Longest Palindromic Substring in DSA C++ - Build from Scratch

Longest Palindromic Substring

📖 Scenario: Imagine you are building a text analysis tool that finds the longest palindrome inside a given word or sentence. A palindrome is a sequence of characters that reads the same backward as forward, like "madam" or "racecar".

🎯 Goal: Build a program that finds and prints the longest palindromic substring inside a given string.

📋 What You'll Learn

Create a string variable with a specific value.

Create helper variables to track the longest palindrome found.

Implement a function to expand around the center and find palindromes.

Use loops and conditions to find the longest palindromic substring.

Print the longest palindromic substring found.

💡 Why This Matters

🌍 Real World

Finding palindromic substrings is useful in text analysis, DNA sequence analysis, and data compression.

💼 Career

Understanding string manipulation and palindrome detection is important for software developers working with text processing, bioinformatics, and algorithm design.

1

Create the input string

Create a std::string variable called input and set it to "babad".

DSA C++

# Your code here

Hint

Use std::string input = "babad"; to create the string.

2

Add variables to track longest palindrome

Add two int variables called start and maxLength and set them to 0 and 1 respectively.

DSA C++

#include 
#include 

int main() {
    std::string input = "babad";
    int start = 0;
    int maxLength = 1;
    // Your code here
    return 0;
}

Hint

Use int start = 0; and int maxLength = 1; to track the palindrome.

3

Implement palindrome expansion function and find longest palindrome

Write a function called expandAroundCenter that takes const std::string& s, int left, and int right and returns the length of the palindrome by expanding around the center. Then, use a for loop with int i = 0; i < input.length(); i++ to check palindromes of odd and even lengths and update start and maxLength accordingly.

DSA C++

#include 
#include 

int expandAroundCenter(const std::string& s, int left, int right) {
    // Your code here
}

int main() {
    std::string input = "babad";
    int start = 0;
    int maxLength = 1;

    // Your code here

    return 0;
}

Hint

Use a helper function to expand around centers and a loop to find the longest palindrome.

4

Print the longest palindromic substring

Print the longest palindromic substring from input using start and maxLength with std::cout.

DSA C++

#include 
#include 

int expandAroundCenter(const std::string& s, int left, int right) {
    while (left >= 0 && right  len2) ? len1 : len2;
        if (len > maxLength) {
            maxLength = len;
            start = i - (len - 1) / 2;
        }
    }

    std::cout << input.substr(start, maxLength) << std::endl;
}

Hint

Use std::cout << input.substr(start, maxLength) << std::endl; to print the result.

Practice

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

easy

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

B. Find the longest substring with all unique characters

C. Find the longest substring with increasing characters

D. Find the longest substring that contains only vowels

Solution

1. Step 1: Understand the problem statement

   The problem asks to find the longest part of a string that is a palindrome, meaning it reads the same forwards and backwards.

2. Step 2: Compare options with the problem goal

   Only Find the longest substring that reads the same forwards and backwards describes finding a substring that reads the same forwards and backwards, which matches the palindrome definition.

3. Final Answer:

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

4. Quick Check:

   Longest Palindromic Substring = Find the longest substring that reads the same forwards and backwards [OK]

Hint: Look for substring that reads same forwards and backwards [OK]

Common Mistakes:

• Confusing palindrome with unique characters
• Thinking about substrings with vowels only
• Mixing substring with subsequence

2. Which of the following C++ code snippets correctly initializes a 2D vector dp of size n x n with false values for the Longest Palindromic Substring problem?

easy

A. std::vector dp(n, std::vector<int>(n, false));

B. std::vector<bool> dp(n, std::vector<bool>(n, false));

C. std::vector dp(n, n, false);

D. std::vector dp(n, std::vector<bool>(n, false));

Solution

1. Step 1: Understand 2D vector initialization syntax

   To create a 2D vector of booleans with size n x n, use vector of vectors: std::vector dp(n, std::vector<bool>(n, false));

2. Step 2: Check each option's correctness

   std::vector dp(n, std::vector<bool>(n, false)); uses correct syntax. std::vector<bool> dp(n, std::vector<bool>(n, false)); tries to assign vector<bool> to vector<bool>, which is invalid. std::vector dp(n, std::vector<int>(n, false)); uses int instead of bool. std::vector dp(n, n, false); uses invalid constructor syntax.

