Longest Palindromic Substring in DSA Javascript - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of longest palindrome substring length

What is the output of the following JavaScript code that finds the length of the longest palindromic substring?

DSA Javascript

function longestPalindromeLength(s) {
  let maxLen = 1;
  for (let i = 0; i < s.length; i++) {
    let left = i, right = i;
    while (left >= 0 && right < s.length && s[left] === s[right]) {
      maxLen = Math.max(maxLen, right - left + 1);
      left--;
      right++;
    }
    left = i;
    right = i + 1;
    while (left >= 0 && right < s.length && s[left] === s[right]) {
      maxLen = Math.max(maxLen, right - left + 1);
      left--;
      right++;
    }
  }
  return maxLen;
}
console.log(longestPalindromeLength("babad"));

A 4

B 2

C 1

D 3

💡 Hint

Check palindromes centered at each character and between characters.

The longest palindromic substring in "babad" is either "bab" or "aba", both length 3.

❓ Predict Output

intermediate

Output of longest palindrome substring

What is the output of this code that returns the longest palindromic substring itself?

DSA Javascript

function longestPalindrome(s) {
  if (s.length < 1) return "";
  let start = 0, end = 0;
  for (let i = 0; i < s.length; i++) {
    let len1 = expandAroundCenter(s, i, i);
    let len2 = expandAroundCenter(s, i, i + 1);
    let len = Math.max(len1, len2);
    if (len > end - start) {
      start = i - Math.floor((len - 1) / 2);
      end = i + Math.floor(len / 2);
    }
  }
  return s.substring(start, end + 1);
}
function expandAroundCenter(s, left, right) {
  while (left >= 0 && right < s.length && s[left] === s[right]) {
    left--;
    right++;
  }
  return right - left - 1;
}
console.log(longestPalindrome("cbbd"));

A "cbbd"

B "bb"

C "b"

D "cb"

💡 Hint

Look for the longest substring that reads the same forwards and backwards.

The longest palindromic substring in "cbbd" is "bb".

🧠 Conceptual

advanced

Time complexity of longest palindromic substring algorithm

What is the time complexity of the expand-around-center approach to find the longest palindromic substring in a string of length n?

A O(n^2)

B O(n log n)

C O(n)

D O(n^3)

💡 Hint

Consider that for each character you expand outwards checking palindrome.

For each of the n centers, expanding can take up to n steps, resulting in O(n^2) time.

🔧 Debug

advanced

Identify the error in palindrome substring code

What error will this code produce when run?

DSA Javascript

function longestPalindrome(s) {
  let maxLen = 0;
  let start = 0;
  for (let i = 0; i < s.length; i++) {
    let left = i, right = i;
    while (left >= 0 && right < s.length && s[left] === s[right]) {
      if (right - left + 1 > maxLen) {
        maxLen = right - left + 1;
        start = left;
      }
      left--;
      right++;
    }
  }
  return s.substring(start, start + maxLen);
}
console.log(longestPalindrome(null));

A ReferenceError: s is not defined

B Returns empty string ""

C TypeError: Cannot read property 'length' of null

D SyntaxError: Unexpected token

💡 Hint

Check what happens if input is null.

The code tries to access s.length but s is null, causing a TypeError.

🚀 Application

expert

Longest palindromic substring in a large string

Given a string of length 100000 consisting of only 'a' characters, what is the length of the longest palindromic substring?

A 100000

B 1

C 50000

D 99999

💡 Hint

All characters are the same, so the entire string is a palindrome.

A string with all identical characters is itself a palindrome, so the longest palindromic substring is the whole string.

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 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 substring inside a string that is a palindrome.

3. Final Answer:

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

4. Quick Check:

   Longest Palindromic Substring = Find palindrome substring [OK]

Hint: Look for substrings that mirror around a center [OK]

Common Mistakes:

• Confusing palindrome with unique characters
• Thinking about subsequences instead of substrings
• Ignoring the order of characters

2. Which of the following JavaScript code snippets correctly initializes a 2D array dp for dynamic programming in the Longest Palindromic Substring problem?

easy

A. const dp = Array.from({ length: n }, () => Array(n).fill(false));

B. const dp = Array(n).fill(Array(n).fill(false));

C. const dp = new Array(n).fill(new Array(n).fill(false));

D. const dp = Array(n).map(Array(n).fill(false));

Solution

1. Step 1: Understand 2D array initialization in JavaScript

   Using Array.from with a mapping function creates independent inner arrays.

2. Step 2: Analyze each option

   B and C fill with the same inner array reference, causing bugs. D uses map incorrectly by passing an array instead of a function, which won't work. A correctly creates independent arrays.

