# Maximum Weight Difference in C++ Program

In this problem, we are given an array arr[] and a number M. Our task is to create a program to calculate the Maximum Weight Difference in C++.

## Problem description

We will find M elements from the array such that the absolute difference
between the sum and the sum of the rest elements is maximum.

Let’s take an example to understand the problem,

## Input

arr[] = {3, 1, 6, 9, 4} M = 3

## Output

15

## Explanation

We will consider 4,6,9. The sum is 19. The absolute difference with the sum of rest numbers is

|19 − 4| = 15

## Solution Approach

A simple solution to the problem is by finding all subsequences of the array, finding the sum elements of the subarray, and the rest. And return the maximum difference.

A more efficient solution is found by using the fact that maximum weight difference i.e. difference of the sum of elements and the rest is maximum if we consider m maximum elements or m minimum elements for subsequence.

So, we will check for the maximum sum difference for a subsequence of m largest elements and rest array or subsequence of m smallest elements and rest array.

And return the maximum of both.

## Algorithm

Initialize

maxSum , maxSumDiff, minSumDiff

Step 1

sort the array in descending order.

Step 2

Loop for i −> 0 to n

Step 2.1

if (i < m) −> maxSumDiff += arr[i]

Step 2.2

else −> maxSumDiff −= arr[i]

Step 2

Loop for i −> n to 0

Step 2.1

if (i > m) −> minSumDiff += arr[i]

Step 2.2

else −> minSumDiff −= arr[i]

Step 3

if maxSumDiff > minSumDiff −> maxSum = maxSumDiff.

Step 4

if maxSumDiff < minSumDiff −> maxSum = minSumDiff.

Step 5

return maxSum.

## Example

Program to illustrate the working of our solution,

Live Demo

#include <bits/stdc++.h>
using namespace std;
int maxWeightDifference(int arr[], int N, int M){
int maxabsDiff = −1000;
sort(arr, arr + N);
int sumMin = 0, sumMax = 0, arrSum = 0;
for(int i = 0; i < N; i++){
arrSum += arr[i];
if(i < M)
sumMin += arr[i];
if(i >= (N−M))
sumMax += arr[i];
}
maxabsDiff = max(abs(sumMax − (arrSum − sumMax)), abs(sumMin −
(arrSum − sumMin)));
return maxabsDiff;
}
int main(){
int arr[] = {3, 1, 6, 9, 4} ;
int M = 3;
int N = sizeof(arr)/sizeof(arr[0]);
cout<<"The maximum weight difference is "<<maxWeightDifference(arr,N, M);
return 0;
}

## Output

The maximum weight difference is 15

Updated on: 09-Dec-2020

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