Prime points (Points that split a number into two primes)

Given a n-digit number. Prime point is the index of the digit whose left and right side numbers 
are prime. Print all the prime points of the number. If no prime point exists print -1.

Examples:

Input : 2317
Output : 1 2
Explanation : Left and right side numbers of index 
              point 1 are 2 and 17 respectively and
              both are primes. Left and right side 
              numbers of index point 2 are 23 and 7 
              respectively and both are prime. 

Input : 2418
Output : -1
Explanation : No index point has both the left 
              and right side numbers as prime.

Note: First and last index can never be a prime 
      point as they do not have left and right 
      side numbers pair.

Algorithm

   Count number of digits of the given number, n.
   If count == 1 || count == 2
       print "Not Possible"      
   Else 
   {
      For index points = 1 to (count - 1)
      {
         Calculate left number(L) and right number(R)
             If both L and R are prime
             print index point i
      }
   }
      
How to find L and R for an index point 'i'?
   L = n / (10(count-i))
   R = n % (10(count-i-1))

Prime number checking is based on optimized school method

C++

// C++ program to print all prime points
#include <bits/stdc++.h>
using namespace std;

// Function to count number of digits
int countDigits(int n)
{
    int count = 0;
    while (n > 0)
    {
        count++;
        n = n/10;
    }
    return count;
}

// Function to check whether a number is
// prime or not. Returns 0 if prime else -1
int checkPrime(int n)
{
    // Corner cases
    if (n <= 1)
        return -1;
    if (n <= 3)
        return 0;

    // This is checked so that we can skip
    // middle five numbers in below loop
    if (n%2 == 0 || n%3 == 0)
        return -1;

    for (int i=5; i*i<=n; i=i+6)
        if (n%i == 0 || n%(i+2) == 0)
            return -1;

    return 0;
}

// Function to print prime points
void printPrimePoints(int n)
{
    // counting digits
    int count = countDigits(n);

    // As single and double digit numbers do not
    // have left and right number pairs
    if (count==1 || count==2)
    {
        cout << "-1";
        return;
    }

    // Finding all left and right pairs. Printing
    // the prime points accordingly. Discarding
    // first and last index point
    bool found = false;
    for (int i=1; i<(count-1); i++)
    {
        // Calculating left number
        int left = n / ((int)pow(10,count-i));

        // Calculating right number
        int right = n % ((int)pow(10,count-i-1));

        // Prime point condition
        if (checkPrime(left) == 0 &&
            checkPrime(right) == 0)
        {
            cout << i << " ";
            found = true;
        }
    }

    // No prime point found
    if (found == false)
        cout << "-1";
}

// Driver Program
int main()
{
    int n = 2317;
    printPrimePoints(n);
    return 0;
}

Java

// Java program to print
// all prime points
import java.io.*;

class GFG
{
// Function to count
// number of digits
static int countDigits(int n)
{
    int count = 0;
    while (n > 0)
    {
        count++;
        n = n / 10;
    }
    return count;
}

// Function to check whether
// a number is prime or not.
// Returns 0 if prime else -1
static int checkPrime(int n)
{
    // Corner cases
    if (n <= 1)
        return -1;
    if (n <= 3)
        return 0;

    // This is checked so that
    // we can skip middle five
    // numbers in below loop
    if (n % 2 == 0 || n % 3 == 0)
        return -1;

    for (int i = 5;
             i * i <= n; i = i + 6)
        if (n % i == 0 ||
            n % (i + 2) == 0)
            return -1;

    return 0;
}

// Function to print
// prime points
static void printPrimePoints(int n)
{
    // counting digits
    int count = countDigits(n);

    // As single and double
    // digit numbers do not
    // have left and right
    // number pairs
    if (count == 1 || count == 2)
    {
        System.out.print("-1");
        return;
    }

    // Finding all left and right
    // pairs. Printing the prime
    // points accordingly. Discarding
    // first and last index point
    boolean found = false;
    for (int i = 1; i < (count - 1); i++)
    {
        // Calculating left number
        int left = n / ((int)Math.pow(10,
                                  count - i));

        // Calculating right number
        int right = n % ((int)Math.pow(10,
                                   count - i - 1));

        // Prime point condition
        if (checkPrime(left) == 0 &&
            checkPrime(right) == 0)
        {
                System.out.print(i + " ");
            found = true;
        }
    }

    // No prime point found
    if (found == false)
            System.out.print("-1");
}

// Driver Code
public static void main (String[] args)
{
    int n = 2317;
    printPrimePoints(n);
}
}

// This code is contributed by ajit

Python3

# python3 program to print all prime points

# Function to count number of digits
def countDigits(n):
    count = 0
    while (n > 0):
        count+=1
        n = n//10

    return count

#Function to check whether a number is
# prime or not. Returns 0 if prime else -1
def checkPrime(n):
    # Corner cases
    if (n <= 1):
        return -1
    if (n <= 3):
        return 0

    # This is checked so that we can skip
    # middle five numbers in below loop
    if (n%2 == 0 or n%3 == 0):
        return -1

    i=5
    while i*i<=n:
        if (n%i == 0 or n%(i+2) == 0):
            return -1
        i+=6

    return 0

# Function to print prime points
def printPrimePoints(n):

    # counting digits
    count = countDigits(n)

    # As single and double digit numbers do not
    # have left and right number pairs
    if (count==1 or count==2):

        print ("-1")
        return


    # Finding all left and right pairs. Printing
    # the prime points accordingly. Discarding
    # first and last index point
    found = False
    for i in range(1,(count-1)):
        #Calculating left number
        left = n //(pow(10,count-i))

        #Calculating right number
        right = n % (pow(10,count-i-1))

