Palindrome Detection in DSA Javascript - Time & Space Complexity

Time Complexity: Palindrome Detection

O(n)

Understanding Time Complexity

We want to know how the time needed to check if a word or phrase is a palindrome changes as the input gets longer.

How does the number of steps grow when the input size grows?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

function isPalindrome(str) {
  const len = str.length;
  for (let i = 0; i < len / 2; i++) {
    if (str[i] !== str[len - 1 - i]) {
      return false;
    }
  }
  return true;
}
    

This code checks if a string reads the same forwards and backwards by comparing characters from the start and end moving towards the center.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: A single loop that compares pairs of characters.
• How many times: The loop runs about half the length of the string.

How Execution Grows With Input

As the string gets longer, the number of comparisons grows roughly half as fast.

Input Size (n)	Approx. Operations
10	5 comparisons
100	50 comparisons
1000	500 comparisons

Pattern observation: The number of steps grows linearly with input size, but only half as many checks are needed.

Final Time Complexity

Time Complexity: O(n)

This means the time to check a palindrome grows in direct proportion to the length of the string.

Common Mistake

[X] Wrong: "Checking a palindrome takes time proportional to the square of the string length because of nested loops."

[OK] Correct: The code only uses one loop that runs half the string length, so it grows linearly, not quadratically.

Interview Connect

Understanding how palindrome checking scales helps you explain your code clearly and shows you can analyze efficiency, a key skill in interviews.

Self-Check

"What if we changed the code to check every character against every other character? How would the time complexity change?"

Practice

1. What does a palindrome string mean in simple terms?

easy

A. A string that contains only vowels

B. A string that reads the same forwards and backwards

C. A string with all unique characters

D. A string that ends with a special character

Solution

1. Step 1: Understand palindrome definition

   A palindrome is a word or phrase that reads the same forwards and backwards, like 'madam' or 'racecar'.

2. Step 2: Compare options with definition

   Only A string that reads the same forwards and backwards matches this definition exactly.

3. Final Answer:

   A string that reads the same forwards and backwards -> Option B

4. Quick Check:

   Palindrome = same forwards and backwards [OK]

Hint: Palindrome means same forwards and backwards [OK]

Common Mistakes:

• Confusing palindrome with unique characters
• Thinking palindrome means only vowels
• Assuming palindrome ends with special character

2. Which of the following JavaScript code snippets correctly checks if a string str is a palindrome?

easy

A. return str === str.split('').reverse().join('');

B. return str === str.toUpperCase();

C. return str.length === 0;

D. return str.indexOf('a') !== -1;

Solution

1. Step 1: Understand palindrome check logic

   To check palindrome, reverse the string and compare with original.

2. Step 2: Analyze code snippets

   return str === str.split('').reverse().join(''); reverses the string and compares it correctly. Others do unrelated checks.

3. Final Answer:

   return str === str.split('').reverse().join(''); -> Option A

4. Quick Check:

   Reverse and compare = return str === str.split('').reverse().join(''); [OK]

Hint: Reverse string and compare to original [OK]

Common Mistakes:

• Using toUpperCase instead of reversing
• Checking string length instead of content
• Searching for a character instead of palindrome

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

function isPalindrome(s) {
  s = s.toLowerCase().replace(/[^a-z0-9]/g, '');
  return s === s.split('').reverse().join('');
}
console.log(isPalindrome('A man, a plan, a canal: Panama'));

medium

A. false

B. undefined

C. SyntaxError

D. true

Solution

1. Step 1: Normalize string by removing non-alphanumeric and lowercasing

   The string becomes 'amanaplanacanalpanama' after cleaning.

2. Step 2: Check if cleaned string equals its reverse

   Reversing 'amanaplanacanalpanama' gives the same string, so returns true.

3. Final Answer:

   true -> Option D

4. Quick Check:

   Clean and compare reversed string = true [OK]

Hint: Ignore case and non-letters, then compare reversed [OK]

Common Mistakes:

• Not removing spaces and punctuation
• Ignoring case differences
• Expecting false due to original formatting

4. Find the error in this palindrome check function:

function checkPalindrome(str) {
  for(let i = 0; i < str.length; i++) {
    if(str[i] !== str[str.length - i]) {
      return false;
    }
  }
  return true;
}

medium

A. Index for comparison should be str.length - i - 1

B. No error, function works correctly

C. Function should convert string to lowercase first

D. Loop should run only till half the string length

Solution

1. Step 1: Analyze index used for comparison

   Index str.length - i is off by one because string indices start at 0.

2. Step 2: Correct index calculation

   It should be str.length - i - 1 to compare correct characters from end.

3. Final Answer:

   Index for comparison should be str.length - i - 1 -> Option A

4. Quick Check:

   Off-by-one index error fixed by subtracting 1 [OK]

Hint: Remember last index is length - 1 [OK]

Common Mistakes:

• Using full length instead of half for loop
• Ignoring off-by-one in index
• Assuming case sensitivity causes error here

5. You want to check if a sentence is a palindrome ignoring spaces, punctuation, and case. Which approach is best to implement in JavaScript?

hard

A. Check if string length is even or odd first

B. Compare original string with reversed string directly

C. Remove non-alphanumeric characters, convert to lowercase, then compare with reversed string

D. Count vowels and consonants and compare counts

Solution

1. Step 1: Understand requirements for ignoring spaces, punctuation, and case

   We must clean the string by removing unwanted characters and normalize case.

2. Step 2: Choose approach that cleans and compares reversed string

   Remove non-alphanumeric characters, convert to lowercase, then compare with reversed string correctly removes non-alphanumeric characters, converts to lowercase, then compares reversed string.

3. Final Answer:

   Remove non-alphanumeric characters, convert to lowercase, then compare with reversed string -> Option C

4. Quick Check:

   Clean and compare reversed string for sentence palindrome [OK]

Hint: Clean string before palindrome check for sentences [OK]

Common Mistakes:

• Comparing raw strings with punctuation
• Ignoring case differences
• Using vowel/consonant counts which is unrelated