Longest Palindromic Substring in DSA Rust - 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.

intermediate

How does expanding around center help find palindromes?

By choosing a center and expanding left and right while characters match, we find palindromes centered there.

intermediate

Why do we check both odd and even length palindromes separately?

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

intermediate

What is the time complexity of the expand around center approach for Longest Palindromic Substring?

The time complexity is O(n^2), where n is the length of the string, because we expand around each center.

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

A Compare characters from start and end moving towards the center

B Sort the substring and check if it matches original

C Count vowels in the substring

D Reverse the substring and check if it is different

Checking characters from start and end moving towards the center confirms palindrome property.

In the expand around center method, how many centers are there for a string of length n?

A n/2

B n

C n^2

D 2n - 1

There are n centers for odd length palindromes and n-1 for even length, totaling 2n - 1.

Which of these is NOT a valid palindrome?

A racecar

B hello

C madam

D abba

"hello" is not the same backward and forward, so it is not a palindrome.

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

A bab

B aba

C Both A and B are correct

D bad

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

Why is dynamic programming sometimes used for this problem?

A To store results of smaller substrings and avoid repeated checks

B To sort the string first

C To count characters

D To reverse the string

Dynamic programming stores palindrome checks for substrings to avoid repeated work.

Explain how the expand around center approach finds the longest palindromic substring.

Think about how palindromes mirror around their center.

Describe why checking both odd and even length palindromes is necessary.

Consider examples like 'aba' and 'abba'.

Practice

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

easy

A. Find the longest substring that contains only vowels

B. Find the longest substring with all unique characters

C. Find the longest substring with increasing characters

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

Solution

1. Step 1: Understand palindrome definition

   A palindrome reads the same forwards and backwards, like 'madam' or 'racecar'.

2. Step 2: Identify problem goal

   The problem asks to find the longest continuous part of a string that is a palindrome.

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: Look for substring that mirrors itself [OK]

Common Mistakes:

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

2. Which Rust code snippet correctly declares a function header for finding the longest palindromic substring in a string slice s?

easy

A. fn longest_palindrome(s: &str) -> &str { }

B. fn longest_palindrome(s: String) -> String { }

C. fn longest_palindrome(s: &String) -> &String { }

D. fn longest_palindrome(s: str) -> str { }

Solution

1. Step 1: Understand Rust string types

   Rust uses &str for string slices and String for owned strings.

2. Step 2: Choose correct function signature

   Function should take a string slice &str and return a string slice &str for substring references.

3. Final Answer:

   fn longest_palindrome(s: &str) -> &str { } -> Option A

4. Quick Check:

   Use &str for slices in function signature [OK]

Hint: Use &str for input and output substrings [OK]

Common Mistakes:

• Using owned String when slice is better
• Returning owned String unnecessarily
• Incorrect parameter types like str without &

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

fn main() {
    let s = "babad";
    let result = longest_palindrome(s);
    println!("{}", result);
}

fn longest_palindrome(s: &str) -> &str {
    let chars: Vec<char> = s.chars().collect();
    let mut start = 0;
    let mut max_len = 1;

    for i in 0..chars.len() {
        let mut left = i as i32;
        let mut right = i as i32;

        while left >= 0 && right < chars.len() as i32 && chars[left as usize] == chars[right as usize] {
            if (right - left + 1) > max_len {
                start = left as usize;
                max_len = (right - left + 1) as usize;
            }
            left -= 1;
            right += 1;
        }
    }

    &s[start..start + max_len]
}

medium

A. aba

B. bad

C. bab

D. babad

Solution

1. Step 1: Understand the code logic

   The code expands around each character to find odd-length palindromes and tracks the longest.

2. Step 2: Trace the input "babad"

   At index 0: palindrome "b" (length 1), index 1: "bab" (length 3), index 2: "aba" (length 3). The first longest palindrome found is "bab".

3. Final Answer:

   bab -> Option C

4. Quick Check:

   Longest palindrome substring = bab [OK]

Hint: Expand around center, pick first longest palindrome [OK]

Common Mistakes:

• Assuming palindrome must be unique
• Returning entire string instead of substring
• Confusing substring indices

4. Identify the bug in this Rust function that tries to find the longest palindromic substring:

fn longest_palindrome(s: &str) -> &str {
    let chars: Vec<char> = s.chars().collect();
    let mut start = 0;
    let mut max_len = 1;

    for i in 0..chars.len() {
        let mut left = i as i32;
        let mut right = i as i32 + 1;

        while left >= 0 && right < chars.len() as i32 && chars[left as usize] == chars[right as usize] {
            if (right - left + 1) > max_len {
                start = left as usize;
                max_len = (right - left + 1) as usize;
            }
            left -= 1;
            right += 1;
        }
    }

    &s[start..start + max_len]
}

medium

A. The max_len should start at 0, not 1

B. The initial right pointer should be equal to i, not i + 1

C. The loop should iterate from 1 to length, not 0 to length

D. The function should return a String, not &str

Solution

1. Step 1: Analyze pointer initialization

   Right pointer starts at i + 1, which only checks even-length palindromes, missing odd-length ones.

2. Step 2: Correct pointer for odd-length palindromes

   To check odd-length palindromes, right pointer should start at i, same as left pointer.

3. Final Answer:

   The initial right pointer should be equal to i, not i + 1 -> Option B

4. Quick Check:

   Right pointer = i for odd-length palindrome check [OK]

Hint: Start right pointer same as left for odd palindromes [OK]

Common Mistakes:

• Only checking even-length palindromes
• Wrong loop range causing index errors
• Returning wrong type causing borrow issues

5. Given the string "forgeeksskeegfor", which approach correctly finds the longest palindromic substring and what is that substring?

hard

A. Expand around center method; longest palindrome is "geeksskeeg"

B. Dynamic programming with substring table; longest palindrome is "forgeeksskeegfor"

C. Brute force checking all substrings; longest palindrome is "ss"

D. Using hash map for character counts; longest palindrome is "ks"

Solution

1. Step 1: Understand approaches to find longest palindrome

   Expand around center and dynamic programming are common methods; brute force is slow but correct.

2. Step 2: Identify longest palindrome in given string

   "forgeeksskeegfor" contains "geeksskeeg" as the longest palindrome substring, not the entire string.

3. Step 3: Match approach and answer

   Expand around center method efficiently finds "geeksskeeg"; dynamic programming would too but not the full string.

4. Final Answer:

   Expand around center method; longest palindrome is "geeksskeeg" -> Option A

5. Quick Check:

   Longest palindrome = geeksskeeg by center expansion [OK]

Hint: Expand around centers to find longest palindrome fast [OK]

Common Mistakes:

• Assuming entire string is palindrome
• Using character counts instead of substring checks
• Confusing brute force with efficient methods