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

Recall & Review

beginner

What is a palindrome?

A palindrome is a word, phrase, 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 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 time complexity of the expand-around-center approach for this problem?

O(n²), where n is the length of the string, because we check palindromes centered at each character and between characters.

intermediate

Why is dynamic programming used in the Longest Palindromic Substring problem?

Because it stores results of smaller palindrome checks to avoid repeated work, improving efficiency.

What is the simplest way to check if a substring is a palindrome?

A Reverse the substring and compare with original

B Compare characters from both ends moving inward

C Sort the substring and check equality

D Count vowels in the substring

Checking characters from both ends moving inward ensures palindrome property.

Which approach expands around centers to find palindromes?

A Expand Around Center

B Dynamic Programming

C Divide and Conquer

D Greedy

Expand Around Center checks palindromes by expanding from each character or pair.

What is the worst-case time complexity of the brute force method for this problem?

A O(n³)

B O(n)

C O(n²)

D O(log n)

Brute force checks all substrings (O(n²)) and palindrome check per substring (O(n)) leading to O(n³).

In dynamic programming for this problem, what does the DP table store?

A Number of vowels in substring s[i..j]

B Length of substring s[i..j]

C Whether substring s[i..j] is a palindrome

D Index of first character

DP table stores true/false if substring s[i..j] is palindrome.

Which of these is NOT a valid palindrome?

A a

B racecar

C madam

D hello

"hello" is not the same backward and forward.

Explain how the expand-around-center method finds the longest palindromic substring.

Think of checking palindromes by growing outwards from the middle.

Describe how dynamic programming helps optimize finding the longest palindromic substring.

Remember storing results to reuse them.

Practice

1. What is the main goal when finding the Longest Palindromic Substring in a given string?

easy

A. To find the longest substring with all unique characters

B. To find the longest substring that contains only vowels

C. To find the longest continuous sequence of characters that reads the same backward and forward

D. To find the longest substring that is sorted alphabetically

Solution

1. Step 1: Understand palindrome definition

   A palindrome reads the same backward and forward, like 'madam' or 'racecar'.

2. Step 2: Identify substring requirement

   The substring must be continuous characters in the string, not scattered.

3. Final Answer:

   To find the longest continuous sequence of characters that reads the same backward and forward -> Option C

4. Quick Check:

   Longest palindromic substring = continuous palindrome [OK]

Hint: Look for continuous same backward-forward sequences [OK]

Common Mistakes:

• Confusing substring with subsequence
• Looking for unique characters instead of palindrome
• Ignoring continuity of characters

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

easy

A. int maxLength = 0; int start = -1; int len = strlen(s);

B. int maxLength = 1; int start = 0; int len = strlen(s);

C. int maxLength = 1; int start = 0; int len = length(s);

D. int maxLength = 1; int start = 0; int len = s.length;

Solution

1. Step 1: Check correct function for string length in C

   In C, strlen() is used to get string length, not length() or s.length.

2. Step 2: Verify variable initialization

   Longest palindrome length starts at 1 (single char), start index at 0, and length is string length.

3. Final Answer:

   int maxLength = 1; int start = 0; int len = strlen(s); -> Option B

4. Quick Check:

   Use strlen() for string length in C [OK]

Hint: Use strlen() to get string length in C [OK]

Common Mistakes:

• Using length() instead of strlen() in C
• Initializing maxLength to 0 instead of 1
• Using Java or C++ string length syntax in C

3. What will be the output of the following C code snippet that finds the longest palindromic substring length?

char s[] = "babad";
int maxLength = 1, start = 0;
int len = strlen(s);
for (int i = 0; i < len; i++) {
    int low = i - 1;
    int high = i + 1;
    while (high < len && s[high] == s[i])
        high++;
    while (low >= 0 && s[low] == s[i])
        low--;
    while (low >= 0 && high < len && s[low] == s[high]) {
        low--;
        high++;
    }
    int length = high - low - 1;
    if (maxLength < length) {
        maxLength = length;
        start = low + 1;
    }
}
printf("%d", maxLength);

medium

A. 3

B. 2

C. 4

D. 5

Solution

1. Step 1: Understand the palindrome expansion logic

   The code expands around each character to find palindromes, including duplicates and symmetric characters.

2. Step 2: Trace the longest palindrome in "babad"

   Longest palindromic substrings are "bab" or "aba", both length 3.

3. Final Answer:

   3 -> Option A

4. Quick Check:

   Longest palindrome in "babad" = 3 [OK]

Hint: Check palindrome centers and expand outwards [OK]

Common Mistakes:

• Assuming entire string is palindrome
• Counting non-continuous characters
• Ignoring multiple palindrome centers

4. Identify the bug in the following C code snippet intended to find the longest palindromic substring length:

char s[] = "cbbd";
int maxLength = 1, start = 0;
int len = strlen(s);
for (int i = 0; i < len; i++) {
    int low = i - 1;
    int high = i + 1;
    while (low >= 0 && high < len && s[low] == s[high]) {
        low--;
        high++;
    }
    int length = high - low - 1;
    if (maxLength < length) {
        maxLength = length;
        start = low + 1;
    }
}
printf("%d", maxLength);

medium

A. The code does not check for even length palindromes correctly

B. The variable 'start' is not updated properly

C. The initial maxLength should be 0, not 1

D. The loops use wrong comparison operators

Solution

1. Step 1: Analyze palindrome detection logic

   The code expands around a single center character, missing even length palindromes like "bb" in "cbbd".

2. Step 2: Identify missing even length palindrome check

   Even length palindromes require checking centers between characters, which is not done here.

3. Final Answer:

   The code does not check for even length palindromes correctly -> Option A

4. Quick Check:

   Missing even length palindrome check = bug [OK]

Hint: Check centers between characters for even palindromes [OK]

Common Mistakes:

• Only checking odd length palindromes
• Not updating start index correctly
• Wrong initial maxLength value

5. Given the string "forgeeksskeegfor", which approach correctly finds the longest palindromic substring and what is its length? A) Brute force method, length 8 B) Dynamic programming method, length 12 C) Expand around center method, length 12 D) Expand around center method, length 10

hard

A. Brute force method, length 8

B. Dynamic programming method, length 12

C. Expand around center method, length 12

D. Expand around center method, length 10

Solution

1. Step 1: Identify longest palindrome in "forgeeksskeegfor"

   The longest palindromic substring is "geeksskeeg", length 10.

2. Step 2: Check method correctness and length

   Expand around center method can find the longest palindrome correctly. The longest palindrome is "geeksskeeg" (length 10).

3. Step 3: Re-examine options

   Expand around center method, length 10 says expand around center method, length 10 which is correct. Other options have incorrect lengths or methods.

4. Final Answer:

   Expand around center method, length 10 -> Option D

5. Quick Check:

   Longest palindrome "geeksskeeg" length 10 [OK]

Hint: Longest palindrome is "geeksskeeg" length 10 [OK]

Common Mistakes:

• Assuming full string is palindrome
• Confusing length 12 with actual palindrome length
• Mixing method with incorrect length