Largest palindrome which is product of two n-digit numbers

Given a value n, find out the largest palindrome number which is product of two n digit numbers.

Examples :

Input  : n = 2
Output : 9009 
9009 is the largest number which is product of two 
2-digit numbers. 9009 = 91*99.

Input : n = 3
Output : 906609

Below are steps to find the required number.
1) Find a lower limit on n digit numbers. For example, for n = 2, lower_limit is 10.
2) Find an upper limit on n digit numbers. For example, for n = 2, upper_limit is 99.
3) Consider all pairs of numbers where ever number lies in range [lower_limit, upper_limit]

Below is the implementation of above steps.

C++

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// C++ problem to find out the 
// largest palindrome number which
// is product of two n digit numbers
#include <iostream>
using namespace std;
  
// Function to calculate largest 
// palindrome which is product of
// two n-digits numbers 
int larrgestPalindrome(int n)
{
    int upper_limit = 0;
  
    // Loop to calculate upper bound
    // (largest number of n-digit)
    for (int i = 1; i <= n; i++)
    {
        upper_limit *= 10;
        upper_limit += 9;
    }
  
    // largest number of n-1 digit. 
    // One plus this number is lower
    // limit which is product of two numbers.
    int lower_limit = 1 + upper_limit / 10;
  
    // Initialize result
    int max_product = 0; 
    for (int i = upper_limit; 
             i >= lower_limit; 
             i--)
    {
        for (int j = i; j >= lower_limit; j--)
        {
            // calculating product of
            // two n-digit numbers
            int product = i * j;
            if (product < max_product)
                break;
            int number = product;
            int reverse = 0;
  
            // calculating reverse of 
            // product to check whether
            // it is palindrome or not
            while (number != 0)
            {
                reverse = reverse * 10 + 
                          number % 10;
                number /= 10;
            }
  
            // update new product if exist 
            // and if greater than previous one 
            if (product == reverse && 
                product > max_product)
                  
                max_product = product;
        }
    }
    return max_product;
}
  
// Driver code
int main()
{
    int n = 2;
    cout << larrgestPalindrome(n);
    return 0;
}

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Java

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// Java problem to find out the
// largest palindrome number 
// which is product of two 
// n digit numbers.
  
class GFG
{
    // Function to calculate largest
    // palindrome which isproduct of
    // two n-digits numbers 
    static int larrgestPalindrome(int n)
    {
        int upper_limit = 0;
      
        // Loop to calculate upper bound
        // (largest number    of n-digit)
        for (int i=1; i<=n; i++)
        {
            upper_limit *= 10;
            upper_limit += 9;
        }
      
        // largest number of n-1 digit. 
        // One plus this number 
        // is lower limit which is 
        // product of two numbers.
        int lower_limit = 1 + upper_limit / 10;
      
        // Initialize result
        int max_product = 0;
          
        for (int i = upper_limit; i >= lower_limit; i--)
        {
            for (int j = i; j >= lower_limit; j--)
            {
                // calculating product of two 
                // n-digit numbers
                int product = i * j;
                if (product < max_product)
                    break;
                int number = product;
                int reverse = 0;
      
                // calculating reverse of product
                // to check whether it is 
                // palindrome or not
                while (number != 0)
                {
                    reverse = reverse * 10 + number % 10;
                    number /= 10;
                }
      
                // update new product if exist and if
                // greater than previous one
                if (product == reverse && product > max_product)
                    max_product = product;
            }
        }
        return max_product;
    }
      
    // Driver code
    public static void main (String[] args)
    {
      
        int n = 2;
        System.out.print(larrgestPalindrome(n));
    }
}
  
// This code is contributed by Anant Agarwal.

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Python3

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# Python problem to find
# out the largest palindrome
# number which is product of
# two n digit numbers.
  
