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Palindromic Selfie Numbers

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  • Difficulty Level : Medium
  • Last Updated : 12 May, 2022

Given a number x, find it’s palindromic selfie number according to selfie multiplicative rule. If such a number doesn’t exist, then print “No such number exists”. 
A Palindromic selfie number satisfies the selfie multiplicative rule such that there exists another number y with x * reverse_digits_of(x) = y * reverse_digits_of(y), with the condition that the number y is obtained by some ordering of the digits in x, i.e x and y should have same digits with different order.
Examples : 
 

Input : 1224
Output : 2142
Explanation :
Because, 1224 X 4221 = 2142 X 2412
And all digits of 2142 are formed by a different 
permutation of the digits in 1224
(Note: The valid output is either be 2142 or 2412)

Input : 13452
Output : 14532
Explanation :
Because, 13452 X 25431 = 14532 X 23541
And all digits of 14532 are formed by a different 
permutation of the digits in 13452

Input : 12345
Output : No such number exists
Explanation :
Because, with no combination of digits 1, 2, 3, 4, 5 
could we get a number that satisfies 
12345 X 54321 = number X reverse_of_its_digits

 

Approach : 
 

  • The idea is to break down the number and obtain all permutations of the digits in the number.
  • Then, the number and its palindrome are removed from the set of permutations obtained, which will form the LHS of our equality.
  • To check for RHS, we now iterate over all other permutations equating
 LHS = current_number X palindrome(current_number) 
  • As soon as we get a match, we exit the loop with an affirmative message, else print “No such number available”.

Below is implementation of above approach : 
 

Java




// Java program to find palindromic selfie numbers
import java.util.*;
 
public class palindrome_selfie {
    // To store all permutations of digits in the number
    Set<Integer> all_permutes = new HashSet<Integer>();
 
    int number; // input number
 
    public palindrome_selfie(int num)
    {
        number = num;
    }
 
    // Function to reverse the digits of a number
    public int palindrome(int num)
    {
        int reversednum = 0;
        int d;
        while (num > 0) {
            d = num % 10; // Extract last digit
 
            // Append it at the beg
            reversednum = reversednum * 10 + d;
            num = num / 10// Reduce number until 0
        }
 
        return reversednum;
    }
 
    // Function to check palindromic selfie
    public void palin_selfie()
    {
        // Length of the number required for
        // calculating all permutations of the digits
        int l = String.valueOf(number).length() - 1;
         
        this.permute(number, 0, l); // Calculate all permutations
         
        /* Remove the number and its palindrome from
           the obtained set as this is the LHS of
           multiplicative equality */
        all_permutes.remove(palindrome(number));
        all_permutes.remove(number);
 
        boolean flag = false; // Denotes the status result
 
        // Iterate over all other numbers
        Iterator it = all_permutes.iterator();
        while (it.hasNext()) {
            int number2 = (int)it.next();
 
            // Check for equality x*palin(x) = y*palin(y)
            if (number * palindrome(number) ==
                         number2 * palindrome(number2)) {
                System.out.println("Palindrome multiplicative" +
                                    "selfie of "+ number + " is  : "
                                     + number2);
 
                flag = true; // Answer found
                break;
            }
        }
 
        // If no such number found
        if (flag == false) {
            System.out.println("Given number has no palindrome selfie.");
        }
    }
 
    // Function to get all possible permutations
    // of the digits in num
    public void permute(int num, int l, int r)
    {
        // Adds the new permutation obtained in the set
        if (l == r)
            all_permutes.add(num);
 
        else {
            for (int i = l; i <= r; i++) {
 
                // Swap digits to get a different ordering
                num = swap(num, l, i);
 
                // Recurse to next pair of digits
                permute(num, l + 1, r);
                num = swap(num, l, i); // Swap back
            }
        }
    }
 
    // Function that swaps the digits i and j in the num
    public int swap(int num, int i, int j)
    {
        char temp;
 
        // Convert int to char array
        char[] charArray = String.valueOf(num).toCharArray();
 
