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

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++

filter_none

edit
close

play_arrow

link
brightness_4
code

// 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;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// 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

chevron_right


Python3

filter_none

edit
close

play_arrow

link
brightness_4
code

# 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

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// 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 

chevron_right


Output:

3



My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.



Improved By : AnkitRai01