In this problem, you have to calculate the largest palindrome number that can be made from​ the product of two n-digit integers.



# Algorithm

* Calculate the upper and lower bound (i.e., for n = 2, lowerBound = 10 and upperBound = 99 )
* Search for the highest product palindrome in reverse order (i.e., start a loop from 99 * 99 )
* Check whether or not each product is a palindrome.

# Code

# Python Implementation

# function
def PalindromeProductNumber(n): 

	upperBound = 0
	lowerBound = 0
    # Calculating upper bound
	for i in range(1, n+1): 
	
		upperBound =upperBound * 10
		upperBound =upperBound + 9
	
	# Calculating lower bound
	lowerBound = 1 + lowerBound//10

	max_prdt = 0 
	for i in range(upperBound,lowerBound-1, -1): 
		for j in range(i,lowerBound-1,-1): 
		    # calculating products in a range
			product = i * j 
			if (product < max_prdt): 
				break
			number = product 
			reverse_num = 0
			# checking whether a number is palindrome
			while (number != 0): 
			
				reverse_num = reverse_num * 10 + number % 10
				number =number // 10
			# updating product
			if (product == reverse_num and product > max_prdt): 
				max_prdt = product 
		
	
	return max_prdt 


n = 2
print(PalindromeProductNumber(n)) 


Python

// Java Implementation
class Main 
{ 
    // function
	static int PalindromeProductNumber(int n) 
	{ 
		int upperBound = 0; 
	    int lowerBound = 0;
		// calculating upper bound
		for (int i=1; i<=n; i++) 
		{ 
			upperBound *= 10; 
			upperBound += 9; 
		} 
		// calculating lower bound
		lowerBound = 1 + lowerBound / 10; 
	 
		int max_prdt = 0; 
		
		for (int i = upperBound; i >= lowerBound; i--) 
		{ 
			for (int j = i; j >= lowerBound; j--) 
			{ 
				// calculating product of two numbers
				int product = i * j; 
				if (product < max_prdt) 
					break; 
				int number = product; 
				int reverse_num = 0; 
				// checking palindrome
				while (number != 0) 
				{ 
					reverse_num = reverse_num * 10 + number % 10; 
					number /= 10; 
				} 
				// updating the max_prdt 
				if (product == reverse_num && product > max_prdt) 
					max_prdt = product; 
			} 
		} 
		return max_prdt; 
	} 
	
	public static void main (String[] arguments) 
	{ 
	
		int n = 2; 
		System.out.print(PalindromeProductNumber(n)); 
	} 
} 


Java

Project Euler problem 4: Largest palindrome product

Calculate the largest palindrome from the product of two n-digit integers by checking products in descending order.