Longest Palindrome in a String

Time: O(n^2)

Space: O(1)

Intuition

Expand around each center. For each character (and each gap between characters), expand outward as long as characters match. Track the maximum expansion. O(nÂ²) time, O(1) space.

Algorithm

1For each center (2n-1 centers for odd + even): expand while valid.
2ExpandAroundCenter(left, right): while left>=0 and right<n and s[left]==s[right]: left--, right++.
3Track max length and start index.

Example Walkthrough

Input: s = "babad"

1.Center at i=1("a"): expand â†’ "bab"(len=3). Center at i=2("b"): expand â†’ "aba"(len=3).
2.Return "bab" (first found).

Output: "bab"

Common Pitfalls

•Check both odd (single-char center) and even (between-char center) palindromes.

Longest Palindrome in a String.java

Java

// Approach: Expand-around-center for each character and each pair. Track max palindrome found.
// Time: O(n^2) Space: O(1)
class Solution {
    static String longestPalindrome(String s) {
        int maxLength = 0;
        String longest = "";

        for (int i = 0; i < s.length(); i++) {

            String odd = check(s, i, i);
            if (odd.length() > maxLength) {
                maxLength = odd.length();
                longest = odd;
            }

            String even = check(s, i, i + 1);
            if (even.length() > maxLength) {
                maxLength = even.length();
                longest = even;
            }
        }

        return longest;
    }

    static String check(String s, int left, int right) {
        
        while (left >= 0 && right < s.length() && s.charAt(left) == s.charAt(right)) {
            left--;
            right++;
        }

        return s.substring(left + 1, right);
    }
}

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