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[0] – 3| = 2 ? 2 
|arr[1] – 3| = 1 ? 2 
|arr[2] – 3| = 0 ? 2 
|arr[3] – 3| = 1 ? 2 
|arr[4] – 3| = 2 ? 2 
Input: arr[] = {1, 6, 20}, K = 1 
Output: -1 
Explanation:
It is not possible to equalize the array 

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 <bits/stdc++.h>
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[0]);

    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

Javascript

<script>
// Javascript 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
function equalize(arr, n, k)
{

    // Finding the minimum element
    // from the array
    let min_ele
        = arr.sort((a, b) => a - b)[0];

    // Boolean variable to check if the
    // array can be equalized or not
    let flag = true;

    // Traversing the array
    for (let 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

let K = 2;
let arr = [ 1, 2, 3, 4, 5 ];
let N = arr.length;

document.write(equalize(arr, N, K));

// This code is contributed by _saurabh_jaiswal
</script>

Output:

3

Time Complexity: O(n), to traverse the array where n is the size of the given array 
Auxiliary Space: O(1), as no extra space is used