Palindrome Detection in DSA Typescript - Time & Space Complexity

Time Complexity: Palindrome Detection

O(n)

Understanding Time Complexity

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

How many steps does it take to confirm the input reads the same forwards and backwards?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

function isPalindrome(s: string): boolean {
  let left = 0;
  let right = s.length - 1;
  while (left < right) {
    if (s[left] !== s[right]) {
      return false;
    }
    left++;
    right--;
  }
  return true;
}
    

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

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Comparing characters at positions from the start and end of the string.
• How many times: Up to half the length of the string, since it moves inward from both ends.

How Execution Grows With Input

As the string gets longer, the number of character 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 comparisons 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 constant time because you only look at the first and last characters."

[OK] Correct: You need to compare pairs of characters moving inward, which grows with the string length, not just one pair.

Interview Connect

Understanding how palindrome checking scales helps you explain your code clearly and shows you can analyze simple algorithms well.

Self-Check

"What if we only checked characters up to a quarter of the string length? How would that affect the time complexity?"

Practice

1. What does it mean if a string is a palindrome?

easy

A. The string has no spaces

B. The string reads the same forwards and backwards

C. The string contains only letters

D. The string is all uppercase

Solution

1. Step 1: Understand palindrome definition

   A palindrome is a word or phrase that reads the same forwards and backwards.

2. Step 2: Compare options with definition

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

3. Final Answer:

   The string 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 uppercase or letter-only strings
• Thinking palindrome means no spaces
• Assuming palindrome means all lowercase

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

easy

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

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

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

D. return str === str.split('').reverse();

Solution

1. Step 1: Understand string reversal in TypeScript

   To reverse a string, split it into characters, reverse the array, then join back.

2. Step 2: Check each option's correctness

   return str === str.split('').reverse().join(''); uses split(''), reverse(), join('') correctly. Others miss correct methods or arguments.

3. Final Answer:

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

4. Quick Check:

   Correct string reversal syntax = return str === str.split('').reverse().join(''); [OK]

Hint: Use split(''), reverse(), join('') to reverse strings [OK]

Common Mistakes:

• Using reverse() directly on string (not an array)
• Using split() without arguments returns whole string as one element
• Forgetting to join array back to string

3. What will be the output of this TypeScript code?

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

medium

A. true

B. false

C. SyntaxError

D. undefined

Solution

1. Step 1: Clean the string

   The string is converted to lowercase and non-alphanumeric characters removed, resulting in 'amanaplanacanalpanama'.

2. Step 2: Check palindrome condition

   This cleaned string equals its reverse, so function returns true.

3. Final Answer:

   true -> Option A

4. Quick Check:

   Cleaned string equals reversed = true [OK]

Hint: Clean string before checking palindrome for accurate result [OK]

Common Mistakes:

• Not cleaning string before palindrome check
• Assuming spaces or punctuation affect palindrome
• Confusing true/false output

4. Find the error in this palindrome check function:

function checkPalindrome(str: string): boolean {
  const reversed = str.split('').reverse();
  return str === reversed;
}

medium

A. reverse() does not work on strings

B. Function missing return type

C. split('') is incorrect usage

D. reversed is an array, not a string

Solution

1. Step 1: Analyze reversed variable type

   reversed is an array after split and reverse, not a string.

2. Step 2: Compare string with array

   Comparing string to array returns false always; need to join array back to string.

3. Final Answer:

   reversed is an array, not a string -> Option D

4. Quick Check:

   Compare string to string, not array [OK]

Hint: Join reversed array back to string before comparing [OK]

Common Mistakes:

• Comparing string directly to array
• Forgetting to join reversed array
• Assuming split('') returns string

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

hard

A. Convert to lowercase, remove non-alphanumeric chars, then compare with reversed

B. Compare original string with reversed string directly

C. Remove spaces only, then compare

D. Convert to uppercase and compare with reversed uppercase

Solution

1. Step 1: Understand palindrome ignoring spaces and punctuation

   We must clean the string by removing spaces and punctuation and normalize case.

2. Step 2: Choose correct cleaning and comparison

   Convert to lowercase, remove non-alphanumeric chars, then compare with reversed cleans string by removing non-alphanumeric characters and lowercases it before comparing with reversed.

3. Final Answer:

   Convert to lowercase, remove non-alphanumeric chars, then compare with reversed -> Option A

4. Quick Check:

   Clean and normalize before palindrome check [OK]

Hint: Clean string fully before palindrome check for accuracy [OK]

Common Mistakes:

• Only removing spaces but not punctuation
• Comparing without case normalization
• Assuming uppercase conversion alone is enough