 # [LeetCode/LintCode] Largest Palindrome Product

### Problem

Find the largest palindrome made from the product of two n-digit numbers.

Since the result could be very large, you should return the largest palindrome mod 1337.

### Example

Input: 2
Output: 987
Explanation: 99 x 91 = 9009, 9009 % 1337 = 987

### Solution

``````public class Solution {
/**
* @param n: the number of digit
* @return: the largest palindrome mod 1337
*/
public int largestPalindrome(int n) {
// when n == 1, largest palindrome would be single-digit
if (n == 1) return 9;

// get the maximum and the minimum factors
long maxFactor = (long)Math.pow(10, n)-1;
long minFactor = (long)Math.pow(10, n-1);

// get the largest product first, then use the first half to create palindrome
long maxProduct = (long)maxFactor * (long)maxFactor;
long maxHalf = maxProduct / (long)Math.pow(10, n);

// initialize result palindrome to 0, and set the flag to check if result found and end the while loop
long palindrome = 0;
boolean palindromeFound = false;

while (!palindromeFound) {
// generate the latest largest palindrome in each cycle
palindrome = generatePalindrome(maxHalf);

for (long i = maxFactor; i >= minFactor; i--) {
// the generated palindrome cannot be larger than maxFactor * maxFactor
if (palindrome / i > i || palindrome / maxFactor > maxFactor) {
break;
}

if (palindrome % i == 0) {
palindromeFound = true;
break;
}
}
//when for loop ends, decrease maxHalf by 1 to generate the next palindrome
maxHalf--;
}

return (int)(palindrome % 1337);
}

public long generatePalindrome(long num) {
String str = String.valueOf(num) + new StringBuilder().append(num).reverse().toString();
return Long.parseLong(str);
}
}``````