Maximize sum of absolute difference between adjacent elements in Array with sum K

Last Updated : 30 Sep, 2022

Given two integers N and K, the task is to maximize the sum of absolute differences between adjacent elements of an array of length N and sum K.

Examples:

Input: N = 5, K = 10
Output: 20
Explanation:
The array arr[] with sum 10 can be {0, 5, 0, 5, 0}, maximizing the sum of absolute difference of adjacent elements ( 5 + 5 + 5 + 5 = 20)

Input: N = 2, K = 10
Output: 10

Approach:
To maximize the sum of adjacent elements, follow the steps below:

If N is 2, the maximum sum possible is K by placing K in 1 index and 0 on the other.
If N is 1, the maximum sum possible will always be 0.
For all other values of N, the answer will be 2 * K.

Illustration:
For N = 3, the arrangement {0, K, 0} maximizes the sum of absolute difference between adjacent elements to 2 * K.
For N = 4, the arrangement {0, K/2, 0, K/2} or {0, K, 0, 0} maximizes the required sum of absolute difference between adjacent elements to 2 * K.

Below is the implementation of the above approach:

C++

// C++ program to maximize the
// sum of absolute differences
// between adjacent elements
#include <bits/stdc++.h>
using namespace std;

// Function for maximizing the sum
int maxAdjacentDifference(int N, int K)
{
    // Difference is 0 when only
    // one element is present
    // in array
    if (N == 1) {
        return 0;
    }

    // Difference is K when
    // two elements are
    // present in array
    if (N == 2) {
        return K;
    }

    // Otherwise
    return 2 * K;
}

// Driver code
int main()
{

    int N = 6;
    int K = 11;

    cout << maxAdjacentDifference(N, K);

    return 0;
}

Java

// Java program to maximize the
// sum of absolute differences
// between adjacent elements
import java.util.*;

class GFG{

// Function for maximising the sum
static int maxAdjacentDifference(int N, int K)
{
    
    // Difference is 0 when only
    // one element is present
    // in array
    if (N == 1)
    {
        return 0;
    }

    // Difference is K when
    // two elements are
    // present in array
    if (N == 2) 
    {
        return K;
    }

    // Otherwise
    return 2 * K;
}

// Driver code
public static void main(String[] args)
{
    int N = 6;
    int K = 11;

    System.out.print(maxAdjacentDifference(N, K));
}
}

// This code is contributed by 29AjayKumar

Python3

# Python3 program to maximize the
# sum of absolute differences
# between adjacent elements

# Function for maximising the sum
def maxAdjacentDifference(N, K):

    # Difference is 0 when only
    # one element is present
    # in array
    if (N == 1):
        return 0;
    
    # Difference is K when
    # two elements are
    # present in array
    if (N == 2):
        return K;
    
    # Otherwise
    return 2 * K;

# Driver code
N = 6;
K = 11;
print(maxAdjacentDifference(N, K));

# This code is contributed by Code_Mech

// C# program to maximize the
// sum of absolute differences
// between adjacent elements
using System;

class GFG{

// Function for maximising the sum
static int maxAdjacentDifference(int N, int K)
{
    
    // Difference is 0 when only
    // one element is present
    // in array
    if (N == 1)
    {
        return 0;
    }

    // Difference is K when
    // two elements are
    // present in array
    if (N == 2) 
    {
        return K;
    }

    // Otherwise
    return 2 * K;
}

// Driver code
public static void Main(String[] args)
{
    int N = 6;
    int K = 11;

    Console.Write(maxAdjacentDifference(N, K));
}
}

// This code is contributed by 29AjayKumar

JavaScript

<script>

// JavaScript program to maximize the
// sum of absolute differences
// between adjacent elements

// Function for maximising the sum
function maxAdjacentDifference(N, K)
{
      
    // Difference is 0 when only
    // one element is present
    // in array
    if (N == 1)
    {
        return 0;
    }
  
    // Difference is K when
    // two elements are
    // present in array
    if (N == 2) 
    {
        return K;
    }
  
    // Otherwise
    return 2 * K;
}
 
// Driver Code

    let N = 6;
    let K = 11;
  
    document.write(maxAdjacentDifference(N, K));

// This code is contributed by susmitakundugoaldanga.
</script>