Longest Palindromic Substring

Problem

Return the longest palindromic substring of s.

Constraints

• 1 ≤ s.length ≤ 1000

Approach — Dynamic Programming

This is a Dynamic Programming problem. The idea: break the problem into overlapping subproblems and build the answer up, caching results so nothing is recomputed. Work through the reference code below line by line, then re-derive it yourself in the editor — that's how the pattern sticks.

Complexity: O(n) to O(n²) time.

Solution code

Python

class Solution:
    def longestPalindrome(self, s):
        if not s:
            return ''
        start, end = 0, 0
        def expand(l, r):
            while l >= 0 and r < len(s) and s[l] == s[r]:
                l -= 1; r += 1
            return l + 1, r - 1
        for i in range(len(s)):
            for l, r in (expand(i, i), expand(i, i+1)):
                if r - l > end - start:
                    start, end = l, r
        return s[start:end+1]

Java

class Solution {
    public String longestPalindrome(String s) {
        int start = 0, end = 0;
        for (int i = 0; i < s.length(); i++) {
            int a = expand(s, i, i), b = expand(s, i, i + 1);
            int len = Math.max(a, b);
            if (len > end - start) { start = i - (len - 1) / 2; end = i + len / 2; }
        }
        return s.substring(start, end + 1);
    }
    private int expand(String s, int l, int r) {
        while (l >= 0 && r < s.length() && s.charAt(l) == s.charAt(r)) { l--; r++; }
        return r - l - 1;
    }
}

Practice it

Reading a solution isn't the same as being able to write it under pressure. Open this problem in the in-browser editor, hide the solution, and solve it from scratch — your code runs against real test cases instantly.