct hash for positive elements    for (int i = 0; i <= n - 1; i++)        if (arr[i] > 0)            hashPositive[arr[i]]++;     // calculate subset sum for positive elements    for (int i = 0; i <= n - 1; i++)        if (arr[i] > 0 && hashPositive[arr[i]] == 1)            SubsetSum_1 += arr[i];     // construct hash for negative elements    for (int i = 0; i <= n - 1; i++)        if (arr[i] < 0)            hashNegative[abs(arr[i])]++;     // calculate subset sum for negative elements    for (int i = 0; i <= n - 1; i++)        if (arr[i] < 0 &&            hashNegative[abs(arr[i])] == 1)            SubsetSum_2 += arr[i];     return abs(SubsetSum_1 - SubsetSum_2);} // driver programint 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;}
// Java find maximum// difference of subset sumimport java.util.*;class GFG{   // Function for maximum subset diffpublic static int maxDiff(int arr[],                          int n){  HashMap<Integer,          Integer> hashPositive = new HashMap<>();  HashMap<Integer,          Integer> hashNegative = new HashMap<>();   int SubsetSum_1 = 0,      SubsetSum_2 = 0;   // Construct hash for  // positive elements  for (int i = 0; i <= n - 1; i++)  {    if (arr[i] > 0)    {      if(hashPositive.containsKey(arr[i]))      {        hashPositive.replace(arr[i],        hashPositive.get(arr[i]) + 1);      }      else      {        hashPositive.put(arr[i], 1);      }    }  }   // Calculate subset sum  // for positive elements  for (int i = 0; i <= n - 1; i++)  {    if(arr[i] > 0 &&       hashPositive.containsKey(arr[i]))    {      if(hashPositive.get(arr[i]) == 1)      {        SubsetSum_1 += arr[i];      }    }  }   // Construct hash for  // negative elements  for (int i = 0; i <= n - 1; i++)  {    if (arr[i] < 0)    {      if(hashNegative.containsKey(Math.abs(arr[i])))      {        hashNegative.replace(Math.abs(arr[i]),        hashNegative.get(Math.abs(arr[i])) + 1);      }      else      {        hashNegative.put(Math.abs(arr[i]), 1);      }    }  }   // Calculate subset sum for  // negative elements  for (int i = 0; i <= n - 1; i++)  {    if (arr[i] < 0 &&        hashNegative.containsKey(Math.abs(arr[i])))    {      if(hashNegative.get(Math.abs(arr[i])) == 1)      {        SubsetSum_2 += arr[i];      }    }  }   return Math.abs(SubsetSum_1 - SubsetSum_2);} // Driver codepublic static void main(String[] args){  int arr[] = {4, 2, -3, 3,               -2, -2, 8};  int n = arr.length;  System.out.print("Maximum Difference = " +                    maxDiff(arr, n));}} // This code is contributed by divyeshrabadiya07
# Python3 find maximum difference of subset sum # function for maximum subset diffdef maxDiff(arr, n):     hashPositive = dict()    hashNegative = dict()     SubsetSum_1, SubsetSum_2 = 0, 0     # construct hash for positive elements    for i in range(n):        if (arr[i] > 0):            hashPositive[arr[i]] = \                hashPositive.get(arr[i], 0) + 1     # calculate subset sum for positive elements    for i in range(n):        if (arr[i] > 0 and arr[i] in            hashPositive.keys() and            hashPositive[arr[i]] == 1):            SubsetSum_1 += arr[i]     # construct hash for negative elements    for i in range(n):        if (arr[i] < 0):            hashNegative[abs(arr[i])] = \                hashNegative.get(abs(arr[i]), 0) + 1     # calculate subset sum for negative elements    for i in range(n):        if (arr[i] < 0 and abs(arr[i]) in            hashNegative.keys() and            hashNegative[abs(arr[i])] == 1):            SubsetSum_2 += arr[i]     return abs(SubsetSum_1 - SubsetSum_2) # Driver Codearr = [4, 2, -3, 3, -2, -2, 8]n = len(arr)print("Maximum Difference =", maxDiff(arr, n)) # This code is contributed by mohit kumar
// C# find maximum// difference of subset sumusing System;using System.Collections.Generic; class GFG {     // Function for maximum subset diff    static int maxDiff(int[] arr, int n)    {      Dictionary<int, int> hashPositive =        new Dictionary<int, int>();      Dictionary<int, int> hashNegative =        new Dictionary<int, int>();            int SubsetSum_1 = 0, SubsetSum_2 = 0;            // Construct hash for      // positive elements      for (int i = 0; i <= n - 1; i++)      {        if (arr[i] > 0)        {          if(hashPositive.ContainsKey(arr[i]))          {            hashPositive[arr[i]] += 1;          }          else          {            hashPositive.Add(arr[i], 1);          }        }      }            // Calculate subset sum      // for positive elements      for (int i = 0; i <= n - 1; i++)      {        if(arr[i] > 0 && hashPositive.ContainsKey(arr[i]))        {          if(hashPositive[arr[i]] == 1)          {            SubsetSum_1 += arr[i];          }        }      }            // Construct hash for      // negative elements      for (int i = 0; i <= n - 1; i++)      {        if (arr[i] < 0)        {          if(hashNegative.ContainsKey(Math.Abs(arr[i])))          {            hashNegative[Math.Abs(arr[i])] += 1;          }          else          {            hashNegative.Add(Math.Abs(arr[i]), 1);          }        }      }            // Calculate subset sum for      // negative elements      for (int i = 0; i <= n - 1; i++)      {        if (arr[i] < 0 &&            hashNegative.ContainsKey(Math.Abs(arr[i])))        {          if(hashNegative[Math.Abs(arr[i])] == 1)          {            SubsetSum_2 += arr[i];          }        }      }            return Math.Abs(SubsetSum_1 - SubsetSum_2);    }     // Driver code   static 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 divesh072019
<script>// Javascript find maximum// difference of subset sum // Function for maximum subset difffunction maxDiff(arr,n){    let hashPositive = new Map();  let hashNegative = new Map();    let SubsetSum_1 = 0,      SubsetSum_2 = 0;    // Construct hash for  // positive elements  for (let i = 0; i <= n - 1; i++)  {    if (arr[i] > 0)    {      if(hashPositive.has(arr[i]))      {        hashPositive.set(arr[i],        hashPositive.get(arr[i]) + 1);      }      else      {        hashPositive.set(arr[i], 1);      }    }  }    // Calculate subset sum  // for positive elements  for (let i = 0; i <= n - 1; i++)  {    if(arr[i] > 0 &&       hashPositive.has(arr[i]))    {      if(hashPositive.get(arr[i]) == 1)      {        SubsetSum_1 += arr[i];      }    }  }    // Construct hash for  // negative elements  for (let i = 0; i <= n - 1; i++)  {    if (arr[i] < 0)    {      if(hashNegative.has(Math.abs(arr[i])))      {        hashNegative.set(Math.abs(arr[i]),        hashNegative.get(Math.abs(arr[i])) + 1);      }      else      {        hashNegative.set(Math.abs(arr[i]), 1);      }    }  }    // Calculate subset sum for  // negative elements  for (let i = 0; i <= n - 1; i++)  {    if (arr[i] < 0 &&        hashNegative.has(Math.abs(arr[i])))    {      if(hashNegative.get(Math.abs(arr[i])) == 1)      {        SubsetSum_2 += arr[i];      }    }  }    return Math.abs(SubsetSum_1 - SubsetSum_2);         } // Driver code let arr = [4, 2, -3, 3,               -2, -2, 8];let n = arr.length;document.write("Maximum Difference = " +                    maxDiff(arr, n));                     // This code is contributed by rag2127</script>
Maximum Difference = 20
 
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