# 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 = 1Output: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 = 2Output:0Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the

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**Approach:** There are two cases:

- 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. - 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 <bits/stdc++.h>` `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` |

## Javascript

`<script>` `// Javascript implementation of the approach` `// Function to return the maximized sum` `function` `findSum(arr, n, k)` `{` ` ` `// Remove any k internal elements` ` ` `if` `(k <= n - 2)` ` ` `return` `(arr[n - 1] - arr[0]);` ` ` `return` `0;` `}` `// Driver code` `var` `arr = [1, 2, 3, 4];` `var` `n = arr.length;` `var` `k = 1;` `document.write( findSum(arr, n, k));` `</script>` |

**Output:**

3

**Time Complexity:** O(1)

**Auxiliary Space:** O(1)