3. Final Answer:

   std::vector dp(n, std::vector<bool>(n, false)); -> Option D

4. Quick Check:

   Correct 2D vector initialization = std::vector dp(n, std::vector<bool>(n, false)); [OK]

Hint: Use vector of vectors with inner vector initialized [OK]

Common Mistakes:

• Using wrong data type for dp vector
• Incorrect constructor syntax for 2D vector
• Confusing vector<bool> with vector

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

std::string s = "babad";
int n = s.size();
int maxLength = 1;
for (int i = 0; i < n; i++) {
  for (int j = i; j < n; j++) {
    int left = i, right = j;
    bool isPalindrome = true;
    while (left < right) {
      if (s[left] != s[right]) {
        isPalindrome = false;
        break;
      }
      left++; right--;
    }
    if (isPalindrome && (j - i + 1) > maxLength) {
      maxLength = j - i + 1;
    }
  }
}
std::cout << maxLength << std::endl;

medium

A. 3

B. 2

C. 4

D. 5

Solution

1. Step 1: Understand the code logic

   The code checks all substrings of "babad" and updates maxLength if the substring is a palindrome and longer than current maxLength.

2. Step 2: Identify longest palindromic substrings in "babad"

   "bab" and "aba" are palindromes of length 3. No longer palindrome exists.

3. Final Answer:

   3 -> Option A

4. Quick Check:

   Longest palindrome length in "babad" = 3 [OK]

Hint: Check all substrings and update max length if palindrome [OK]

Common Mistakes:

• Assuming entire string is palindrome
• Counting non-palindromic substrings
• Off-by-one errors in substring length

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

std::string s = "cbbd";
int n = s.size();
int maxLength = 1;
for (int i = 0; i < n; i++) {
  for (int j = i; j < n; j++) {
    int left = i, right = j;
    while (left < right) {
      if (s[left] != s[right]) {
        break;
      }
      left++; right--;
    }
    if ((j - i + 1) > maxLength) {
      maxLength = j - i + 1;
    }
  }
}
std::cout << maxLength << std::endl;

medium

A. Incorrect loop ranges for i and j

B. Wrong initialization of maxLength

C. Missing check if substring is palindrome before updating maxLength

D. Using break instead of continue in while loop

Solution

1. Step 1: Analyze palindrome check logic

   The code breaks out of while loop if characters don't match but does not track if substring is palindrome.

2. Step 2: Check maxLength update condition

   maxLength is updated without confirming substring is palindrome, causing incorrect results.

3. Final Answer:

   Missing check if substring is palindrome before updating maxLength -> Option C

4. Quick Check:

   Must confirm palindrome before updating maxLength [OK]

Hint: Always confirm palindrome before updating max length [OK]

Common Mistakes:

• Updating maxLength without palindrome check
• Confusing break and continue in loops
• Incorrect loop boundaries

5. Given the string "forgeeksskeegfor", which approach below efficiently finds the longest palindromic substring and what is its length?

hard

A. Dynamic Programming approach, length 7

B. Expand Around Center approach, length 10

C. Brute Force approach, length 12

D. Manacher's Algorithm, length 8

Solution

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

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

2. Step 2: Choose efficient approach

   Expand Around Center approach efficiently finds palindromes by expanding from each center, suitable for this problem.

3. Final Answer:

   Expand Around Center approach, length 10 -> Option B

4. Quick Check:

   Longest palindrome length = 10 using Expand Around Center [OK]

Hint: Expand from centers to find longest palindrome efficiently [OK]

Common Mistakes:

• Confusing length of palindrome substring
• Choosing less efficient brute force for large strings
• Mixing up algorithm names and their complexities