Thursday, July 28, 2016

Palindromic Primes - GeeksforGeeks


Palindromic Primes - GeeksforGeeks
A palindromic prime (sometimes called a palprime) is a prime number that is also a palindromic number.
Given a number n, print all palindromic primes smaller than or equal to n. For example, If n is 10, the output should be "2, 3, 5, 7′. And if n is 20, the output should be "2, 3, 5, 7, 11′.

bool isPalUtil(int num, int* dupNum)
{
    // Base case (needed for recursion termination):
    // This statement/ mainly compares the first
    // digit with the last digit
    if (oneDigit(num))
        return (num == (*dupNum) % 10);
 
    // This is the key line in this method. Note
    // that all recursive/ calls have a separate
    // copy of num, but they all share same copy
    // of *dupNum. We divide num while moving up
    // the recursion tree
    if (!isPalUtil(num/10, dupNum))
        return false;
 
    // The following statements are executed when
    // we move up the recursion call tree
    *dupNum /= 10;
 
    // At this point, if num%10 contains i'th
    // digit from beiginning, then (*dupNum)%10
    // contains i'th digit from end
    return (num % 10 == (*dupNum) % 10);
}
 
// The main function that uses recursive function
// isPalUtil() to find out whether num is palindrome
// or not
int isPal(int num)
{
    // If num is negative, make it positive
    if (num < 0)
       num = -num;
 
    // Create a separate copy of num, so that
    // modifications made to address dupNum don't
    // change the input number.
    int *dupNum = new int(num); // *dupNum = num
 
    return isPalUtil(num, dupNum);
}
 
// Function to generate all primes and checking
// whether number is palindromic or not
void printPalPrimesLessThanN(int n)
{
    // Create a boolean array "prime[0..n]" and
    // initialize all entries it as true. A value
    // in prime[i] will finally be false if i is
    // Not a prime, else true.
    bool prime[n+1];
    memset(prime, true, sizeof(prime));
 
    for (int p=2; p*p<=n; p++)
    {
        // If prime[p] is not changed, then it is
        // a prime
        if (prime[p] == true)
        {
            // Update all multiples of p
            for (int i=p*2; i<=n; i += p)
                prime[i] = false;
        }
    }
 
    // Print all palindromic prime numbers
    for (int p=2; p<=n; p++)
 
       // checking whether the given number is
       // prime palindromic or not
       if (prime[p] && isPal(p))
          cout << p << " ";
}
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