5 Longest Palindromic Substring

5. Longest Palindromic Substring

1. Question

Given a strings, find the longest palindromic substring ins. You may assume that the maximum length ofsis 1000.

Example:

Input: "babad"

Output: "bab"

Note: "aba" is also a valid answer.

Example:

Input: "cbbd"

Output: "bb"

2. Implementation

(1) DP

思路: 我们用一个2维 boolean数组dp[i][j]判断substring s[i...j]是否为Palindrome, 如果dp[i][j]是true的话，比较当前得到的是palindrome的substring和res的长度大小，比res长度大的话则更新res

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)