# Maximum Weight Difference

You are given an array W, W, …, 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
```

## Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

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++

 `// C++ Program to find maximum weight  ` `// difference ` `#include ` `#include ` `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); ` ` `  `    ``// call the solve function ` `    ``cout << solve(array, n, k); ` ` `  `    ``return` `0; ` `} `

## Java

 `// 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. `

## Python

 `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))`

## C#

 `// 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. `

## PHP

 ` ``\$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  ` `?> `

Output:

```17
```

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Improved By : vt_m, Shivi_Aggarwal

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