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Maximum possible difference of sum of two subsets of an array | Set 2

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  • Last Updated : 25 Aug, 2021

Given an array arr[ ] consisting of N integers, the task is to find maximum difference between the sum of two subsets obtained by partitioning the array into any two non-empty subsets. 
Note: The subsets cannot any common element. A subset can contain repeating elements.

Examples:

Input: arr[] = {1, 3, 2, 4, 5}
Output: 13
Explanation: The partitions {3, 2, 4, 5} and {1} maximizes the difference between the subsets.

Input: arr[] = {1, -5, 3, 2, -7}
Output: 18
Explanation: The partitions {1, 3, 2} and {-5, -7} maximizes the difference between the subsets.

Approach: This problem can be solved using greedy approach. In this problem both the subsets A and B must be non-empty. So we have to put at least one element in both of them. We try to make sum of elements in subset A as greater as possible and sum of elements in subset B as smaller as possible. Finally we print sum(A) – sum(B).

Follow the steps given below to solve the problem:

  • When arr[ ] contains both non-negative and negative numbers, put all non-negative numbers in subset A and negative numbers in subset B, and print sum(A) – sum(B).
  • When all numbers are positive, put all numbers in subset A except the smallest positive number put that in subset B, and print sum(A) – sum(B).
  • When all numbers are negative, put all numbers in subset B except the largest negative put that in subset A, and print sum(A) – sum(B).

Below is the implementation of the above approach:

C++




// C++ Program for the above approach
 
#include <bits/stdc++.h>
using namespace std;
 
int maxSumAfterPartition(int arr[], int n)
{
    // Stores the positive elements
    vector<int> pos;
 
    // Stores the negative elements
    vector<int> neg;
 
    // Stores the count of 0s
    int zero = 0;
 
    // Sum of all positive numbers
    int pos_sum = 0;
 
    // Sum of all negative numbers
    int neg_sum = 0;
 
    // Iterate over the array
    for (int i = 0; i < n; i++) {
 
        if (arr[i] > 0) {
 
            pos.push_back(arr[i]);
            pos_sum += arr[i];
        }
        else if (arr[i] < 0) {
 
            neg.push_back(arr[i]);
            neg_sum += arr[i];
        }
        else {
 
            zero++;
        }
    }
 
    // Stores the difference
    int ans = 0;
 
    // Sort the positive numbers
    // in ascending order
    sort(pos.begin(), pos.end());
 
    // Sort the negative numbers
    // in decreasing order
    sort(neg.begin(), neg.end(), greater<int>());
 
    // Case 1: Include both positive
    // and negative numbers
    if (pos.size() > 0 && neg.size() > 0) {
 
        ans = (pos_sum - neg_sum);
    }
    else if (pos.size() > 0) {
 
        if (zero > 0) {
 
            // Case 2:  When all numbers are
            // positive and array contains 0s
           
              //Put all numbers in subset A and
              //one 0 in subset B
            ans = (pos_sum);
        }
        else {
 
            // Case 3: When all numbers are positive
           
              //Put all numbers in subset A except the 
              //smallest positive number which is put in B
            ans = (pos_sum - 2 * pos[0]);
        }
    }
    else {
        if (zero > 0) {
 
            // Case 4: When all numbers are
            // negative and array contains 0s
 
            // Put all numbers in subset B
            // and one 0 in subset A
            ans = (-1 * neg_sum);
        }
        else {
            // Case 5: When all numbers are negative
 
            // Place the largest negative number
            // in subset A and remaining in B
            ans = (neg[0] - (neg_sum - neg[0]));
        }
    }
 
    return ans;
}
int main()
{
    int arr[] = { 1, 2, 3, -5, -7 };
    int n = sizeof(arr) / sizeof(arr[0]);
 
    cout << maxSumAfterPartition(arr, n);
    return 0;
}


Java




/*package whatever //do not write package name here */
 
import java.io.*;
import java.util.*;
class GFG {
    static int maxSumAfterPartition(int arr[], int n)
    {
        // Stores the positive elements
       ArrayList<Integer> pos
            = new ArrayList<Integer>();
        
 
        // Stores the negative elements
         ArrayList<Integer> neg
            = new ArrayList<Integer>();
 
        // Stores the count of 0s
        int zero = 0;
 
        // Sum of all positive numbers
        int pos_sum = 0;
 
        // Sum of all negative numbers
        int neg_sum = 0;
 
