# Make all elements of an Array equal by adding or subtracting at most K

Given an array arr[] containing positive integers of size N and an integer K, the task is to make all the elements in the array equal to some value D (D > 0) such that |arr[i] – D| ≤ K. Print the value of D or -1 if it is not possible to make the array equal.

Examples:

Input: arr[] = {1, 2, 3, 4, 5}, K = 2
Output: 3
Explanation:
All the elements in the array can be made equal to 3 as:
|arr – 3| = 2 ≤ 2
|arr – 3| = 1 ≤ 2
|arr – 3| = 0 ≤ 2
|arr – 3| = 1 ≤ 2
|arr – 3| = 2 ≤ 2

Input: arr[] = {1, 6, 20}, K = 1
Output: -1
Explanation:
It is not possible to equalize the array

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

Approach: The idea is to first find the minimum element of the array.

• If M is the minimum element of the array, then M + K is the maximum possible value which this minimum element can take in order to satisfy the condition arr[i] – D ≤ K.
• Then, D = M + K, if for all the elements in the array, (M + K) lies in the range [arr[i] – K, arr[i] + K].
• Therefore, we simply iterate over every element in the array and check for this condition.

Below is the implementation of the above approach:

## C++

 `// C++ program to make all elements ` `// of an Array equal by adding or ` `// subtracting at most K ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// Function to equalize the array by ` `// adding or subtracting at most K ` `// value from each element ` `int` `equalize(``int` `arr[], ``int` `n, ``int` `k) ` `{ ` ` `  `    ``// Finding the minimum element ` `    ``// from the array ` `    ``int` `min_ele ` `        ``= *min_element(arr, arr + n); ` ` `  `    ``// Boolean variable to check if the ` `    ``// array can be equalized or not ` `    ``bool` `flag = ``true``; ` ` `  `    ``// Traversing the array ` `    ``for` `(``int` `i = 0; i < n; i++) { ` ` `  `        ``// Checking if the values lie ` `        ``// within the possible range ` `        ``// for each element ` `        ``if` `(!((arr[i] + k) >= min_ele + k ` `              ``&& min_ele + k >= (arr[i] - k))) { ` ` `  `            ``// If any value doesn't lie in ` `            ``// the range then exit the loop ` `            ``flag = ``false``; ` `            ``break``; ` `        ``} ` `    ``} ` ` `  `    ``if` `(flag) { ` ` `  `        ``// Value after equalizing the array ` `        ``return` `min_ele + k; ` `    ``} ` ` `  `    ``// Array cannot be equalized ` `    ``else` `        ``return` `-1; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `K = 2; ` `    ``int` `arr[] = { 1, 2, 3, 4, 5 }; ` `    ``int` `N = ``sizeof``(arr) / ``sizeof``(arr); ` ` `  `    ``cout << equalize(arr, N, K); ` `} `

## Java

 `// Java program to make all elements ` `// of an Array equal by adding or ` `// subtracting at most K ` `import` `java.util.*; ` ` `  `class` `GFG{ ` `  `  `// Function to equalize the array by ` `// adding or subtracting at most K ` `// value from each element ` `static` `int` `equalize(``int` `arr[], ``int` `n, ``int` `k) ` `{ ` `  `  `    ``// Finding the minimum element ` `    ``// from the array ` `    ``int` `min_ele ` `        ``= Arrays.stream(arr).min().getAsInt(); ` `  `  `    ``// Boolean variable to check if the ` `    ``// array can be equalized or not ` `    ``boolean` `flag = ``true``; ` `  `  `    ``// Traversing the array ` `    ``for` `(``int` `i = ``0``; i < n; i++) { ` `  `  `        ``// Checking if the values lie ` `        ``// within the possible range ` `        ``// for each element ` `        ``if` `(!((arr[i] + k) >= min_ele + k ` `              ``&& min_ele + k >= (arr[i] - k))) { ` `  `  `            ``// If any value doesn't lie in ` `            ``// the range then exit the loop ` `            ``flag = ``false``; ` `            ``break``; ` `        ``} ` `    ``} ` `  `  `    ``if` `(flag) { ` `  `  `        ``// Value after equalizing the array ` `        ``return` `min_ele + k; ` `    ``} ` `  `  `    ``// Array cannot be equalized ` `    ``else` `        ``return` `-``1``; ` `} ` `  `  `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``int` `K = ``2``; ` `    ``int` `arr[] = { ``1``, ``2``, ``3``, ``4``, ``5` `}; ` `    ``int` `N = arr.length; ` `  `  `    ``System.out.print(equalize(arr, N, K)); ` `} ` `} ` ` `  `// This code is contributed by Princi Singh `

