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

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 = 10Output:20Explanation:

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 = 10Output: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:

ForN = 3, the arrangement{0, K, 0}maximizes the sum of absolute difference between adjacent elements to2 * K.

ForN = 4, the arrangement{0, K/2, 0, K/2}or{0, K, 0, 0}maximizes the required sum of absolute difference between adjacent elements to2 * 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#

`// 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>` |

**Output:**

22

* Time Complexity: O(1)*.