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);
     }
 }