Maximum Weight Difference

You are given an array W[1], W[2], …, W[N]. Choose K numbers among them such that the absolute difference between the sum of chosen numbers and the sum of remaining numbers is as large as possible.

Examples :

Input : arr[] = [8, 4, 5, 2, 10]
            k = 2
Output: 17

Input : arr[] = [1, 1, 1, 1, 1, 1, 1, 1]
          k = 3
Output: 2



There are two possibilities to get the desired answer. These two are:Choose k largest numbers or Choose k smallest numbers. Choose the best-suited option which fits according to the given values. This is because there are some cases in which the sum of smallest k numbers can be greater than rest of the array and there are some cases in which the sum of largest k numbers can be greater than rest of the sum of the numbers.

Approach :

  • Sort the given array.
  • Get the sum of all the numbers of the array and store it in sum
  • Get the sum of first k numbers of the array and store it in sum1
  • Get the sum of last k numbers of the array and store it in sum2
  • Output the result which is : max(abs(S1-(S-S1)), abs(S2-(S-S2)))

C++

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// C++ Program to find maximum weight 
// difference
#include <iostream>
#include <algorithm>
using namespace std;
  
// return the max value of two numbers
int max(int a, int b)
{
    return a > b ? a : b;
}
  
int solve(int array[], int n, int k)
{
    // sort the given array
    sort(array, array + n);
  
    // Initializing the value to 0
    int sum = 0, sum1 = 0, sum2 = 0;
  
    // Getting the sum of the array
    for (int i = 0; i < n; i++) {
        sum += array[i];
    }
  
    // Getting the sum of first k elements
    for (int i = 0; i < k; i++) {
        sum1 += array[i];
    }
  
    // Getting the sum of (n-k) elements
    for (int i = k; i < n; i++) {
        sum2 += array[i];
    }
  
    // Returning the maximum possible difference.
    return max(abs(sum1 - (sum - sum1)), abs(sum2 - 
                                  (sum - sum2)));
}
  
// Driver function
int main()
{
    int k = 2;
    int array[] = { 8, 4, 5, 2, 10 };
  
    // calculate the numbers of elements in the array
    int n = sizeof(array) / sizeof(array[0]);
  
    // call the solve function
    cout << solve(array, n, k);
  
    return 0;
}

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Java

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// JAVA Code for Maximum Weight Difference
import java.util.*;
  
class GFG {
      
    public static int solve(int array[], int n,
                                        int k)
    {
        // sort the given array
        Arrays.sort(array);
       
        // Initializing the value to 0
        int sum = 0, sum1 = 0, sum2 = 0;
       
        // Getting the sum of the array
        for (int i = 0; i < n; i++) {
            sum += array[i];
        }
       
        // Getting the sum of first k elements
        for (int i = 0; i < k; i++) {
            sum1 += array[i];
        }
       
        // Getting the sum of (n-k) elements
        for (int i = k; i < n; i++) {
            sum2 += array[i];
        }
       
        // Returning the maximum possible difference.
        return Math.max(Math.abs(sum1 - (sum - sum1)),
                       Math.abs(sum2 - (sum - sum2)));
    }
      
    /* Driver program to test above function */
    public static void main(String[] args) 
    {
        int k = 2;
        int array[] = { 8, 4, 5, 2, 10 };
       
        // calculate the numbers of elements
        // in the array
        int n = array.length;
       
        // call the solve function
        System.out.print(solve(array, n, k));
              
    }
}
// This code is contributed by Arnav Kr. Mandal.

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Python

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def solve(array, k):
    
  # Sorting array
  array.sort()
  
  # Getting the sum of all the elements
  sum = sum(array)
  
  # Getting the sum of first k elements
  sum1 = sum(array[:k])
  
  # Getting the sum last (n-k) elements
  sum2 = sum(array[k:])
  
  # Returning the maximum possible difference
  return max(abs(s1-(s-s1)), abs(s2-(s-s2)))
    
# Driver function
k = 2
array =[8, 4, 5, 2, 10]
print(solve(array, k))

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C#

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// C# Code for Maximum Weight Difference
using System;
  
class GFG {
      
    public static int solve(int []array, int n,
                                        int k)
    {
          
        // sort the given array
        Array.Sort(array);
      
        // Initializing the value to 0
        int sum = 0, sum1 = 0, sum2 = 0;
      
        // Getting the sum of the array
        for (int i = 0; i < n; i++) {
            sum += array[i];
        }
      
        // Getting the sum of first k elements
        for (int i = 0; i < k; i++) {
            sum1 += array[i];
        }
      
        // Getting the sum of (n-k) elements
        for (int i = k; i < n; i++) {
            sum2 += array[i];
        }
      
        // Returning the maximum possible difference.
        return Math.Max(Math.Abs(sum1 - (sum - sum1)),
                        Math.Abs(sum2 - (sum - sum2)));
    }
      
    /* Driver program to test above function */
    public static void Main() 
    {
        int k = 2;
        int []array = { 8, 4, 5, 2, 10 };
      
        // calculate the numbers of elements
        // in the array
        int n = array.Length;
      
        // call the solve function
        Console.WriteLine(solve(array, n, k));
              
    }
}
  
// This code is contributed by vt_m.

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PHP

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<?php
// PHP Program to find maximum weight 
// difference
  
// return the max value of two numbers
function maxi($a, $b)
{
    if ($a > $b
    {
        return $a;
    
    else
    {
        return $b;
    }
}
  
function solve(&$arr, $n, $k)
{
    // sort the given array
    sort($arr);
  
    // Initializing the value to 0
    $sum = 0;
    $sum1 = 0;
    $sum2 = 0;
  
    // Getting the sum of the array
    for ($i = 0; $i < $n; $i++) 
    {
        $sum += $arr[$i];
    }
  
    // Getting the sum of first k elements
    for ($i = 0; $i < $k; $i++)
    {
        $sum1 += $arr[$i];
    }
  
    // Getting the sum of (n-k) elements
    for ($i = $k; $i < $n; $i++) 
    {
        $sum2 += $arr[$i];
    }
  
    // Returning the maximum possible difference.
    return maxi(abs($sum1 - ($sum - $sum1)), 
                abs($sum2 - ($sum - $sum2)));
}
  
// DriverCode
$k = 2;
$arr = array(8, 4, 5, 2, 10 );
  
// calculate the numbers of 
// elements in the array
$n = sizeof($arr);
  
// call the solve function
echo (solve($arr, $n, $k));
  
// This code is contributed 
// by Shivi_Aggarwal 
?>

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Output:

17

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Improved By : vt_m, Shivi_Aggarwal



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