Check if the first and last digit of the smallest number forms a prime

Given an array arr[] containing numbers from 0 to 9 only, the task is to form the minimum possible number from the given digits and then check if the first and last digit of the number thus created can be rearranged to form a prime number or not.

Examples:

Input: arr[]={2, 6, 4, 9} 
Output: Minimum number: 2469 
Prime number combinations: 29 
The first and last digits are 2 and 9 respectively. The combinations are 29 and 92. Only 29 is prime.

Input: arr[]={2, 6, 4, 3, 1, 7} 
Output: Minimum number: 123467 
Prime number combinations: 17 71 
The first and last digits are 1 and 7 respectively. The combinations are 17 and 71, and both are primes

Approach:

1. Create a hash of size 10 to store the number of occurrences of the digits in the given array into the hash table.
2. Print the digits the number of times they occur in descending order starting from the digit 0. It is similar to Smallest number by rearranging digits of a given number.
3. For the prime checking, check if the number formed using the first and last digits is prime or not. Do the same for its reverse.

Below is the implementation of above approach: 

C++

// C++ implementation of above approach
#include <bits/stdc++.h>
using namespace std;

// function to check prime
int isPrime(int n)
{
    int i, c = 0;
    for (i = 1; i < n / 2; i++) {
        if (n % i == 0)
            c++;
    }
    if (c == 1)
        return 1;
    else
        return 0;
}

// Function to generate smallest possible
// number with given digits
void findMinNum(int arr[], int n)
{
    // Declare a hash array of size 10
    // and initialize all the elements to zero
    int first = 0, last = 0, num, rev, i;
    int hash[10] = { 0 };

    // store the number of occurrences of the digits
    // in the given array into the hash table
    for (int i = 0; i < n; i++) {
        hash[arr[i]]++;
    }

    // Traverse the hash in ascending order
    // to print the required number
    cout << "Minimum number: ";
    for (int i = 0; i <= 9; i++) {

        // Print the number of times a digits occurs
        for (int j = 0; j < hash[i]; j++)
            cout << i;
    }

    cout << endl;

    // extracting the first digit
    for (i = 0; i <= 9; i++) {
        if (hash[i] != 0) {
            first = i;
            break;
        }
    }
    // extracting the last digit
    for (i = 9; i >= 0; i--) {
        if (hash[i] != 0) {
            last = i;
            break;
        }
    }

    num = first * 10 + last;
    rev = last * 10 + first;

    // printing the prime combinations
    cout << "Prime combinations: ";
    if (isPrime(num) && isPrime(rev))
        cout << num << " " << rev;

    else if (isPrime(num))
        cout << num;

    else if (isPrime(rev))
        cout << rev;

    else
        cout << "No combinations exist";
}

// Driver code
int main()
{
    int arr[] = { 1, 2, 4, 7, 8};
    findMinNum(arr, 5);

    return 0;
}

Java

// Java implementation of above approach

import java.io.*;

class SmallPrime
{

// function to check prime
static boolean isPrime(int n)
{
    int i, c = 0;
    for (i = 1; i < n / 2; i++)
    {
        if (n % i == 0)
            c++;
    }
    if (c == 1)
    {
        return true;
    }
    else
    {
        return false;
    }
}

// Function to generate smallest possible
// number with given digits
static void findMinNum(int arr[], int n)
{
    // Declare a hash array of size 10
    // and initialize all the elements to zero
    int first = 0, last = 0, num, rev, i;
    int hash[] = new int[10];

    // store the number of occurrences of the digits
    // in the given array into the hash table
    for ( i = 0; i < n; i++)
    {
        hash[arr[i]]++;
    }

    // Traverse the hash in ascending order
    // to print the required number
    System.out.print("Minimum number: ");
    for ( i = 0; i <= 9; i++)
    {

        // Print the number of times a digits occurs
        for (int j = 0; j < hash[i]; j++)
            System.out.print(i);

    }
    System.out.println();

    System.out.println();
    // extracting the first digit
    for (i = 0; i <= 9; i++)
    {
        if (hash[i] != 0)
        {
            first = i;
            break;
        }
    }
    // extracting the last digit
    for (i = 9; i >= 0; i--)
    {
        if (hash[i] != 0)
        {
            last = i;
            break;
        }
    }

    num = first * 10 + last;
    rev = last * 10 + first;

