Related Articles

# Maximise sum of absolute difference between adjacent elements in Array with sum K

• Difficulty Level : Expert
• Last Updated : 06 May, 2021

Given two integers N and K, the task is to maximise 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:

• 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 ``using` `namespace` `std;` `// Function for maximising 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#

 `// 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

 ``
Output:
`22`

Time Complexity: O(1).

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.

My Personal Notes arrow_drop_up