Largest palindrome which is product of two n-digit numbers

Difficulty Level : Medium
Last Updated : 25 Apr, 2018

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

Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

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++

// 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; 
} 

Java

// 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. 

Python3

# 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. 

C#

// 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. 

PHP

<?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. 
?> 

Output :

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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Related Articles

Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

C++

Java

Python3

C#

PHP