    // printing the prime combinations
    System.out.print( "Prime combinations: ");
    if (isPrime(num) && isPrime(rev))
    {
        System.out.println(num + " " + rev);
    }
    else if (isPrime(num))
    {
        System.out.println(num);
    }
    else if (isPrime(rev))
    {
        System.out.println(rev);
    }

    else
    {
        System.out.println("No combinations exist");
    }
}

// Driver code

    public static void main (String[] args)
    {
       SmallPrime smallprime = new SmallPrime();
       int arr[] = {1, 2, 4, 7, 8};
       smallprime.findMinNum(arr, 5);
    }
}

// This code has been contributed by inder_verma.

Python3

# Python3 implementation of above
# approach
import math as mt

# function to check prime
def isPrime(n):
    i, c = 0, 0
    for i in range(1, n // 2):
        if (n % i == 0):
            c += 1

    if (c == 1):
        return 1
    else:
        return 0

# Function to generate smallest possible
# number with given digits
def findMinNum(arr, n):

    # Declare a Hash array of size 10
    # and initialize all the elements to zero
    first, last = 0, 0
    Hash = [0 for i in range(10)]

    # store the number of occurrences of
    # the digits in the given array into
    # the Hash table
    for i in range(n):
        Hash[arr[i]] += 1

    # Traverse the Hash in ascending order
    # to print the required number
    print("Minimum number: ", end = "")
    for i in range(0, 10):

        # Print the number of times
        # a digits occurs
        for j in range(Hash[i]):
            print(i, end = "")

    print()

    # extracting the first digit
    for i in range(10):
        if (Hash[i] != 0):
            first = i
            break

    # extracting the last digit
    for i in range(9, -1, -1):
        if (Hash[i] != 0):
            last = i
            break

    num = first * 10 + last
    rev = last * 10 + first

    # printing the prime combinations
    print("Prime combinations: ", end = "")
    if (isPrime(num) and isPrime(rev)):
        print(num, " ", rev)
    elif (isPrime(num)):
        print(num)
    elif (isPrime(rev)):
        print(rev)
    else:
        print("No combinations exist")

# Driver code
arr = [ 1, 2, 4, 7, 8]
findMinNum(arr, 5)

# This code is contributed by
# Mohit kumar 29

C#

// C# implementation of above approach
using System;

class GFG
{

// function to check prime
static bool isPrime(int n)
{
    int i, c = 0;
    for (i = 1; i < n / 2; i++)
    {
        if (n % i == 0)
        {
            c++;
        }
    }
    if (c == 1)
    {
        return true;
    }
    else
    {
        return false;
    }
}

// Function to generate smallest
// possible number with given digits
static void findMinNum(int[] arr, int n)
{
    // Declare a hash array of
    // size 10 and initialize
    // all the elements to zero
    int first = 0, last = 0, num, rev, i;
    int[] hash = new int[10];

    // store the number of occurrences
    // of the digits in the given array
    // into the hash table
    for (i = 0; i < n; i++)
    {
        hash[arr[i]]++;
    }

    // Traverse the hash in ascending order
    // to print the required number
    Console.Write("Minimum number: ");
    for (i = 0; i <= 9; i++)
    {

        // Print the number of times
        // a digits occurs
        for (int j = 0; j < hash[i]; j++)
        {
            Console.Write(i);
        }

    }
    Console.WriteLine();

    Console.WriteLine();

    // extracting the first digit
    for (i = 0; i <= 9; i++)
    {
        if (hash[i] != 0)
        {
            first = i;
            break;
        }
    }

    // extracting the last digit
    for (i = 9; i >= 0; i--)
    {
        if (hash[i] != 0)
        {
            last = i;
            break;
        }
    }

    num = first * 10 + last;
    rev = last * 10 + first;

    // printing the prime combinations
    Console.Write("Prime combinations: ");
    if (isPrime(num) && isPrime(rev))
    {
        Console.WriteLine(num + " " + rev);
    }
    else if (isPrime(num))
    {
        Console.WriteLine(num);
    }
    else if (isPrime(rev))
    {
        Console.WriteLine(rev);
    }
    else
    {
        Console.WriteLine("No combinations exist");
    }
}

