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

• Difficulty Level : Easy
• Last Updated : 09 Jul, 2021

Given an array A[] consisting of positive integers, the task is to find the minimum value of |A[x] – A[y]| + |A[y] – A[z]| of any triplet (A[x], A[y], A[z]) from an array.

Examples:

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.

Input: A[] = { 1, 1, 2, 3 }
Output: 1
Explanation:
For x = 0, y = 1, z = 2
|A[x] – A[y]| + |A[y] – A[z]| = 0 + 1 = 1, which is maximum possible

Input : A[] = { 1, 1, 1 }
Output : 0

Approach : The problem can be solved greedily. Follow the steps below to solve the problem:

1. Traverse the array.
2. Sort the array in ascending order.
3. Traverse the array using a variable i over indices [0, N – 3]. For every ith index, set x = i, y = i + 1, z = i + 2
4. Calculate the sum of the triplet (x, y, z).
5. Update the minimum sum possible.
6. Print the minimum sum obtained.

Below is the implementation of the above approach:

## C++

 `// C++ Program for the above approach` `#include ``using` `namespace` `std;` `// Function to find minimum``// sum of absolute differences``// of pairs of a triplet``int` `minimum_sum(``int` `A[], ``int` `N)``{``    ``// Sort the array``    ``sort(A, A + N);` `    ``// Stores the minimum sum``    ``int` `sum = INT_MAX;` `    ``// Traverse the array``    ``for` `(``int` `i = 0; i <= N - 3; i++) {` `        ``// Update the minimum sum``        ``sum = min(sum,``                  ``abs``(A[i] - A[i + 1]) +``                  ``abs``(A[i + 1] - A[i + 2]));``    ``}` `    ``// Print the minimum sum``    ``cout << sum;``}` `// Driver Code``int` `main()``{` `    ``// Input``    ``int` `A[] = { 1, 1, 2, 3 };``    ``int` `N = ``sizeof``(A) / ``sizeof``(A);` `    ``// Function call to find minimum``    ``// sum of absolute differences``    ``// of pairs in a triplet``    ``minimum_sum(A, N);` `    ``return` `0;``}`

## Java

 `// Java program for the above approach``import` `java.util.*;``class` `GFG``{``  ` `// Function to find minimum``// sum of absolute differences``// of pairs of a triplet``static` `int` `minimum_sum(``int` `[]A, ``int` `N)``{``  ` `    ``// Sort the array``    ``Arrays.sort(A);` `    ``// Stores the minimum sum` `    ``int` `sum = ``2147483647``;` `    ``// Traverse the array``    ``for` `(``int` `i = ``0``; i <= N - ``3``; i++) {` `        ``// Update the minimum sum``        ``sum = Math.min(sum,Math.abs(A[i] - A[i + ``1``]) + Math.abs(A[i + ``1``] - A[i + ``2``]));``    ``}` `    ``// Print the minimum sum``    ``return` `sum;``}` `// Driver Code``public` `static` `void` `main(String[] args)``{``  ` `    ``// Input``    ``int` `[]A = { ``1``, ``1``, ``2``, ``3` `};``    ``int` `N = A.length;` `    ``// Function call to find minimum``    ``// sum of absolute differences``    ``// of pairs in a triplet``    ``System.out.print(minimum_sum(A, N));``}``}` `// This code is contributed by splevel62.`

## Python3

 `# Python 3 Program for the above approach``import` `sys` `# Function to find minimum``# sum of absolute differences``# of pairs of a triplet``def` `minimum_sum(A, N):``  ` `    ``# Sort the array``    ``A.sort(reverse ``=` `False``)` `    ``# Stores the minimum sum``    ``sum` `=` `sys.maxsize` `    ``# Traverse the array``    ``for` `i ``in` `range``(N ``-` `2``):``      ` `        ``# Update the minimum sum``        ``sum` `=` `min``(``sum``, ``abs``(A[i] ``-` `A[i ``+` `1``]) ``+` `abs``(A[i ``+` `1``] ``-` `A[i ``+` `2``]))` `    ``# Print the minimum sum``    ``print``(``sum``)` `# Driver Code``if` `__name__ ``=``=` `'__main__'``:``  ` `    ``# Input``    ``A ``=` `[``1``, ``1``, ``2``, ``3``]``    ``N ``=` `len``(A)` `    ``# Function call to find minimum``    ``# sum of absolute differences``    ``# of pairs in a triplet``    ``minimum_sum(A, N)``    ` `    ``# This code is contributed by ipg2016107`

## C#

 `// C# Program for the above approach``using` `System;``using` `System.Collections.Generic;``class` `GFG``{``   ` `// Function to find minimum``// sum of absolute differences``// of pairs of a triplet``static` `int` `minimum_sum(``int` `[]A, ``int` `N)``{``  ` `    ``// Sort the array``    ``Array.Sort(A);` `    ``// Stores the minimum sum` `    ``int` `sum = 2147483647;` `    ``// Traverse the array``    ``for` `(``int` `i = 0; i <= N - 3; i++) {` `        ``// Update the minimum sum``        ``sum = Math.Min(sum,Math.Abs(A[i] - A[i + 1]) + Math.Abs(A[i + 1] - A[i + 2]));``    ``}` `    ``// Print the minimum sum``    ``return` `sum;``}` `// Driver Code``public` `static` `void` `Main()``{` `    ``// Input``    ``int` `[]A = { 1, 1, 2, 3 };``    ``int` `N = A.Length;` `    ``// Function call to find minimum``    ``// sum of absolute differences``    ``// of pairs in a triplet``    ``Console.WriteLine(minimum_sum(A, N));``}``}` `// This code is contributed by bgangwar59.`

## Javascript

 ``
Output:
`1`

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

My Personal Notes arrow_drop_up