Find whether it is possible to make array elements same using one external number

Given an Array, three operations can be performed using any external number x.

1. Add x to an element once
2. Subtract x from an element once
3. Perform no operation on the element
   1. Count of unique elements is 1. Answer is YES with x = 0
   2. Count of unique elements is 2. Answer is YES with x = Difference of two unique elements.
   3. Count of unique elements is 3.
      • If difference between mid and max is same as difference between mid and min, answer is YES with x = difference between mid and max or mid and min.
      • Otherwise answer is NO.

In Python, we can quickly find unique elements using set in Python.

C++

// C++ Program to find an element X
// that can be used to operate on an array and
// get equal elements

#include<bits/stdc++.h>
using namespace std;

// Prints "YES" and an element x if we can
// equalize array using x. Else prints "NO"
void canEqualise(int array[], int n)
{
    // We all the unique elements (using set
    // function).
    set<int> s;
    for(int i=0;i<n;i++)
    {
        s.insert(array[i]);
    }

    // if there are only 1 or 2 unique elements,
    // then we can add or subtract x from one of them
    // to get the other element
    if(s.size() == 1)
        cout<<"YES " << "0";
    else if (s.size() == 2)
    {
        auto x = s.begin();
        s.erase(x);
        auto y = s.begin();
        s.erase(y);
       cout<<"YES " << (*y-*x);
    }


    // If count of unique elements is three, then
    // difference between the middle and minimum
    // should be same as difference between maximum
    // and middle
    else if (s.size() == 3)
    {
        auto x = s.begin();
        s.erase(x);
        auto y = s.begin();
        s.erase(y);
        auto z = s.begin();
        s.erase(z);

        if ((*z-*y)==(*y-*x))
            cout<<"YES " << (*z-*y);
        else
            cout<<"NO";
    }


    // if there are more than three unique elements, then
    // we cannot add or subtract the same value from all
    // the elements.
    else
        cout<<"NO";

}

// Driver code
int main()
{
    int array[] = {55, 52, 52, 49, 52};
    int n = sizeof(array) / sizeof(array[0]);
    canEqualise(array,n);
}

// This code is contributed by Aarti_Rathi

Java

// Java Program to find an element X
// that can be used to operate on an array and
// get equal elements

// Importing generic java libraries
import java.util.*;

public class GFG {

    // Prints "YES" and an element x if we can
    // equalize array using x. Else prints "NO"
    static void canEqualise(int array[], int n)
    {
        // We all the unique elements (using set
        // function).
        Set<Integer> s = new HashSet<Integer>();
        for (int i = 0; i < n; i++) {
            s.add(array[i]);
        }

        // if there are only 1 or 2 unique elements,
        // then we can add or subtract x from one of them
        // to get the other element
        if (s.size() == 1)
            System.out.println("YES 0");
        else if (s.size() == 2) {
            int x = s.stream().findFirst().get();
            s.remove(x);
            int y = s.stream().findFirst().get();
            s.remove(y);
            System.out.println("YES " + (y - x));
        }

        // If count of unique elements is three, then
        // difference between the middle and minimum
        // should be same as difference between maximum
        // and middle
        else if (s.size() == 3) {
            int x = s.stream().findFirst().get();
            s.remove(x);
            int y = s.stream().findFirst().get();
            s.remove(y);
            int z = s.stream().findFirst().get();
            s.remove(z);

            if ((z - y) == (y - x))
                System.out.println("YES " + (z - y));
            else
                System.out.println("NO");
        }

        // if there are more than three unique elements,
        // then we cannot add or subtract the same value
        // from all the elements.
        else
            System.out.println("NO");
    }

    // Driver code
    public static void main(String[] args)
    {
        int array[] = { 55, 52, 52, 49, 52 };
        int n = array.length;
        canEqualise(array, n);
    }
}

// This code is contributed by Aarti_Rathi

Python

# Program in python 2.x to find an element X
# that can be used to operate on an array and
# get equal elements

# Prints "YES" and an element x if we can
# equalize array using x. Else prints "NO"
def canEqualise(array):

    # We all the unique elements (using set
    # function). Then we sort unique elements.
    uniques = sorted(set(array))

    # if there are only 1 or 2 unique elements,
    # then we can add or subtract x from one of them
    # to get the other element
    if len(uniques) == 1:
        print("YES " + "0")
    elif len(uniques) == 2:
        print("YES " + str(uniques[1] - uniques[0]))

