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Minimum sum of absolute differences between pairs of a triplet from an array
• Difficulty Level : Easy
• Last Updated : 26 Feb, 2021

Given an array A[] consiting 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:

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 minuimum 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[0]);` `    ``// 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 minuimum 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 minuimum 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 minuimum 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.`

Output:
`1`

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

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