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Minimum value of X to make all array elements equal by either decreasing or increasing by X
• Last Updated : 10 Oct, 2019
Given an array of N elements and you can perform two operations on it:
• Increase any of the array element by X once.
• Decrease any of the array element by X once.

The task is to find the minimum most value of X such that all array elements are equal by either applying operation 1, 2 or not applying any operation. If all the array elements cannot be made equal, then print -1.

Examples:

Input: a[] = {1, 4, 4, 7, 4, 1}
Output: 3
Increase the first and last element by 3.
Decrease the fourth element by 3.

Input: {1, 5, 7, 9, 1}
Output: -1

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: Since both the operations can only be applied once on an array element, the common point of observation is that if there are more than 3 unique elements than the answer is -1. There can arise three cases which are solved in the following ways:

• If there are 3 unique elements, if abs(el2-el1) == abs(el3-el2), then the answer is abs(el2-el1). If they are not equal then the answer is -1.
• If there are 2 unique elements, the answer is (el2 – el1) / 2, if el2 – el1 is even, else the answer is (el2 – el1)
• If there is a single unique element, then the answer is 0

Below is the implementation of the above approach:

## C++

 `// C++ program to implement``// the above approach`` ` `#include ``using` `namespace` `std;`` ` `// Function that returns the``// minimum value of X``int` `findMinimumX(``int` `a[], ``int` `n)``{`` ` `    ``// Declare a set``    ``set<``int``> st;`` ` `    ``// Iterate in the array element``    ``// and insert them into the set``    ``for` `(``int` `i = 0; i < n; i++)``        ``st.insert(a[i]);`` ` `    ``// If unique elements is 1``    ``if` `(st.size() == 1)``        ``return` `0;`` ` `    ``// Unique elements is 2``    ``if` `(st.size() == 2) {``        ``// Get both el2 and el1``        ``int` `el1 = *st.begin();``        ``int` `el2 = *st.rbegin();`` ` `        ``// Check if they are even``        ``if` `((el2 - el1) % 2 == 0)``            ``return` `(el2 - el1) / 2;``        ``else``            ``return` `(el2 - el1);``    ``}`` ` `    ``// If there are 3 unique elements``    ``if` `(st.size() == 3) {``        ``// Get three unique elements``        ``auto` `it = st.begin();``        ``int` `el1 = *it;``        ``it++;``        ``int` `el2 = *it;``        ``it++;``        ``int` `el3 = *it;`` ` `        ``// Check if their difference is same``        ``if` `((el2 - el1) == (el3 - el2))``            ``return` `el2 - el1;``        ``else``            ``return` `-1;``    ``}`` ` `    ``// More than 3 unique elements``    ``return` `-1;``}`` ` `// Driver code``int` `main()``{``    ``int` `a[] = { 1, 4, 4, 7, 4, 1 };``    ``int` `n = ``sizeof``(a) / ``sizeof``(a);``    ``cout << findMinimumX(a, n);`` ` `    ``return` `0;``}`

## Java

 `// Java implementation of the approach``import` `java.util.HashSet;``import` `java.util.Iterator;``import` `java.util.Set;`` ` `class` `GFG ``{``     ` `    ``// Function that returns the``    ``// minimum value of X``    ``static` `int` `findMinimumX(``int` `a[], ``int` `n)``    ``{`` ` `        ``// Declare a set``        ``Set st = ``new` `HashSet<>();`` ` `        ``// Iterate in the array element``        ``// and insert them into the set``        ``for` `(``int` `i = ``0``; i < n; i++)``            ``st.add(a[i]);`` ` `        ``// If unique elements is 1``        ``if` `(st.size() == ``1``)``            ``return` `0``;`` ` `        ``// Unique elements is 2``        ``if` `(st.size() == ``2``) ``        ``{``            ``// Get both el2 and el1``            ``Iterator it = st.iterator();``            ``int` `el1 = it.next();``            ``int` `el2 = it.next();`` ` `            ``// Check if they are even``            ``if` `((el2 - el1) % ``2` `== ``0``)``                ``return` `(el2 - el1) / ``2``;``            ``else``                ``return` `(el2 - el1);``        ``}`` ` `        ``// If there are 3 unique elements``        ``if` `(st.size() == ``3``) ``        ``{``            ``// Get three unique elements``            ``Iterator it = st.iterator();``            ``int` `el1 = it.next();``            ``int` `el2 = it.next();``            ``int` `el3 = it.next();`` ` `            ``// Check if their difference is same``            ``if` `((el2 - el1) == (el3 - el2))``                ``return` `el2 - el1;``            ``else``                ``return` `-``1``;``        ``}`` ` `        ``// More than 3 unique elements``        ``return` `-``1``;``    ``}`` ` `    ``// Driver code``    ``public` `static` `void` `main(String[] args) ``    ``{``        ``int` `a[] = {``1``, ``4``, ``4``, ``7``, ``4``, ``1``};``        ``int` `n = a.length;``        ``System.out.println(findMinimumX(a, n));``    ``}``}`` ` `// This code is contributed by``// Rajnis09`

