> 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/5-longest-palindromic-substring.md).

# 5 Longest Palindromic Substring

## 5. [Longest Palindromic Substring](https://leetcode.com/problems/longest-palindromic-substring/description/)

## 1. Question

Given a string**s**, find the longest palindromic substring in**s**. You may assume that the maximum length of**s**is 1000.

**Example:**

```
Input: "babad"

Output: "bab"

Note: "aba" is also a valid answer.
```

**Example:**

```
Input: "cbbd"

Output: "bb"
```

## 2. Implementation

**(1) DP**

```java
class Solution {
    public String longestPalindrome(String s) {
        int n = s.length();
        String res = null;

        boolean[][] dp = new boolean[n][n];

        for (int j = 0; j < n; j++) {
            for (int i = j; i >= 0; i--) {
                if (s.charAt(i) == s.charAt(j) && (j - i <= 2 || dp[i + 1][j - 1])) {
                    dp[i][j] = true;
                }

                if (dp[i][j] && (res == null || j - i + 1 > res.length())) {
                    res = s.substring(i, j + 1);
                }
            }
        }
        return res;
    }
}
```

## 3. Time & Space Complexity

**DP:** 时间复杂度O(n^2), 空间复杂度O(n^2)