Find the Longest Palindromic Substring

Question

The question asks the candidate to find the longest palindromic substring within a given string, which is a common problem in coding interviews.

Codemia · Accepted Answer

To find the longest palindromic substring, I will use the **expand around center** technique. This approach involves treating each character (and each pair of characters for even-length palindromes) as a potential center of a palindrome and expanding outwards to find the longest palindrome possible from that center.

The algorithm can be implemented as follows:

1. Initialize a variable to keep track of the start and end indices of the longest palindrome found.
2. Iterate through each character in the string, treating it as a center.
3. For each center, expand outwards while the characters on both sides are equal.
4. Update the start and end indices if a longer palindrome is found.
5. Return the substring from the start to end indices.

Here is the Python code for the solution:

```python
def longest_palindromic_substring(s: str) -> str:
    if not s:
        return ""

start, end = 0, 0

for i in range(len(s)):
        len1 = expand_around_center(s, i, i)  # Odd length palindromes
        len2 = expand_around_center(s, i, i + 1)  # Even length palindromes
        max_len = max(len1, len2)

if max_len > end - start:
            start = i - (max_len - 1) // 2
            end = i + max_len // 2

return s[start:end + 1]

def expand_around_center(s: str, left: int, right: int) -> int:
    while left >= 0 and right < len(s) and s[left] == s[right]:
        left -= 1
        right += 1
    return right - left - 1
```

The time complexity of this algorithm is **O(n^2)**, where n is the length of the string. This is because for each character, we may expand outwards to the length of the string in the worst case. The space complexity is **O(1)** since we only use a few variables for tracking indices.

It's important to consider edge cases, such as:
- An empty string, which should return an empty result.
- A string with no palindromic substrings, where the longest palindrome is just a single character.
- Strings where all characters are the same, which should return the entire string.

Interviewers look for clarity in the explanation of the approach, the ability to write clean and efficient code, and a solid understanding of time and space complexities. They also appreciate candidates who can discuss edge cases and potential optimizations.

Find the Longest Palindromic Substring

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