        // Swap the ith and jth character
        temp = charArray[i];
        charArray[i] = charArray[j];
        charArray[j] = temp;
 
        // Convert back to int and return
        return Integer.valueOf(String.valueOf(charArray));
    }
 
    // Driver Function
    public static void main(String args[])
    {
        // First example, input = 145572
        palindrome_selfie example1 = new palindrome_selfie(145572);
        example1.palin_selfie();
 
        // Second example, input = 19362
        palindrome_selfie example2 = new palindrome_selfie(19362);
        example2.palin_selfie();
 
        // Third example, input = 4669
        palindrome_selfie example3 = new palindrome_selfie(4669);
        example3.palin_selfie();
    }
}


C#




// C# program to find palindromic selfie numbers
using System;
using System.Collections.Generic;
 
public class palindrome_selfie
{
    // To store all permutations of digits in the number
    HashSet<int> all_permutes = new HashSet<int>();
 
    int number; // input number
 
    public palindrome_selfie(int num)
    {
        number = num;
    }
 
    // Function to reverse the digits of a number
    public int palindrome(int num)
    {
        int reversednum = 0;
        int d;
        while (num > 0)
        {
            d = num % 10; // Extract last digit
 
            // Append it at the beg
            reversednum = reversednum * 10 + d;
            num = num / 10; // Reduce number until 0
        }
        return reversednum;
    }
 
    // Function to check palindromic selfie
    public void palin_selfie()
    {
        // Length of the number required for
        // calculating all permutations of the digits
        int l = String.Join("",number).Length - 1;
         
        this.permute(number, 0, l); // Calculate all permutations
         
        /* Remove the number and its palindrome from
        the obtained set as this is the LHS of
        multiplicative equality */
        all_permutes.Remove(palindrome(number));
        all_permutes.Remove(number);
 
        bool flag = false; // Denotes the status result
 
        // Iterate over all other numbers
        foreach (var number2 in all_permutes)
        {
 
            // Check for equality x*palin(x) = y*palin(y)
            if (number * palindrome(number) ==
                        number2 * palindrome(number2))
            {
                Console.WriteLine("Palindrome multiplicative" +
                                    "selfie of "+ number + " is : "
                                    + number2);
 
                flag = true; // Answer found
                break;
            }
        }
 
        // If no such number found
        if (flag == false)
        {
            Console.WriteLine("Given number has "+
                            "no palindrome selfie.");
        }
    }
 
    // Function to get all possible
    // permutations of the digits in num
    public void permute(int num, int l, int r)
    {
        // Adds the new permutation obtained in the set
        if (l == r)
            all_permutes.Add(num);
 
        else
        {
            for (int i = l; i <= r; i++)
            {
 
                // Swap digits to get a different ordering
                num = swap(num, l, i);
 
                // Recurse to next pair of digits
                permute(num, l + 1, r);
                num = swap(num, l, i); // Swap back
            }
        }
    }
 
    // Function that swaps the
    // digits i and j in the num
    public int swap(int num, int i, int j)
    {
        char temp;
 
        // Convert int to char array
        char[] charArray = String.Join("",num).ToCharArray();
 
        // Swap the ith and jth character
        temp = charArray[i];
        charArray[i] = charArray[j];
        charArray[j] = temp;
 
        // Convert back to int and return
        return int.Parse(String.Join("",charArray));
    }
 
    // Driver code
    public static void Main(String []args)
    {
        // First example, input = 145572
        palindrome_selfie example1 = new palindrome_selfie(145572);
        example1.palin_selfie();
 
        // Second example, input = 19362
        palindrome_selfie example2 = new palindrome_selfie(19362);
        example2.palin_selfie();
 
        // Third example, input = 4669
        palindrome_selfie example3 = new palindrome_selfie(4669);
        example3.palin_selfie();
    }
}
 
// This code contributed by Rajput-Ji


Output : 

Palindrome multiplicative selfie of 145572 is  : 157452
Given number has no palindrome selfie.
Palindrome multiplicative selfie of 4669 is  : 6496


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