        // Iterate over the array
        for (int i = 0; i < n; i++) {
 
            if (arr[i] > 0) {
 
                pos.add(arr[i]);
                pos_sum += arr[i];
            }
            else if (arr[i] < 0) {
 
                neg.add(arr[i]);
                neg_sum += arr[i];
            }
            else {
 
                zero++;
            }
        }
 
        // Stores the difference
        int ans = 0;
 
        // Sort the positive numbers
        // in ascending order
        Collections.sort(pos);
 
        // Sort the negative numbers
        // in decreasing order
        Collections.sort(neg);
 
        // Case 1: Include both positive
        // and negative numbers
        if (pos.size() > 0 && neg.size() > 0) {
 
            ans = (pos_sum - neg_sum);
        }
        else if (pos.size() > 0) {
 
            if (zero > 0) {
 
                // Case 2:  When all numbers are
                // positive and array contains 0s
 
                // Put all numbers in subset A and
                // one 0 in subset B
                ans = (pos_sum);
            }
            else {
 
                // Case 3: When all numbers are positive
 
                // Put all numbers in subset A except the
                // smallest positive number which is put in
                // B
                ans = (pos_sum - 2 * pos.get(0));
            }
        }
        else {
            if (zero > 0) {
 
                // Case 4: When all numbers are
                // negative and array contains 0s
 
                // Put all numbers in subset B
                // and one 0 in subset A
                ans = (-1 * neg_sum);
            }
            else {
                // Case 5: When all numbers are negative
 
                // Place the largest negative number
                // in subset A and remaining in B
                ans = (neg.get(0) - (neg_sum - neg.get(0)));
            }
        }
 
        return ans;
    }
 
  // Driver code
    public static void main(String[] args)
    {
        int arr[] = { 1, 2, 3, -5, -7 };
        int n = 5;
        System.out.println(maxSumAfterPartition(arr, n));
    }
}
 
// This code is contributed by maddler.


Python3




# Python 3 Program for the above approach
 
def maxSumAfterPartition(arr, n):
    # Stores the positive elements
    pos = []
 
    # Stores the negative elements
    neg = []
 
    # Stores the count of 0s
    zero = 0
 
    # Sum of all positive numbers
    pos_sum = 0
 
    # Sum of all negative numbers
    neg_sum = 0
 
    # Iterate over the array
    for i in range(n):
        if (arr[i] > 0):
            pos.append(arr[i])
            pos_sum += arr[i]
 
        elif(arr[i] < 0):
            neg.append(arr[i])
            neg_sum += arr[i]
 
        else:
            zero += 1
 
    # Stores the difference
    ans = 0
 
    # Sort the positive numbers
    # in ascending order
    pos.sort()
 
    # Sort the negative numbers
    # in decreasing order
    neg.sort(reverse=True)
 
    # Case 1: Include both positive
    # and negative numbers
    if (len(pos) > 0 and len(neg) > 0):
 
        ans = (pos_sum - neg_sum)
    elif(len(pos) > 0):
        if (zero > 0):
 
            # Case 2:  When all numbers are
            # positive and array contains 0s
           
              #Put all numbers in subset A and
              #one 0 in subset B
            ans = (pos_sum)
        else:
 
            # Case 3: When all numbers are positive
           
              #Put all numbers in subset A except the 
              #smallest positive number which is put in B
            ans = (pos_sum - 2 * pos[0])
    else:
        if (zero > 0):
            # Case 4: When all numbers are
            # negative and array contains 0s
 
            # Put all numbers in subset B
            # and one 0 in subset A
            ans = (-1 * neg_sum)
        else:
            # Case 5: When all numbers are negative
 
            # Place the largest negative number
            # in subset A and remaining in B
            ans = (neg[0] - (neg_sum - neg[0]))
 
    return ans
 
if __name__ == '__main__':
    arr = [1, 2, 3, -5, -7]
    n = len(arr)
    print(maxSumAfterPartition(arr, n))
     
    # This code is contributed by ipg2016107.


C#




// C# Program for the above approach
using System;
using System.Collections.Generic;
 
class GFG{
 
static int maxSumAfterPartition(int []arr, int n)
{
    // Stores the positive elements
    List<int> pos = new List<int>();
 
    // Stores the negative elements
    List<int> neg = new List<int>();
 
    // Stores the count of 0s
    int zero = 0;
 
    // Sum of all positive numbers
    int pos_sum = 0;
 
