Mastering the Longest Palindromic Substring Problem on LeetCode
The Longest Palindromic Substring is a classic LeetCode challenge that tests your understanding of string manipulation, dynamic programming, and algorithm optimization. It's a common favorite in technical interviews, thanks to its deceptively simple prompt and the wealth of approaches it offers.
Problem Statement
Given a string
s, return the longest palindromic substring ins.
A palindrome is a word or phrase that reads the same backward as forward, such as "racecar" or "abba". Your task is to find the longest contiguous substring within the input string that satisfies this property.
Example:
Input: s = "babad"
Output: "bab"
Explanation: "aba" is also a valid answer.
Why This Problem Matters for Interviews
Palindromes pop up all the time in interviews because they:
- Test your grasp of string indexing and boundaries
- Encourage creative brute force and optimal solutions
- Open the door to time/space complexity discussions
Interviewers love this problem because there’s more than one correct solution, but only a few are truly efficient. The best candidates not only solve it but can clearly explain their reasoning and optimizations.
Three Key Approaches to Solve Longest Palindromic Substring
Let's explore the most popular solutions, ranked from naive to optimal.
1. Brute Force (Not Recommended for Production)
You can check every possible substring and see if it’s a palindrome, but this results in O(n³) time complexity—a sure way to time out on large inputs.
def longestPalindrome(s: str) -> str:
n = len(s)
result = ""
for i in range(n):
for j in range(i, n):
substring = s[i:j+1]
if substring == substring[::-1] and len(substring) > len(result):
result = substring
return result
Tip: Understand brute force so you can explain why it's not ideal and how you’d optimize.
2. Expand Around Center (Optimal for Interviews)
A palindrome mirrors around its center. For a string of length n, there are 2n - 1 possible centers (each character and the gaps between them). Expand outward from each center and track the longest palindrome found.
Time Complexity: O(n²)
Space Complexity: O(1)
def longestPalindrome(s: str) -> str:
if not s or len(s) < 1:
return ""
start, end = 0, 0
def expand_around_center(left, right):
while left >= 0 and right < len(s) and s[left] == s[right]:
left -= 1
right += 1
return left + 1, right - 1
for i in range(len(s)):
# Odd-length palindromes
l1, r1 = expand_around_center(i, i)
# Even-length palindromes
l2, r2 = expand_around_center(i, i + 1)
if r1 - l1 > end - start:
start, end = l1, r1
if r2 - l2 > end - start:
start, end = l2, r2
return s[start:end+1]
3. Dynamic Programming (Good for Practice)
Dynamic programming offers a way to build up the solution, but with extra space usage. You create a table where dp[i][j] is True if s[i:j+1] is a palindrome.
Time Complexity: O(n²)
Space Complexity: O(n²)
def longestPalindrome(s: str) -> str:
n = len(s)
dp = [[False]*n for _ in range(n)]
res = ""
for i in range(n-1, -1, -1):
for j in range(i, n):
if s[i] == s[j] and (j - i < 3 or dp[i+1][j-1]):
dp[i][j] = True
if j - i + 1 > len(res):
res = s[i:j+1]
return res
Key Interview Talking Points
Interviewers want to see more than just code. Here’s how you can stand out:
- Explain the brute force and why it fails on large inputs.
- Discuss the O(n²) center expansion as the optimal approach for this problem.
- Mention time and space complexity clearly.
- If you know about Manacher’s Algorithm (O(n)), mention it, but note it’s rarely required in interviews.
- Show off edge-case awareness:
- Empty string? Single character? All identical characters?
Big O Complexity Recap
| Approach | Time Complexity | Space Complexity |
|---|---|---|
| Brute Force | O(n³) | O(n) |
| Expand Around Center | O(n²) | O(1) |
| Dynamic Programming | O(n²) | O(n²) |
Pro Interview Tips
- Always clarify the problem with your interviewer: ask if the input string can be empty or contain non-alphanumeric characters.
- Explain your reasoning before you code: talk through possible approaches, trade-offs, and why you’re choosing one.
- Practice with test cases