L3 · FAANGDynamic programming~18 min · 6 tests

Longest Palindromic Substring

Find the longest palindromic substring by expanding around every centre in O(n²) time and O(1) space, handling odd and even lengths. Common FAANG medium.

The problem

Return the longest substring of s that is a palindrome. If several share the longest length, return the one that starts first.

Examples

Example 1
Input
```
longest_palindrome('babad')
```
Expected output
```
'bab'
```
Example 2
Input
```
longest_palindrome('cbbd')
```
Expected output
```
'bb'
```

+ 4 hidden tests on Submit.

Edge cases to ask about

Even-length palindromes
Single character
Empty string

Hints

0/3

How an interviewer scores this

0/9

1. Understand the problemRestate it, ask about edge cases and input size.
2. Write a brute-force solutionCorrect first, clever later.
3. Get the correct outputautoAll visible examples pass.
4. Analyse time complexityautoCommit to a Big-O in the Complexity Lab.
5. Analyse space complexityautoExtra memory, not the input.
6. Identify the bottleneckautoMeasure your code — where does it bend?
7. OptimiseUsually: a set or dict instead of a scan.
8. Explain why it worksSay it out loud to Solvi.
9. Test the edge casesautoSubmit passes every hidden test.

Python 3.13 · longest_palindrome

def longest_palindrome(s):
    """Longest palindromic substring (earliest on ties)."""
    # Write your solution here
    pass

⌘/Ctrl + Enter runs the examples

Your code runs in real CPython inside your browser — nothing is sent anywhere. The first run downloads the interpreter (about 6 MB, once). Your code is saved on this device as you type.

Complexity Lab

What does this cost as n grows?

Interviewers score the analysis as much as the code. Commit to an answer first — then check it, and measure your code against the optimal one at growing input sizes.

Time complexity of the optimal solution

Space complexity (extra memory)

Pick both to reveal the answer.

Measure it

Runs the function on inputs of size 250 up to 16,000 and records the time and peak memory. Slow solutions stop early — a short curve is itself the answer.

From brute force to optimal

The progression an interviewer wants to hear, one step at a time.

Approach	Time	Space	Idea
Check every substring	O(n³)	O(1)
DP table is_pal[i][j]	O(n²)	O(n²)
Expand around 2n − 1 centres	O(n²)	O(1)	Odd centres are characters, even centres are gaps.
bestManacher's algorithm	O(n)	O(n)	Rarely expected — mention it.

Walkthrough of the optimal approach (try it yourself first)

Every palindrome mirrors around a centre — a single character (odd length) or the gap between two characters (even length). From each of the 2n − 1 centres, expand while the ends match and record the longest. O(n²) time, O(1) space.

Forgetting the even-length centres is the usual bug ("cbbd" → "bb").

Complexity: O(n²) time, O(1) space. There are 2n − 1 centres and each expansion can take O(n).

Reveal the reference solution

def longest_palindrome(s):
    best_start, best_len = 0, 0
    for centre in range(len(s)):
        for lo, hi in ((centre, centre), (centre, centre + 1)):
            while lo >= 0 and hi < len(s) and s[lo] == s[hi]:
                lo -= 1
                hi += 1
            length = hi - lo - 1
            if length > best_len:
                best_start, best_len = lo + 1, length
    return s[best_start:best_start + best_len]

Follow-ups interviewers ask

Count all palindromic substrings.
Explain Manacher's O(n) idea.

Frequently asked interview questions

Core interview concepts, complexities, and follow-ups scored by hiring teams.

What is the time complexity of Longest Palindromic Substring in Python?

The optimal solution runs in O(n²) time and O(1) auxiliary space. There are 2n − 1 centres and each expansion can take O(n).

What is the brute-force approach, and how do you optimise it?

Check every substring: O(n³) time, O(1) space. DP table is_pal[i][j]: O(n²) time, O(n²) space. Expand around 2n − 1 centres: O(n²) time, O(1) space. Odd centres are characters, even centres are gaps. Manacher's algorithm: O(n) time, O(n) space. Rarely expected — mention it.

What follow-up questions do interviewers ask about Longest Palindromic Substring?

Count all palindromic substrings. Explain Manacher's O(n) idea.