# Maximizing array sum with given operation

There is an array consisting of (2 * n – 1) integers. We can change sign of exactly n elements in the array. In other words, we can select exactly n array elements, and multiply each of them by -1. Find the maximum sum of the array.

Examples :

```Input : arr[] = 50 50 50
Output : 150
There is no need to change anything.
The sum of elements equals 150
which is maximum.

Input :  arr[] = -1 -100 -1
Output : 100
Change the sign of the first two
elements. Sum of the elements
equal to 100.
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:

Step 1:- Iterate the loop for 2*n-1 times and repeat the steps 2, 3 and 4.
Step 2:- Calculate no. of negative numbers (neg).
Step 3:- Calculate the sum (sum) of the array by taking absolute values of the numbers.
Step 4:- Find the minimum number of the array by taking absolute values of the numbers (min).
Step 5:- Check if the no. of negative numbers is odd and the value of n (given) is even then subtract two times m from the sum and this will be max_sum of the array else, the value of sum will be the max_sum of the array.

Below is the implementation of the above approach:

## C++

 `// CPP program to get the maximum ` `// sum of the array. ` `#include ` `using` `namespace` `std; ` ` `  `// function to find maximum sum ` `int` `maxSum(``int` `arr[], ``int` `n) ` `{ ` `    ``int` `neg = 0, sum = 0,  ` `     ``m = INT_MAX, max_sum; ` `     `  `    ``// step 1 ` `    ``for` `(``int` `i = 0; i < 2 * n - 1; i++) { ` `     `  `        ``// step 2 ` `        ``neg += (arr[i] < 0); ` `     `  `        ``// step 3 ` `        ``sum += ``abs``(arr[i]); ` `     `  `        ``// step 4 ` `        ``m = min(m, ``abs``(arr[i])); ` `    ``} ` `     `  `    ``// step 5 ` `    ``if` `(neg % 2 && n % 2 == 0) { ` `        ``max_sum = sum -= 2 * m; ` `        ``return` `(max_sum); ` `    ``} ` `     `  `    ``max_sum = sum; ` `    ``return` `(max_sum); ` `} ` ` `  `// Driver Function ` `int` `main() ` `{ ` `    ``int` `arr[] = { -1, -100, -1 }; ` `    ``int` `n = 2; ` `    ``cout << maxSum(arr, n) << endl; ` `    ``return` `0; ` `} `

## Java

 `// Java program to get the maximum ` `// sum of the array. ` `import` `java.io.*; ` `import` `java.math.*; ` ` `  `class` `GFG { ` ` `  `// function to find maximum sum ` `static` `int` `maxSum(``int` `arr[], ``int` `n) { ` `    ``int` `neg = ``0``, sum = ``0``, m = ``100000000``, max_sum; ` ` `  `    ``// step 1 ` `    ``for` `(``int` `i = ``0``; i < ``2` `* n - ``1``; i++) { ` ` `  `    ``// step 2 ` `    ``if` `(arr[i] < ``0``) ` `        ``neg += ``1``; ` ` `  `    ``// step 3 ` `    ``sum += Math.abs(arr[i]); ` ` `  `    ``// step 4 ` `    ``m = Math.min(m, Math.abs(arr[i])); ` `    ``} ` ` `  `    ``// step 5 ` `    ``if` `(neg % ``2` `== ``1` `&& n % ``2` `== ``0``) { ` `    ``max_sum = sum -= ``2` `* m; ` `    ``return` `(max_sum); ` `    ``} ` ` `  `    ``max_sum = sum; ` `    ``return` `(max_sum); ` `} ` ` `  `// Driver Function ` `public` `static` `void` `main(String args[]) { ` `    ``int` `arr[] = {-``1``, -``100``, -``1``}; ` `    ``int` `n = ``2``; ` `    ``System.out.println(maxSum(arr, n)); ` `} ` `} ` ` `  `/*This code is contributed by Nikita Tiwari.*/`

## Python3

 `# Python3 code to get the maximum ` `# sum of the array. ` `import` `sys ` ` `  `# function to find maximum sum ` `def` `maxSum (arr, n): ` `    ``neg ``=` `0` `    ``sum` `=` `0` `    ``m ``=` `sys.maxsize ` `     `  `    ``# step 1 ` `    ``for` `i ``in` `range``(``2` `*` `n ``-` `1``): ` `         `  `        ``# step 2 ` `        ``neg ``+``=` `(arr[i] < ``0``) ` `         `  `        ``# step 3 ` `        ``sum` `+``=` `abs``(arr[i]) ` `         `  `        ``# step 4 ` `        ``m ``=` `min``(m, ``abs``(arr[i])) ` `     `  `    ``# step 5 ` `    ``if` `neg ``%` `2` `and` `n ``%` `2` `=``=` `0``: ` `        ``max_sum ``=` `sum` `-` `2` `*` `m ` `        ``return` `(max_sum) ` `     `  `    ``max_sum ``=` `sum` `    ``return` `max_sum ` `     `  `# Driver Code ` `arr ``=` `[ ``-``1``, ``-``100``, ``-``1` `] ` `n ``=` `2` `print``( maxSum(arr, n)) ` ` `  `# This code is contributed by "Sharad_Bhardwaj". `

## C#

 `// C# program to get the maximum ` `// sum of the array. ` `using` `System; ` ` `  `class` `GFG  ` `{ ` ` `  `// function to find maximum sum ` `static` `int` `maxSum(``int` `[]arr, ``int` `n) ` `{ ` `    ``int` `neg = 0, sum = 0;  ` `    ``int` `m = 100000000, max_sum; ` ` `  `    ``// step 1 ` `    ``for` `(``int` `i = 0; i < 2 * n - 1; i++)  ` `    ``{ ` ` `  `        ``// step 2 ` `        ``if` `(arr[i] < 0) ` `        ``neg += 1; ` ` `  `        ``// step 3 ` `        ``sum += Math.Abs(arr[i]); ` ` `  `        ``// step 4 ` `        ``m = Math.Min(m, Math.Abs(arr[i])); ` `    ``} ` ` `  `    ``// step 5 ` `    ``if` `(neg % 2 == 1 && n % 2 == 0) ` `    ``{ ` `        ``max_sum = sum -= 2 * m; ` `        ``return` `(max_sum); ` `    ``} ` ` `  `    ``max_sum = sum; ` `    ``return` `(max_sum); ` `} ` ` `  `// Driver Code ` `public` `static` `void` `Main() ` `{ ` `    ``int` `[]arr = {-1, -100, -1}; ` `    ``int` `n = 2; ` `    ``Console.WriteLine(maxSum(arr, n)); ` `} ` `} ` ` `  `// This code is contributed by vt_m. `

## PHP

 ` `

Output :

```100
```

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