Check if a number is prime in Flipped Upside Down, Mirror Flipped and Mirror Flipped Upside Down

Given an integer N, the task is to check if N is a prime number in Flipped Down, Mirror Flipped and Mirror Flipped Down forms of the given number.
Examples:

Input: N = 120121 
Output: Yes
Explanation:
Flipped forms of the number:
Flipped Upside Down – 151051
Mirror Flipped              – 121021
Mirror Upside Down   – 150151
Since 1510151 and 121021 are both prime numbers, the flipped numbers are prime.

Input: N = 12
Output: No
Explanation:
Flipped forms of the number:
Flipped Upside Down – 15
Mirror Flipped              – 21
Mirror Upside Down   – 51
All the flipped numbers are not prime.

Approach: Follow the steps below to solve the problem:

1. Since the number N has to be prime in each of the Flipped upside down, Mirror Flipped and Mirror Upside Down forms, the only possible digits it should contain are {0, 1, 2, 5, 8}.
2. Therefore, the problem reduces to check if the number is prime or not and if it is made up of the digits 0, 1, 2, 5, and 8 only.
3. If found to be true, print “Yes“.
4. Otherwise, print “No“.

Below is the implementation of the above approach:

C++

// C++ program to implement
// the above approach

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

// Function to check if N
// contains digits
// 0, 1, 2, 5, 8 only
bool checkDigits(int n)
{
    // Extract digits of N
    do {
        int r = n % 10;

        // Return false if any of
        // these digits are present
        if (r == 3 || r == 4 || r == 6
            || r == 7 || r == 9)
            return false;

        n /= 10;
    } while (n != 0);

    return true;
}

// Function to check if
// N is prime or not
bool isPrime(int n)
{
    if (n <= 1)
        return false;

    // Check for all factors
    for (int i = 2; i * i <= n; i++) {
        if (n % i == 0)
            return false;
    }
    return true;
}

// Function to check if n is prime
// in all the desired forms
int isAllPrime(int n)
{
    return isPrime(n)
           && checkDigits(n);
}

// Driver Code
int main()
{
    int N = 101;

    if (isAllPrime(N))
        cout << "Yes";
    else
        cout << "No";
    return 0;
}

Java

// Java program to implement
// the above approach
import java.util.*;
class GFG{

// Function to check if N
// contains digits
// 0, 1, 2, 5, 8 only
static boolean checkDigits(int n)
{
  // Extract digits of N
  do
  {
    int r = n % 10;

    // Return false if any of
    // these digits are present
    if (r == 3 || r == 4 ||
        r == 6 || r == 7 || r == 9)
      return false;

    n /= 10;
  } while (n != 0);

  return true;
}

// Function to check if
// N is prime or not
static boolean isPrime(int n)
{
  if (n <= 1)
    return false;

  // Check for all factors
  for (int i = 2; i * i <= n; i++)
  {
    if (n % i == 0)
      return false;
  }
  return true;
}

// Function to check if n is prime
// in all the desired forms
static boolean isAllPrime(int n)
{
  return isPrime(n) &&
         checkDigits(n);
}

// Driver Code
public static void main(String[] args)
{
  int N = 101;

  if (isAllPrime(N))
    System.out.print("Yes");
  else
    System.out.print("No");
}
}

// This code is  contributed by gauravrajput1

Python3

# Python3 program to implement
# the above approach

# Function to check if N
# contains digits
# 0, 1, 2, 5, 8 only
def checkDigits(n):

    # Extract digits of N
    while True:
        r = n % 10

        # Return false if any of
        # these digits are present
        if (r == 3 or r == 4 or
            r == 6 or r == 7 or
            r == 9):
            return False

        n //= 10

        if n == 0:
            break

    return True

# Function to check if
# N is prime or not
def isPrime(n):

    if (n <= 1):
        return False

    # Check for all factors
    for i in range(2, n + 1):
        if i * i > n:
            break

        if (n % i == 0):
            return False

    return True

# Function to check if n is prime
# in all the desired forms
def isAllPrime(n):

    return isPrime(n) and checkDigits(n)

# Driver Code
if __name__ == '__main__':

    N = 101

    if (isAllPrime(N)):
        print("Yes")
    else:
        print("No")

# This code is contributed by mohit kumar 29

C#

// C# program to implement
// the above approach
using System;

class GFG{

// Function to check if N
// contains digits
// 0, 1, 2, 5, 8 only
static bool checkDigits(int n)
{

  // Extract digits of N
  do
  {
    int r = n % 10;

    // Return false if any of
    // these digits are present
    if (r == 3 || r == 4 ||
        r == 6 || r == 7 ||
        r == 9)
      return false;

    n /= 10;
  } while (n != 0);

  return true;
}

// Function to check if
// N is prime or not
static bool isPrime(int n)
{
  if (n <= 1)
    return false;

  // Check for all factors
  for (int i = 2; i * i <= n; i++)
  {
    if (n % i == 0)
      return false;
  }
  return true;
}

// Function to check if n is prime
// in all the desired forms
static bool isAllPrime(int n)
{
  return isPrime(n) &&
         checkDigits(n);
}

// Driver Code
public static void Main(String[] args)
{
  int N = 101;

  if (isAllPrime(N))
    Console.Write("Yes");
  else
    Console.Write("No");
}
}

// This code is contributed by Rajput-Ji

Javascript

<script>

// Javascript program to implement
// the above approach

// Function to check if N
// contains digits
// 0, 1, 2, 5, 8 only
function checkDigits(n)
{
    // Extract digits of N
    do {
        var r = n % 10;

        // Return false if any of
        // these digits are present
        if (r == 3 || r == 4 || r == 6
            || r == 7 || r == 9)
            return false;

        n = parseInt(n/10);
    } while (n != 0);

    return true;
}

// Function to check if
// N is prime or not
function isPrime(n)
{
    if (n <= 1)
        return false;

    // Check for all factors
    for (var i = 2; i * i <= n; i++) {
        if (n % i == 0)
            return false;
    }
    return true;
}

// Function to check if n is prime
// in all the desired forms
function isAllPrime(n)
{
    return isPrime(n)
           && checkDigits(n);
}

// Driver Code

var N = 101;
if (isAllPrime(N))
    document.write("Yes");
else
    document.write("No");


</script>

Output:

Yes

Time Complexity: O(N)
Auxiliary Space: O(1)