# Maximize the sum of differences of consecutive elements after removing exactly K elements

Given a sorted array arr[] of length N and an integer K such that K < N, the task is to remove exactly K elements from the array such that the sum of the differences of the consecutive elements of the array is maximized.

Examples:

Input: arr[] = {1, 2, 3, 4}, K = 1
Output: 3
Let’s consider all the possible cases:
a) Remove arr[0]: arr[] = {2, 3, 4}, ans = 2
b) Remove arr[1]: arr[] = {1, 3, 4}, ans = 3
c) Remove arr[2]: arr[] = {1, 2, 4}, ans = 3
d) Remove arr[3]: arr[] = {1, 2, 3}, ans = 2
3 is the maximum of all the answers.

Input: arr[] = {1, 2, 10}, K = 2
Output: 0

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

Approach: There are two cases:

1. If K < N – 1 then the answer will be arr[N – 1] – arr[0]. This is because any K elements from the N – 2 internal elements of the array can be deleted without affecting the maximized sum of differences. For example, if any single element has to be removed from 1, 2, 3 and 4 then no matter whether 2 is removed or 3 is removed the final sum of difference will remain the same i.e. ((3 – 1) + (4 – 3)) = 3 which is equal to ((2 – 1) + (4 – 2)) = 3.
2. If K = N – 1 then the answer will be 0 because only a single element remains that is both the minimum and the maximum. Thus, the answer is 0.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to return the maximized sum ` `int` `findSum(``int``* arr, ``int` `n, ``int` `k) ` `{ ` ` `  `    ``// Remove any k internal elements ` `    ``if` `(k <= n - 2) ` `        ``return` `(arr[n - 1] - arr[0]); ` ` `  `    ``return` `0; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `arr[] = { 1, 2, 3, 4 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(``int``); ` `    ``int` `k = 1; ` ` `  `    ``cout << findSum(arr, n, k); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the approach  ` `class` `GFG  ` `{ ` `     `  `    ``// Function to return the maximized sum  ` `    ``static` `int` `findSum(``int` `[]arr, ``int` `n, ``int` `k)  ` `    ``{  ` `     `  `        ``// Remove any k internal elements  ` `        ``if` `(k <= n - ``2``)  ` `            ``return` `(arr[n - ``1``] - arr[``0``]);  ` `     `  `        ``return` `0``;  ` `    ``}  ` `     `  `    ``// Driver code  ` `    ``public` `static` `void` `main (String[] args) ` `    ``{  ` `        ``int` `arr[] = { ``1``, ``2``, ``3``, ``4` `};  ` `        ``int` `n = arr.length;  ` `        ``int` `k = ``1``;  ` `     `  `        ``System.out.println(findSum(arr, n, k));  ` `    ``}  ` `} ` ` `  `// This code is contributed by AnkitRai01 `

## Python3

 `# Python3 implementation of the approach  ` ` `  `# Function to return the maximized sum  ` `def` `findSum(arr, n, k) : ` ` `  `    ``# Remove any k internal elements  ` `    ``if` `(k <``=` `n ``-` `2``) : ` `        ``return` `(arr[n ``-` `1``] ``-` `arr[``0``]); ` `         `  `    ``return` `0``; ` `     `  `# Driver code  ` `if` `__name__ ``=``=` `"__main__"` `:  ` ` `  `    ``arr ``=` `[ ``1``, ``2``, ``3``, ``4` `];  ` `    ``n ``=` `len``(arr);  ` `    ``k ``=` `1``;  ` ` `  `    ``print``(findSum(arr, n, k));  ` `     `  `# This code is contributed by AnkitRai01 `

## C#

 `// C# implementation of the approach  ` `using` `System; ` ` `  `class` `GFG  ` `{  ` `     `  `    ``// Function to return the maximized sum  ` `    ``static` `int` `findSum(``int` `[]arr,  ` `                       ``int` `n, ``int` `k)  ` `    ``{  ` `     `  `        ``// Remove any k internal elements  ` `        ``if` `(k <= n - 2)  ` `            ``return` `(arr[n - 1] - arr[0]);  ` `     `  `        ``return` `0;  ` `    ``}  ` `     `  `    ``// Driver code  ` `    ``public` `static` `void` `Main ()  ` `    ``{  ` `        ``int` `[]arr = { 1, 2, 3, 4 };  ` `        ``int` `n = arr.Length;  ` `        ``int` `k = 1;  ` `     `  `        ``Console.WriteLine(findSum(arr, n, k));  ` `    ``}  ` `}  ` ` `  `// This code is contributed by AnkitRai01  `

Output:

```3
```

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Improved By : AnkitRai01