Strings

Expansion Logic: Longest Palindromic Substring

Mar 2026

8 min read

Standard DP for palindromes is O(N^2) space. Expanding around the center maintains the same time complexity while dropping the auxiliary space to O(1).

Implementation

java

class Solution {
    public String longestPalindrome(String s) {
        int start = 0, end = 0;
        for (int i = 0; i < s.length(); i++) {
            int len1 = expand(s, i, i);     // Odd length
            int len2 = expand(s, i, i + 1); // Even length
            int len = Math.max(len1, len2);
            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 left, int right) {
        while (left >= 0 && right < s.length() && s.charAt(left) == s.charAt(right)) {
            left--; right++;
        }
        return right - left - 1;
    }
}