// Driver code
public static void Main()
{
    int[] arr = {1, 2, 4, 7, 8};
    findMinNum(arr, 5);
}
}

// This code is contributed
// by PrinciRaj1992

PHP

<?php
// PHP implementation of above approach

// function to check prime
function isPrime($n)
{
    $c = 0;
    for ($i = 1; $i < $n / 2; $i++)
    {
        if ($n % $i == 0)
            $c++;
    }
    if ($c == 1)
        return 1;
    else
        return 0;
}

// Function to generate smallest possible
// number with given digits
function findMinNum($arr, $n)
{
    // Declare a hash array of size 10
    // and initialize all the elements to zero
    $first = 0; $last = 0;
    $num; $rev ; $i;
    $hash = array_fill(0, 20, 0);

    // store the number of occurrences of
    // the digits in the given array into
    // the hash table
    for ($i = 0; $i < $n; $i++)
    {
        $hash[$arr[$i]]++;
    }

    // Traverse the hash in ascending order
    // to print the required number
    echo "Minimum number: ";
    for ( $i = 0; $i <= 9; $i++)
    {

        // Print the number of times a
        // digits occurs
        for ($j = 0; $j < $hash[$i]; $j++)
            echo $i;
    }

    // extracting the first digit
    for ($i = 0; $i <= 9; $i++)
    {
        if ($hash[$i] != 0)
        {
            $first = $i;
            break;
        }
    }

    // extracting the last digit
    for ($i = 9; $i >= 0; $i--)
    {
        if ($hash[$i] != 0)
        {
            $last = $i;
            break;
        }
    }

    $num = $first * 10 + $last;
    $rev = $last * 10 + $first;

    // printing the prime combinations
    echo "\nPrime combinations: ";
    if (isPrime($num) && isPrime($rev))
        echo $num. " " . $rev;

    else if (isPrime($num))
        echo $num;

    else if (isPrime($rev))
        echo $rev;

    else
        echo "No combinations exist";
}

// Driver Code
$arr = array(1, 2, 4, 7, 8);
findMinNum($arr, 5);

// This code is contributed
// by Rajput-Ji
?>

Javascript

<script>
      // JavaScript implementation of above approach
      // function to check prime
      function isPrime(n) {
        var i,
          c = 0;
        for (i = 1; i < n / 2; i++) {
          if (n % i == 0) c++;
        }
        if (c == 1) return 1;
        else return 0;
      }

      // Function to generate smallest possible
      // number with given digits
      function findMinNum(arr, n) {
        // Declare a hash array of size 10
        // and initialize all the elements to zero
        var first = 0,
          last = 0,
          num,
          rev,
          i;
        var hash = new Array(10).fill(0);

        // store the number of occurrences of the digits
        // in the given array into the hash table
        for (var i = 0; i < n; i++) {
          hash[arr[i]]++;
        }

        // Traverse the hash in ascending order
        // to print the required number
        document.write("Minimum number: ");
        for (var i = 0; i <= 9; i++) {
          // Print the number of times a digits occurs
          for (var j = 0; j < hash[i]; j++) document.write(i);
        }

        document.write("<br>");

        // extracting the first digit
        for (i = 0; i <= 9; i++) {
          if (hash[i] != 0) {
            first = i;
            break;
          }
        }
        // extracting the last digit
        for (i = 9; i >= 0; i--) {
          if (hash[i] != 0) {
            last = i;
            break;
          }
        }

        num = first * 10 + last;
        rev = last * 10 + first;

        // printing the prime combinations
        document.write("Prime combinations: ");
        if (isPrime(num) && isPrime(rev)) document.write(num + " " + rev);
        else if (isPrime(num)) document.write(num);
        else if (isPrime(rev)) document.write(rev);
        else document.write("No combinations exist");
      }

      // Driver code
      var arr = [1, 2, 4, 7, 8];
      findMinNum(arr, 5);
    </script>

Output

Minimum number: 12478
Prime combinations: No combinations exist

Time Complexity: O(n),The time complexity of this algorithm is O(n) where n is the size of the array. 
Space Complexity: O(1),The space complexity is O(1) since no extra space is used.