3. Final Answer:

   const dp = Array.from({ length: n }, () => Array(n).fill(false)); -> Option A

4. Quick Check:

   Correct 2D array init = const dp = Array.from({ length: n }, () => Array(n).fill(false)); [OK]

Hint: Use Array.from with arrow function for independent inner arrays [OK]

Common Mistakes:

• Using fill with object references causing shared inner arrays
• Using map on uninitialized arrays
• Not initializing inner arrays separately

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

function longestPalindrome(s) {
  let maxLen = 1, start = 0;
  for (let i = 0; i < s.length; i++) {
    for (let j = i; j < s.length; j++) {
      let substr = s.slice(i, j + 1);
      if (substr === substr.split('').reverse().join('') && substr.length > maxLen) {
        maxLen = substr.length;
        start = i;
      }
    }
  }
  return s.slice(start, start + maxLen);
}
console.log(longestPalindrome('babad'));

medium

A. "aba"

B. "babad"

C. "bad"

D. "bab"

Solution

1. Step 1: Understand the nested loops and palindrome check

   The code checks all substrings and updates the longest palindrome found.

2. Step 2: Trace substrings in 'babad'

   Palindromes found include 'bab' and 'aba', both length 3. The code updates maxLen and start when it finds 'aba' last (i=1,j=3), because the condition uses >, so it updates only if strictly longer. 'bab' is found first but 'aba' is found later and has the same length, so it is not updated. Actually, the code updates only if substr.length > maxLen, so the first palindrome of length 3 is 'bab' (i=0,j=2), maxLen becomes 3. Then 'aba' (i=1,j=3) is also length 3, so substr.length > maxLen is false (3 > 3 is false), so maxLen and start are not updated. Therefore, the returned palindrome is 'bab'.

3. Final Answer:

   "bab" -> Option D

4. Quick Check:

   First longest palindrome found = "bab" [OK]

Hint: Check all substrings; first longest palindrome returned [OK]

Common Mistakes:

• Assuming 'aba' is returned instead of 'bab'
• Confusing substring with subsequence
• Ignoring order of substring checks

4. The following code attempts to find the longest palindromic substring but has a bug. What is the bug?

function longestPalindrome(s) {
  let maxLen = 1, start = 0;
  for (let i = 0; i < s.length; i++) {
    for (let j = i; j < s.length; j++) {
      let substr = s.slice(i, j + 1);
      if (substr === substr.split('').reverse().join('') && substr.length >= maxLen) {
        maxLen = substr.length;
        start = i;
      }
    }
  }
  return s.slice(start, start + maxLen);
}
console.log(longestPalindrome('cbbd'));

medium

A. The reverse method does not work on strings

B. The slice method is used incorrectly

C. Using >= causes the last palindrome to be chosen instead of the first

D. The loop ranges are off by one

Solution

1. Step 1: Analyze the condition with >=

   The condition uses >=, so if two palindromes have the same length, the later one overwrites the earlier.

2. Step 2: Understand effect on output

   For input 'cbbd', palindromes 'bb' and 'b' exist. Using >= picks the last palindrome of max length, which may not be desired.

3. Final Answer:

   Using >= causes the last palindrome to be chosen instead of the first -> Option C

4. Quick Check:

   Condition >= picks last palindrome [OK]

Hint: Use > to pick first longest palindrome found [OK]

Common Mistakes:

• Thinking slice is incorrect
• Believing reverse doesn't work on strings
• Ignoring >= vs > difference

5. Given the string s = 'forgeeksskeegfor', which approach below efficiently finds the longest palindromic substring and what is that substring?

hard

A. Expand around center approach; longest palindrome is 'eeksskee'

B. Dynamic programming with 2D table; longest palindrome is 'geeksskeeg'

C. Sorting characters and checking; longest palindrome is 'ss'

D. Brute force checking all substrings; longest palindrome is 'forgeeksskeegfor'

Solution

1. Step 1: Understand problem and input

   The string 'forgeeksskeegfor' contains a long palindrome 'geeksskeeg'.

2. Step 2: Evaluate approaches

   Brute force checking all substrings is inefficient and won't find the full string palindrome. Sorting characters loses order, so 'ss' is incorrect. Dynamic programming with 2D table finds 'geeksskeeg' correctly, unlike other options.

3. Final Answer:

   Dynamic programming with 2D table; longest palindrome is 'geeksskeeg' -> Option B

4. Quick Check:

   DP approach finds 'geeksskeeg' efficiently [OK]

Hint: Use DP table to track palindromes efficiently [OK]

Common Mistakes:

• Assuming whole string is palindrome
• Using sorting which breaks character order
• Confusing expand around center with brute force