## Python3

 `# Python 3 program to implement``# the above approach`` ` `# Function that returns the``# minimum value of X``def` `findMinimumX(a, n):``     ` `    ``# Declare a set``    ``st ``=` `set``()`` ` `    ``# Iterate in the array element``    ``# and insert them into the set``    ``for` `i ``in` `range``(n):``        ``st.add(a[i])`` ` `    ``# If unique elements is 1``    ``if` `(``len``(st) ``=``=` `1``):``        ``return` `0`` ` `    ``# Unique elements is 2``    ``if` `(``len``(st) ``=``=` `2``):``         ` `        ``# Get both el2 and el1``        ``st ``=` `list``(st)``        ``el1 ``=` `st[``0``]``        ``el2 ``=` `st[``1``]`` ` `        ``# Check if they are even``        ``if` `((el2 ``-` `el1) ``%` `2` `=``=` `0``):``            ``return` `int``((el2 ``-` `el1) ``/` `2``)``        ``else``:``            ``return` `(el2 ``-` `el1)`` ` `    ``# If there are 3 unique elements``    ``if` `(``len``(st) ``=``=` `3``):``        ``st ``=` `list``(st)``         ` `        ``# Get three unique elements``        ``el1 ``=` `st[``0``]``        ``el2 ``=` `st[``1``]``        ``el3 ``=` `st[``2``]`` ` `        ``# Check if their difference is same``        ``if` `((el2 ``-` `el1) ``=``=` `(el3 ``-` `el2)):``            ``return` `el2 ``-` `el1``        ``else``:``            ``return` `-``1`` ` `    ``# More than 3 unique elements``    ``return` `-``1`` ` `# Driver code``if` `__name__ ``=``=` `'__main__'``:``    ``a ``=` `[``1``, ``4``, ``4``, ``7``, ``4``, ``1``]``    ``n ``=` `len``(a)``    ``print``(findMinimumX(a, n))`` ` `# This code is contributed by``# Surendra_Gangwar`

## C#

 `// C# implementation of the approach``using` `System;``using` `System.Collections.Generic; `` ` `class` `GFG ``{``     ` `    ``// Function that returns the``    ``// minimum value of X``    ``static` `int` `findMinimumX(``int` `[]a, ``int` `n)``    ``{`` ` `        ``// Declare a set``        ``List<``int``> st = ``new` `List<``int``>();`` ` `        ``// Iterate in the array element``        ``// and insert them into the set``        ``for` `(``int` `i = 0; i < n; i++)``            ``if``(!st.Contains(a[i]))``                ``st.Add(a[i]);`` ` `        ``// If unique elements is 1``        ``if` `(st.Count == 1)``            ``return` `0;`` ` `        ``// Unique elements is 2``        ``if` `(st.Count == 2) ``        ``{``            ``// Get both el2 and el1``            ``int` `el1 = st;``            ``int` `el2 = st;`` ` `            ``// Check if they are even``            ``if` `((el2 - el1) % 2 == 0)``                ``return` `(el2 - el1) / 2;``            ``else``                ``return` `(el2 - el1);``        ``}`` ` `        ``// If there are 3 unique elements``        ``if` `(st.Count == 3) ``        ``{``            ``// Get three unique elements``            ``int` `el1 = st;``            ``int` `el2 = st;``            ``int` `el3 = st;`` ` `            ``// Check if their difference is same``            ``if` `((el2 - el1) == (el3 - el2))``                ``return` `el2 - el1;``            ``else``                ``return` `-1;``        ``}`` ` `        ``// More than 3 unique elements``        ``return` `-1;``    ``}`` ` `    ``// Driver code``    ``public` `static` `void` `Main(String[] args) ``    ``{``        ``int` `[]a = {1, 4, 4, 7, 4, 1};``        ``int` `n = a.Length;``        ``Console.WriteLine(findMinimumX(a, n));``    ``}``} ``     ` `// This code is contributed by Princi Singh`
Output:
```3
```

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