# Function to calculate largest
# palindrome which is
#  product of two n-digits numbers
     
def larrgestPalindrome(n):
  
    upper_limit = 0
   
    # Loop to calculate upper
    # bound(largest number
    # of n-digit)
    for i in range(1, n+1):
      
        upper_limit =upper_limit * 10
        upper_limit =upper_limit + 9
      
   
    # largest number of n-1 digit.
    # One plus this number 
    # is lower limit which is
    # product of two numbers.
    lower_limit = 1 + upper_limit//10
   
    max_product = 0 # Initialize result
    for i in range(upper_limit,lower_limit-1, -1):
      
        for j in range(i,lower_limit-1,-1):
          
            # calculating product of
            # two n-digit numbers
            product = i * j
            if (product < max_product):
                break
            number = product
            reverse = 0
   
            # calculating reverse of
            # product to check
            # whether it is palindrome or not
            while (number != 0):
              
                reverse = reverse * 10 + number % 10
                number =number // 10
              
   
             # update new product if exist and if
             # greater than previous one
            if (product == reverse and product > max_product):
                max_product = product
          
      
    return max_product
  
# Driver code
  
n = 2
print(larrgestPalindrome(n))
  
# This code is contributed
# by Anant Agarwal.

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C#

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// C# problem to find out the
// largest palindrome number 
// which is product of two 
// n digit numbers.
using System;
  
class GFG
{
    // Function to calculate largest
    // palindrome which isproduct of
    // two n-digits numbers 
    static int larrgestPalindrome(int n)
    {
        int upper_limit = 0;
      
        // Loop to calculate upper bound
        // (largest number of n-digit)
        for (int i = 1; i <= n; i++)
        {
            upper_limit *= 10;
            upper_limit += 9;
        }
      
        // largest number of n-1 digit. 
        // One plus this number 
        // is lower limit which is 
        // product of two numbers.
        int lower_limit = 1 + upper_limit / 10;
      
        // Initialize result
        int max_product = 0;
          
        for (int i = upper_limit; i >= lower_limit; i--)
        {
            for (int j = i; j >= lower_limit; j--)
            {
                // calculating product of two 
                // n-digit numbers
                int product = i * j;
                if (product < max_product)
                    break;
                int number = product;
                int reverse = 0;
      
                // calculating reverse of product
                // to check whether it is 
                // palindrome or not
                while (number != 0)
                {
                    reverse = reverse * 10 + number % 10;
                    number /= 10;
                }
      
                // update new product if exist and if
                // greater than previous one
                if (product == reverse && product > max_product)
                    max_product = product;
            }
        }
        return max_product;
    }
      
    // Driver code
    public static void Main ()
    {
      
        int n = 2;
        Console.Write(larrgestPalindrome(n));
    }
}
  
// This code is contributed by nitin mittal.

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PHP

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<?php
// PHP problem to find out 
// the largest palindrome 
// number which is product 
// of two n digit numbers
  
// Function to calculate 
// largest palindrome which 
// is product of two n-digit numbers
function larrgestPalindrome($n)
{
    $upper_limit = 0;
  
    // Loop to calculate upper bound 
    // (largest number of n-digit) 
    for ($i = 1; $i <= $n; $i++)
    {
        $upper_limit *= 10;
        $upper_limit += 9;
    }
  
    // largest number of n-1 digit
    // One plus this number 
    // is lower limit which is 
    // product of two numbers.
    $lower_limit = 1 + (int)($upper_limit / 10);
  
    // Initialize result
    $max_product = 0; 
    for ($i = $upper_limit
         $i >= $lower_limit
         $i--)
    {
        for ($j = $i
             $j >= $lower_limit
             $j--)
        {
            // calculating product of
            // two n-digit numbers
            $product = $i * $j;
            if ($product < $max_product)
                break;
            $number = $product;
            $reverse = 0;
  
            // calculating reverse of 
            // product to check whether
            // it is palindrome or not 
            while ($number != 0)
            {
                $reverse = $reverse * 10 + 
                           $number % 10;
                $number = (int)($number / 10);
            }
  
            // update new product if exist 
            // and if greater than previous one
            if ($product == $reverse && 
                $product > $max_product)
                  
                $max_product = $product;
        }
    }
    return $max_product;
}
  
// Driver code
$n = 2;
echo(larrgestPalindrome($n));
  
// This code is contributed by Ajit.
?>

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Output :

9009

The approach used in this post is simple and straightforward. Please comment if you find a better approach.

This article is contributed by Shivam Pradhan(anuj_charm). If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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Improved By : nitin mittal, jit_t



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