Given a string s, find the longest palindromic subsequence's length in s. You may assume that the maximum length of s is 1000.
Example 1:
Input:
"bbbab"
Output:
4
One possible longest palindromic subsequence is "bbbb".

Example 2:
Input:
"cbbd"
Output:
2
One possible longest palindromic subsequence is "bb".
求最长回文子序列

动态规划问题，因为有“讨价还价”。
注意j从i+1开始。

class Solution {
    public int longestPalindromeSubseq(String s) {
        int n = s.length();
        int[][] dp = new int[n][n];
        for(int i=n-1;i>=0;i--){
            dp[i][i]=1;
            // j start from i+1
            for(int j=i+1;j<n;j++){
                if(s.charAt(i)==s.charAt(j)){
                    dp[i][j]=dp[i+1][j-1]+2;
                }else{
                    dp[i][j]=Math.max(dp[i+1][j],dp[i][j-1]);
                }
            }
        }
        return dp[0][n-1];
    }
}