Longest Palindromic Substring in DSA Python - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a palindrome?

A palindrome is a word, phrase, number, or sequence that reads the same backward as forward, like 'madam' or 'racecar'.

beginner

What does the 'Longest Palindromic Substring' problem ask for?

It asks to find the longest continuous part (substring) of a string that is a palindrome.

beginner

How can you check if a substring is a palindrome?

By comparing characters from the start and end moving towards the center, ensuring they match.

intermediate

What is the center expansion technique in finding palindromes?

It means starting from a center point and expanding outwards to check for palindromes around that center.

intermediate

Why do we consider both odd and even length centers in palindrome search?

Because palindromes can have a single center character (odd length) or two center characters (even length), so both cases must be checked.

What is the time complexity of the naive approach to find the longest palindromic substring by checking all substrings?

A O(n^3)

B O(n^2)

C O(n)

D O(log n)

The naive approach checks all substrings (O(n^2)) and each substring palindrome check takes O(n), so total O(n^3).

In the center expansion method, how many centers do we consider for a string of length n?

A n^2

B n

C 2n - 1

D n/2

We consider n centers for odd length palindromes and n-1 centers for even length palindromes, total 2n - 1.

Which data structure is primarily used to store the longest palindromic substring during the algorithm?

A Stack

B Queue

C Hash Map

D String variables or indices

We keep track of start and end indices or the substring itself as a string variable.

What is the output of the longest palindromic substring algorithm for input 'babad'?

A bab

B bab or aba

C aba

D bad

Both 'bab' and 'aba' are valid longest palindromic substrings of length 3.

Which approach is more efficient for longest palindromic substring: dynamic programming or center expansion?

A Center expansion with O(n^2) time and O(1) space

B Sorting the string

C Naive approach with O(n^3) time

D Dynamic programming with O(n^2) time and space

Center expansion uses O(n^2) time but only O(1) space, making it more space efficient than DP.

Explain how the center expansion technique works to find the longest palindromic substring.

Think about starting from the middle and moving left and right.

Describe why we need to check both odd and even length palindromes separately.

Consider palindromes like 'aba' and 'abba'.

Practice

1. What is the main goal of the Longest Palindromic Substring problem?

easy

A. Count the total number of palindromic substrings

B. Reverse the string and compare with original

C. Check if the entire string is a palindrome

D. Find the longest substring that reads the same forwards and backwards

Solution

1. Step 1: Understand the problem statement

   The problem asks to find the longest continuous part of the string that reads the same forwards and backwards.

2. Step 2: Differentiate from related problems

   Counting palindromic substrings or checking the whole string is different from finding the longest palindromic substring.

3. Final Answer:

   Find the longest substring that reads the same forwards and backwards -> Option D

4. Quick Check:

   Longest palindromic substring = Find longest palindrome [OK]

Hint: Longest palindrome means longest continuous mirrored substring [OK]

Common Mistakes:

• Confusing substring with subsequence
• Counting all palindromes instead of longest
• Checking whole string palindrome only

2. Which of the following Python code snippets correctly initializes variables to find the longest palindromic substring?

easy

A. start, max_len = 0, 1

B. start = max_len = None

C. start, max_len = 1, 0

D. start = max_len = 0

Solution

1. Step 1: Understand variable roles

   We need to track the start index and maximum length of the palindrome found. Starting with 0 and 1 is common because a single character is a palindrome.

2. Step 2: Check initialization correctness

   start, max_len = 0, 1 sets start=0 and max_len=1, which is correct. start, max_len = 1, 0 reverses values incorrectly. Options A, B, and C do not set max_len properly.

3. Final Answer:

   start, max_len = 0, 1 -> Option A

4. Quick Check:

   Initialize start=0 and max_len=1 for single char palindrome [OK]

Hint: Start at 0, max length at least 1 for single char palindrome [OK]

Common Mistakes:

• Setting max_len to 0 initially
• Using None instead of integers
• Swapping start and max_len values

3. What will be the output of the following code snippet?

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

s = "babad"
length = expand_around_center(s, 1, 1)
print(length)

medium

A. 1

B. 5

C. 3

D. 0

Solution

1. Step 1: Understand the function behavior

   The function expands around the center indices (left and right) while characters match, then returns the length of the palindrome found.

2. Step 2: Trace the expansion for s='babad' at center (1,1)

   Center at index 1 ('a'). Expand left=1, right=1: 'a'=='a' true, expand to left=0, right=2: 'b'=='b' true, expand to left=-1 (stop). Length = right - left - 1 = 3 - (-1) - 1 = 3.

3. Final Answer:

   3 -> Option C

4. Quick Check:

   Expand around center returns palindrome length 3 [OK]

Hint: Expand while chars match, length = right - left - 1 [OK]

Common Mistakes:

• Not subtracting 1 in length calculation
• Confusing indices after expansion
• Assuming length equals right - left

4. Identify the error in the following code snippet for finding the longest palindromic substring:

def longest_palindrome(s):
    start, max_len = 0, 1
    for i in range(len(s)):
        len1 = expand_around_center(s, i, i)
        len2 = expand_around_center(s, i, i+1)
        length = max(len1, len2)
        if length > max_len:
            start = i - length // 2
            max_len = length
    return s[start:start+max_len]

medium

A. The loop should run till len(s)-1 to avoid index error

B. The start index calculation is incorrect for even length palindromes

C. max_len should be initialized to 0 instead of 1

D. expand_around_center function is missing

Solution

1. Step 1: Analyze start index update logic

   For even length palindromes, start index calculation differs because center is between two characters. Using i - length // 2 works for odd length but not always for even length.

2. Step 2: Identify correct start calculation

   For even length, start should be i - (length // 2) + 1 to correctly locate the palindrome start.

3. Final Answer:

   The start index calculation is incorrect for even length palindromes -> Option B

4. Quick Check:

   Start index must adjust differently for even palindromes [OK]

Hint: Adjust start index differently for even-length palindromes [OK]

Common Mistakes:

• Using same start formula for odd and even palindromes
• Ignoring even length palindrome cases
• Not updating max_len properly

5. Given the string "forgeeksskeegfor", which substring is the longest palindromic substring?

hard

A. "geeksskeeg"

B. "forgeeksskeegfor"

C. "geeksskeegf"

D. "eksskeeg"

Solution

1. Step 1: Identify palindromic substrings in the string

   Check substrings that read the same forwards and backwards. "geeksskeeg" is a palindrome of length 10 inside the string.

2. Step 2: Compare lengths of candidate substrings

   "forgeeksskeegfor" is not a palindrome as a whole. "geeksskeegf" and "eksskeeg" are shorter palindromes.

3. Final Answer:

   "geeksskeeg" -> Option A

4. Quick Check:

   Longest palindrome in "forgeeksskeegfor" is "geeksskeeg" [OK]

Hint: Look for longest mirrored substring inside the string [OK]

Common Mistakes:

• Assuming whole string is palindrome
• Choosing substring with extra characters
• Ignoring palindrome length