[leetcode]516. Longest Palindromic Subsequence最大回文子序列

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".

* 子序列不一定连续,双指针，写出状态方程就好写了，二维数组res[sta][end]代表回文的开头和结尾坐标分别是sta和end的长度*/

public int longestPalindromeSubseq(String s) {
        int len = s.length();
        int[][] res = new int[len][len];
        return len(0,len-1,res,s);
    }
    public int len(int sta,int end,int[][] res,String s)
    {
　　　　//由于max函数中要求两个长度，两次求值过程中为了避免重复工作，可以直接利用res中已经存在的值，可以提高很多效率
        if (res[sta][end] != 0)
            return res[sta][end];
        if (sta > end)
            return 0;
        if (sta == end)
            return 1;
        //状态方程：
        //if[s(sta) == s(end)]:d[sta][end] = d[sta+1][end-1] + 2;
        //else[s(sta) != s(end)]:d[sta][end] = max[d[sta+1][end],d[sta][end-1]]
        if (s.charAt(sta) == s.charAt(end))
        {
            res[sta][end] = len(sta+1,end-1,res,s) + 2;
        }
        else
        {
            res[sta][end] = Math.max(len(sta+1,end,res,s),len(sta,end-1,res,s));
        }
        return res[sta][end];
    }