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# Maximum sum of absolute differences between distinct pairs of a triplet from an array

Given an array arr[] consisting of N integers, the task is to find the maximum sum of absolute differences between all distinct pairs of the triplet in the array.

Examples:

Input: arr[] = {1, 2, 3, 4}
Output: 6
Explanation:
The valid triplet is (1, 3, 4) as sum = |1 – 4| + |1 – 3| + |3 – 4| = 6, which is the maximum among all the triplets.

Input: arr[] = {2, 2, 2}
Output: 0

Approach: The idea to solve the given problem is to sort the array in ascending order and find the sum of absolute differences between the pairs of the first and the last two elements of the array. Follow the steps below to solve the problem:

• Initialize a variable, say sum, to store the maximum possible sum.
• Sort the given array arr[] in ascending order.
• Find the sum of differences between the pairs of the first and the last two elements of the array i.e., sum = (arr[N – 2] – arr) + (arr[N – 1] – arr) + (arr[N – 2] – arr[N – 1]).
• After completing the above steps, print the value of the sum as the result.

Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach``#include ``using` `namespace` `std;` `// Function to find the maximum sum of``// absolute differences between``// distinct pairs of triplet in array``void` `maximumSum(``int` `arr[], ``int` `N)``{``    ``// Stores the maximum sum``    ``int` `sum;` `    ``// Sort the array in``    ``// ascending order``    ``sort(arr, arr + N);` `    ``// Sum of differences between``    ``// pairs of the triplet``    ``sum = (arr[N - 1] - arr)``          ``+ (arr[N - 2] - arr)``          ``+ (arr[N - 1] - arr[N - 2]);` `    ``// Print the sum``    ``cout << sum;``}` `// Driver Code``int` `main()``{``    ``int` `arr[] = { 1, 3, 4, 2 };``    ``int` `N = ``sizeof``(arr) / ``sizeof``(arr);``    ``maximumSum(arr, N);` `    ``return` `0;``}`

## Java

 `// Java program for the above approach``import` `java.util.*;``class` `GFG``{` `  ``// Function to find the maximum sum of``  ``// absolute differences between``  ``// distinct pairs of triplet in array``  ``static` `void` `maximumSum(``int``[] arr, ``int` `N)``  ``{` `    ``// Stores the maximum sum``    ``int` `sum;` `    ``// Sort the array in``    ``// ascending order``    ``Arrays.sort(arr);` `    ``// Sum of differences between``    ``// pairs of the triplet``    ``sum = (arr[N - ``1``] - arr[``0``]) + (arr[N - ``2``] - arr[``0``])``      ``+ (arr[N - ``1``] - arr[N - ``2``]);` `    ``// Print the sum``    ``System.out.println(sum);``  ``}` `  ``// Driver Code``  ``public` `static` `void` `main(String[] args)``  ``{``    ``int``[] arr = { ``1``, ``3``, ``4``, ``2` `};``    ``int` `N = arr.length;``    ``maximumSum(arr, N);``  ``}``}` `// This code is contributed by susmitakundugoaldanga.`

## Python3

 `# Python program for the above approach` `# Function to find the maximum sum of``# absolute differences between``# distinct pairs of triplet in array``def` `maximumSum(arr, N):``  ` `    ``# Stores the maximum sum``    ``sum` `=` `0``    ` `    ``# Sort the array in``    ``# ascending order``    ``arr.sort()``    ` `    ``# Sum of differences between``    ``# pairs of the triplet``    ``sum` `=` `(arr[N ``-` `1``] ``-` `arr[``0``]) ``+` `(arr[N ``-` `2``] ``-` `arr[``0``]) ``+` `(arr[N ``-` `1``] ``-` `arr[N ``-` `2``]);` `    ``# Print the sum``    ``print``(``sum``)` `# Driver Code``arr ``=` `[ ``1``, ``3``, ``4``, ``2` `]``N ``=` `len``(arr)``maximumSum(arr, N)` `# This code is contributed by rohitsingh07052.`

## C#

 `// C# program for the above approach``using` `System;``using` `System.Collections.Generic;` `class` `GFG``{` `    ``// Function to find the maximum sum of``    ``// absolute differences between``    ``// distinct pairs of triplet in array``    ``static` `void` `maximumSum(``int``[] arr, ``int` `N)``    ``{``      ` `        ``// Stores the maximum sum``        ``int` `sum;` `        ``// Sort the array in``        ``// ascending order``        ``Array.Sort(arr);` `        ``// Sum of differences between``        ``// pairs of the triplet``        ``sum = (arr[N - 1] - arr) + (arr[N - 2] - arr)``              ``+ (arr[N - 1] - arr[N - 2]);` `        ``// Print the sum``        ``Console.Write(sum);``    ``}` `    ``// Driver Code``    ``public` `static` `void` `Main()``    ``{``        ``int``[] arr = { 1, 3, 4, 2 };``        ``int` `N = arr.Length;``        ``maximumSum(arr, N);``    ``}``}` `// This code is contributed by chitranayal.`

## Javascript

 ``

Output:

`6`

Time Complexity: O(N*log N)
Auxiliary Space: O(1)

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