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++

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// 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);
}

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Java

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// 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

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Python3

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# 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

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C#

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// 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

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Output:

3

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