LeetCode Largest Palindrome Product

原题链接在这里：https://leetcode.com/problems/largest-palindrome-product/description/

题目：

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

Note:

The range of n is [1,8].

题解：

当n=2时，数字可选区间就是(9, 99]. 最大的product 就是 99*99 = 9801. 最大的位数是2n 肯定是个偶数. 

取前一半firstHalf '98', 再拼接'98'的reverse '89'组成新的palindrome '9889'. 然后i在(9,99]之间挨个试palindrome % i == 0.

试不出来firstHalf--, 变'97'重来.

Time Complexity: O((upperBound*upperBound)/10^n  * (upperBound*lowerBound)), upperBound = 10^n, lowerBound = upperBound/10.

Space: O(1).

AC Java:

class Solution {
    public int largestPalindrome(int n) {
        if(n == 1){
            return 9;
        }
        
        int upperBound = (int)Math.pow(10, n) - 1;
        int lowerBound = upperBound/10;
        long max = (long)upperBound * (long)upperBound;
        
        int firstHalf = (int)(max/(long)Math.pow(10,n));
        boolean palFound = false;
        long pal = 0;
        while(!palFound){
            pal = createPal(firstHalf);
            
            for(long i = upperBound;; i--){
                if(pal/i>max || i*i<pal){
                    break;
                }
                if(pal%i == 0){
                    palFound = true;
                    break;
                }
            }
            
            firstHalf--;
        }
        return (int)(pal%1337);
    }
    
    private long createPal(int n){
        String s = n + new StringBuilder().append(n).reverse().toString();
        return Long.valueOf(s);
    }
}