    # If count of unique elements is three, then
    # difference between the middle and minimum
    # should be same as difference between maximum
    # and middle
    elif len(uniques) == 3:
        if uniques[2] - uniques[1] == uniques[1] - uniques[0]:
            X = uniques[2] - uniques[1]
            print("YES " + str(X))
        else:
            print("NO")

    # if there are more than three unique elements, then
    # we cannot add or subtract the same value from all
    # the elements.
    else:
        print("NO")

# Driver code
array = [55, 52, 52, 49, 52]
canEqualise(array)

C#

using System;
using System.Collections.Generic;

public static class GFG {
  // C# Program to find an element X
  // that can be used to operate on an array and
  // get equal elements

  // Prints "YES" and an element x if we can
  // equalize array using x. Else prints "NO"
  public static void canEqualise(int[] array, int n)
  {
    // We all the unique elements (using set
    // function).
    HashSet<int> s = new HashSet<int>();
    for (int i = 0; i < n; i++) {
      s.Add(array[i]);
    }

    // if there are only 1 or 2 unique elements,
    // then we can add or subtract x from one of them
    // to get the other element
    if (s.Count == 1) {
      Console.Write("YES ");
      Console.Write("0");
    }
    else if (s.Count == 2) {
      int x = 0;
      int y = 0;
      int m = 0;
      Console.Write("YES ");
      foreach(var i in s)
      {
        if (m == 0) {
          x = i;
        }
        else {
          y = i;
        }
        m++;
      }
      Console.Write((y - x));
    }

    // If count of unique elements is three, then
    // difference between the middle and minimum
    // should be same as difference between maximum
    // and middle
    else if (s.Count == 3) {
      int x = 0;
      int y = 0;
      int z = 0;
      int m = 0;
      foreach(var i in s)
      {
        if (m == 0) {
          x = i;
        }
        else if (m == 1) {
          y = i;
        }
        else {
          z = i;
        }
        m++;
      }

      if ((z - y) == (y - x)) {
        Console.Write("YES ");
        Console.Write((z - y));
      }
      else {
        Console.Write("NO");
      }
    }

    // if there are more than three unique elements,
    // then we cannot add or subtract the same value
    // from all the elements.
    else {
      Console.Write("NO");
    }
  }

  // Driver code
  public static void Main()
  {
    int[] array = { 55, 52, 52, 49, 52 };
    int n = array.Length;
    canEqualise(array, n);
  }
}
  // This code is contributed by Aarti_Rathi

Javascript

// JavaScript program to find an element X
// that can be used to operate on an array and
// get equal elements
function canEqualise(array, n) {
    // We find all the unique elements (using Set function)
    let s = new Set(array);


    // If there are only 1 or 2 unique elements,
    // then we can add or subtract x from one of them
    // to get the other element
    if (s.size === 1)
        console.log("YES 0");
    else if (s.size === 2) {
        let x = s.values().next().value;
        s.delete(x);
        let y = s.values().next().value;
        s.delete(y);
        console.log(`YES ${y-x}`);
    }

    // If count of unique elements is three, then
    // difference between the middle and minimum
    // should be same as difference between maximum
    // and middle
    else if (s.size === 3) {
        let x = s.values().next().value;
        s.delete(x);
        let y = s.values().next().value;
        s.delete(y);
        let z = s.values().next().value;
        s.delete(z);

        if ((z - y) === (y - x))
            console.log(`YES ${z-y}`);
        else
            console.log("NO");
    }

    // If there are more than three unique elements, then
    // we cannot add or subtract the same value from all
    // the elements.
    else
        console.log("NO");
}

// Driver code
let array = [55, 52, 52, 49, 52];
let n = array.length;
canEqualise(array, n);

OUTPUT

YES 3

Time Complexity: O(n logn)//we are running a for loop for n times and inside the loop the set insert operation is taking place which takes log n time to compute
Auxiliary space: O(n). //since we are using a set to store all the elements of the array

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