    // Sum of all negative numbers
    int neg_sum = 0;
 
    // Iterate over the array
    for (int i = 0; i < n; i++) {
 
        if (arr[i] > 0) {
 
            pos.Add(arr[i]);
            pos_sum += arr[i];
        }
        else if (arr[i] < 0) {
 
            neg.Add(arr[i]);
            neg_sum += arr[i];
        }
        else {
 
            zero++;
        }
    }
 
    // Stores the difference
    int ans = 0;
 
    // Sort the positive numbers
    // in ascending order
    pos.Sort();
 
    // Sort the negative numbers
    // in decreasing order
    neg.Sort();
    neg.Reverse();
 
    // Case 1: Include both positive
    // and negative numbers
    if (pos.Count > 0 && neg.Count > 0) {
 
        ans = (pos_sum - neg_sum);
    }
    else if (pos.Count > 0) {
 
        if (zero > 0) {
 
            // Case 2:  When all numbers are
            // positive and array contains 0s
           
              //Put all numbers in subset A and
              //one 0 in subset B
            ans = (pos_sum);
        }
        else {
 
            // Case 3: When all numbers are positive
           
              //Put all numbers in subset A except the 
              //smallest positive number which is put in B
            ans = (pos_sum - 2 * pos[0]);
        }
    }
    else {
        if (zero > 0) {
 
            // Case 4: When all numbers are
            // negative and array contains 0s
 
            // Put all numbers in subset B
            // and one 0 in subset A
            ans = (-1 * neg_sum);
        }
        else {
            // Case 5: When all numbers are negative
 
            // Place the largest negative number
            // in subset A and remaining in B
            ans = (neg[0] - (neg_sum - neg[0]));
        }
    }
 
    return ans;
}
 
public static void Main()
{
    int []arr = { 1, 2, 3, -5, -7 };
    int n = arr.Length;
 
    Console.Write(maxSumAfterPartition(arr, n));
}
}
 
// This code is contributed by ipg2016107.


Javascript




<script>
        // JavaScript Program to implement
        // the above approach
 
 
 
        function maxSumAfterPartition(arr, n) {
            // Stores the positive elements
            let pos = [];
 
            // Stores the negative elements
            let neg = [];
 
            // Stores the count of 0s
            let zero = 0;
 
            // Sum of all positive numbers
            let pos_sum = 0;
 
            // Sum of all negative numbers
            let neg_sum = 0;
 
            // Iterate over the array
            for (let i = 0; i < n; i++) {
 
                if (arr[i] > 0) {
 
                    pos.push(arr[i]);
                    pos_sum += arr[i];
                }
                else if (arr[i] < 0) {
 
                    neg.push(arr[i]);
                    neg_sum += arr[i];
                }
                else {
 
                    zero++;
                }
            }
 
            // Stores the difference
            let ans = 0;
 
            // Sort the positive numbers
            // in ascending order
            pos.sort(function (a, b) { return a - b })
 
            // Sort the negative numbers
            // in decreasing order
            neg.sort(function (a, b) { return b - a })
 
            // Case 1: Include both positive
            // and negative numbers
            if (pos.length > 0 && neg.length > 0) {
 
                ans = (pos_sum - neg_sum);
            }
            else if (pos.length > 0) {
 
                if (zero > 0) {
 
                    // Case 2:  When all numbers are
                    // positive and array contains 0s
 
                    //Put all numbers in subset A and
                    //one 0 in subset B
                    ans = (pos_sum);
                }
                else {
 
                    // Case 3: When all numbers are positive
 
                    //Put all numbers in subset A except the 
                    //smallest positive number which is put in B
                    ans = (pos_sum - 2 * pos[0]);
                }
            }
            else {
                if (zero > 0) {
 
                    // Case 4: When all numbers are
                    // negative and array contains 0s
 
                    // Put all numbers in subset B
                    // and one 0 in subset A
                    ans = (-1 * neg_sum);
                }
                else {
                    // Case 5: When all numbers are negative
 
                    // Place the largest negative number
                    // in subset A and remaining in B
                    ans = (neg[0] - (neg_sum - neg[0]));
                }
            }
 
            return ans;
        }
 
        let arr = [1, 2, 3, -5, -7];
        let n = arr.length;
 
        document.write(maxSumAfterPartition(arr, n));
 
// This code is contributed by Potta Lokesh
    </script>


Output

18

Time Complexity: O(NlogN)
Auxiliary Space: O(N)


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