        # Prime point condition
        if (checkPrime(left) == 0 and
            checkPrime(right) == 0):

            print (i ,end=" ")
            found = True

    # No prime point found
    if (found == False):
        print ("-1")

# Driver Program
if __name__ == "__main__":

    n = 2317
    printPrimePoints(n)

C#

// C# program to print
// all prime points
using System;

class GFG
{

// Function to count
// number of digits
static int countDigits(int n)
{
    int count = 0;
    while (n > 0)
    {
        count++;
        n = n / 10;
    }
    return count;
}

// Function to check whether
// a number is prime or not.
// Returns 0 if prime else -1
static int checkPrime(int n)
{
    // Corner cases
    if (n <= 1)
        return -1;
    if (n <= 3)
        return 0;

    // This is checked so that
    // we can skip middle five
    // numbers in below loop
    if (n % 2 == 0 ||
        n % 3 == 0)
        return -1;

    for (int i = 5;
             i * i <= n; i = i + 6)
        if (n % i == 0 ||
            n % (i + 2) == 0)
            return -1;

    return 0;
}

// Function to print
// prime points
static void printPrimePoints(int n)
{
    // counting digits
    int count = countDigits(n);

    // As single and double
    // digit numbers do not
    // have left and right
    // number pairs
    if (count == 1 ||
        count == 2)
    {
        Console.Write("-1");
        return;
    }

    // Finding all left and right
    // pairs. Printing the prime
    // points accordingly. Discarding
    // first and last index point
    bool found = false;
    for (int i = 1;
             i < (count - 1); i++)
    {
        // Calculating left number
        int left = n / ((int)Math.Pow(10,
                             count - i));

        // Calculating right number
        int right = n % ((int)Math.Pow(10,
                              count - i - 1));

        // Prime point condition
        if (checkPrime(left) == 0 &&
            checkPrime(right) == 0)
        {
            Console.Write(i + " ");
            found = true;
        }
    }

    // No prime point found
    if (found == false)
            Console.Write("-1");
}

// Driver Code
static public void Main ()
{
    int n = 2317;
    printPrimePoints(n);
}
}

// This code is contributed
// by akt_mit

PHP

<?php
// PHP program to print all prime points

// Function to count number of digits
function countDigits($n)
{
    $count = 0;
    while ($n > 0)
    {
        $count++;
        $n = (int)($n / 10);
    }
    return $count;
}

// Function to check whether a
// number is prime or not.
// Returns 0 if prime else -1
function checkPrime($n)
{
    // Corner cases
    if ($n <= 1)
        return -1;
    if ($n <= 3)
        return 0;

    // This is checked so that we
    // can skip middle five numbers
    // in below loop
    if ($n % 2 == 0 || $n % 3 == 0)
        return -1;

    for ($i = 5; $i * $i <= $n; $i = $i + 6)
        if ($n % $i == 0 || $n % ($i + 2) == 0)
            return -1;

    return 0;
}

// Function to print prime points
function printPrimePoints($n)
{
    // counting digits
    $count = countDigits($n);

    // As single and double digit
    // numbers do not have left
    // and right number pairs
    if ($count == 1 || $count == 2)
    {
        echo "-1";
        return;
    }

    // Finding all left and right pairs.
    // Printing the prime points accordingly.
    // Discarding first and last index point
    $found = false;
    for ($i = 1; $i < ($count - 1); $i++)
    {
        // Calculating left number
        $left = (int)($n /
               ((int)pow(10, $count - $i)));

        // Calculating right number
        $right = $n % ((int)pow(10, $count - $i - 1));

        // Prime point condition
        if (checkPrime($left) == 0 &&
            checkPrime($right) == 0)
        {
            echo $i , " ";
            $found = true;
        }
    }

    // No prime point found
    if ($found == false)
        echo "-1";
}

// Driver Code
$n = 2317;
printPrimePoints($n);

// This code is contributed by ajit
?>

Javascript

<script>

// Javascript program to print
// all prime points

// Function to count
// number of digits
function countDigits(n)
{
    let count = 0;

    while (n > 0)
    {
        count++;
        n = Math.floor(n / 10);
    }
    return count;
}

// Function to check whether
// a number is prime or not.
// Returns 0 if prime else -1
function checkPrime(n)
{

    // Corner cases
    if (n <= 1)
        return -1;
    if (n <= 3)
        return 0;

    // This is checked so that
    // we can skip middle five
    // numbers in below loop
    if (n % 2 == 0 || n % 3 == 0)
        return -1;

    for(let i = 5;
            i * i <= n; i = i + 6)
        if (n % i == 0 ||
            n % (i + 2) == 0)
            return -1;

    return 0;
}

// Function to print
// prime points
function printPrimePoints(n)
{

    // Counting digits
    let count = countDigits(n);

    // As single and double
    // digit numbers do not
    // have left and right
    // number pairs
    if (count == 1 || count == 2)
    {
        document.write("-1");
        return;
    }

    // Finding all left and right
    // pairs. Printing the prime
    // points accordingly. Discarding
    // first and last index point
    let found = false;
    for(let i = 1; i < (count - 1); i++)
    {

        // Calculating left number
        let left = Math.floor(
            n / (Math.pow(10, count - i)));

        // Calculating right number
        let right = n % (Math.pow(
            10, count - i - 1));

        // Prime point condition
        if (checkPrime(left) == 0 &&
            checkPrime(right) == 0)
        {
            document.write(i + " ");
            found = true;
        }
    }

    // No prime point found
    if (found == false)
        document.write("-1");
}

// Driver Code
let n = 2317;

printPrimePoints(n);

// This code is contributed by avanitrachhadiya2155

</script>

Output:

1 2

Time complexity: O(log₁₀n*sqrt(n))
Auxiliary space: O(1)

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