题目描述：

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:

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"bbbab"

Output:

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One possible longest palindromic subsequence is “bbbb”.

Example 2: Input:

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"cbbd"

Output:

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One possible longest palindromic subsequence is “bb”.

二维DP。dp[i][j]表示s[i]到s[j]（含两端）的字符串中最长的回文子串。状态转移方程如下：

  1. i==j，dp[i][j]=1
  2. s[i]==s[j-1]，dp[i][j]=2
  3. s[i]==s[j]， dp[i][j]=dp[i+1][j-1]+2
  4. s[i]!=s[j]，dp[i][j]=max(dp[i+1][j], dp[i][j-1])
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class Solution {
public:
    int longestPalindromeSubseq(string s) {
        vector<vector<int>> dp(s.length(), vector<int>(s.length(), 0));
        if (s.empty()) return 0;
        int maxLen = 1;
        for (int i = 0; i < s.length(); i++) {
            dp[i][i] = 1;
        }
        for (int i = s.length() - 1; i >= 0; i--) {
            for (int j = i + 1; j < s.length(); j++) {
                if (s[i] == s[j]) {
                    if (i + 1 == j) dp[i][j] = 2;
                    else dp[i][j] = dp[i + 1][j - 1] + 2;
                }
                else {
                    dp[i][j] = max(dp[i + 1][j], dp[i][j - 1]);
                }
            }
        }
        return dp[0][s.length() - 1];
    }
};