> For the complete documentation index, see [llms.txt](https://protegejj.gitbook.io/algorithm-practice/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://protegejj.gitbook.io/algorithm-practice/leetcode/dynamic-programming/longest-common-subsequence/516-longest-palindromic-subsequence.md).

# 516     Longest Palindromic Subsequence

## 516. [Longest Palindromic Subsequence](https://leetcode.com/problems/longest-palindromic-subsequence/description/)

## 1. Question

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".

## 2. Implementation

**(1) DP**

```java
class Solution {
    public int longestPalindromeSubseq(String s) {
        if (s == null || s.length() == 0) {
            return 0;
        }

        int n = s.length();
        String revS = new StringBuilder(s).reverse().toString();

        int[][] LCS = new int[n + 1][n + 1];

        for (int i = 0; i <= n; i++) {
            for (int j = 0; j <= n; j++) {
                if (i == 0 || j == 0) {
                    LCS[i][j] = 0;
                }
                else if (s.charAt(i - 1) == revS.charAt(j - 1)) {
                    LCS[i][j] = LCS[i - 1][j - 1] + 1;
                }
                else {
                    LCS[i][j] = Math.max(LCS[i - 1][j], LCS[i][j - 1]);
                }
            }
        }
        return LCS[n][n];
    }
}
```

## 3. Time & Space Complexity

**DP:** 时间复杂度O(n^2), 空间复杂度O(n^2)