## Python3

 `# Python program to make all elements ` `# of an Array equal by adding or ` `# subtracting at most K ` ` `  `# Function to equalize the array by ` `# adding or subtracting at most K ` `# value from each element ` `def` `equalize(arr, n, k): ` ` `  `    ``# Finding the minimum element ` `    ``# from the array ` `    ``min_ele ``=` `min``(arr); ` ` `  `    ``# Boolean variable to check if the ` `    ``# array can be equalized or not ` `    ``flag ``=` `True``; ` ` `  `    ``# Traversing the array ` `    ``for` `i ``in` `range``(n): ` ` `  `        ``# Checking if the values lie ` `        ``# within the possible range ` `        ``# for each element ` `        ``if` `(``not``((arr[i] ``+` `k) >``=` `(min_ele ``+` `k) ``and`  `            ``(min_ele ``+` `k) >``=` `(arr[i] ``-` `k))) : ` ` `  `            ``# If any value doesn't lie in ` `            ``# the range then exit the loop ` `            ``flag ``=` `False``; ` `            ``break``; ` ` `  `    ``if` `(flag):  ` ` `  `        ``# Value after equalizing the array ` `        ``return` `min_ele ``+` `k; ` `     `  `    ``# Array cannot be equalized ` `    ``else``: ` `        ``return` `-``1``; ` ` `  `# Driver code ` `if` `__name__``=``=``'__main__'``:  ` ` `  `    ``K ``=` `2``; ` `    ``arr ``=` `[ ``1``, ``2``, ``3``, ``4``, ``5``] ; ` `    ``N ``=` `len``(arr) ` ` `  `    ``print``(equalize(arr, N, K)) ` ` `  `# This code is contributed by Princi Singh `

## C#

 `// C# program to make all elements ` `// of an Array equal by adding or ` `// subtracting at most K ` `using` `System; ` `using` `System.Linq; ` ` `  `class` `GFG{ ` `   `  `// Function to equalize the array by ` `// adding or subtracting at most K ` `// value from each element ` `static` `int` `equalize(``int` `[]arr, ``int` `n, ``int` `k) ` `{ ` `   `  `    ``// Finding the minimum element ` `    ``// from the array ` `    ``int` `min_ele = arr.Min(); ` `   `  `    ``// Boolean variable to check if the ` `    ``// array can be equalized or not ` `    ``bool` `flag = ``true``; ` `   `  `    ``// Traversing the array ` `    ``for` `(``int` `i = 0; i < n; i++) { ` `   `  `        ``// Checking if the values lie ` `        ``// within the possible range ` `        ``// for each element ` `        ``if` `(!((arr[i] + k) >= min_ele + k ` `              ``&& min_ele + k >= (arr[i] - k))) { ` `   `  `            ``// If any value doesn't lie in ` `            ``// the range then exit the loop ` `            ``flag = ``false``; ` `            ``break``; ` `        ``} ` `    ``} ` `   `  `    ``if` `(flag) { ` `   `  `        ``// Value after equalizing the array ` `        ``return` `min_ele + k; ` `    ``} ` `   `  `    ``// Array cannot be equalized ` `    ``else` `        ``return` `-1; ` `} ` `   `  `// Driver code ` `public` `static` `void` `Main(String[] args) ` `{ ` `    ``int` `K = 2; ` `    ``int` `[]arr = { 1, 2, 3, 4, 5 }; ` `    ``int` `N = arr.Length; ` `   `  `    ``Console.Write(equalize(arr, N, K)); ` `} ` `} ` ` `  `// This code is contributed by Princi Singh `

Output:

```3
```

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