Palindrome Detection in DSA C# - Time & Space Complexity

Time Complexity: Palindrome Detection

O(n)

Understanding Time Complexity

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

The question is: how does the number of steps grow when the input size grows?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

public bool IsPalindrome(string s)
{
    int left = 0;
    int 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 (n/2 times).

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 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: "The palindrome check takes constant time because it just compares characters."

[OK] Correct: The code compares pairs of characters for about half the string length, so the time grows as the string gets longer, not fixed.

Interview Connect

Understanding this time complexity helps you explain how efficient your palindrome check is and compare it to other string operations.

Self-Check

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

Practice

1. What is a palindrome in the context of strings?

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 is empty

Solution

1. Step 1: Understand palindrome definition

   A palindrome is a word or phrase that reads the same forwards and backwards, ignoring spaces and punctuation.

2. Step 2: Apply definition to options

   A string that reads the same forwards and backwards matches this definition exactly, while others describe different string properties.

3. Final Answer:

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

4. Quick Check:

   Palindrome = Same forwards and backwards [OK]

Hint: Check if string reversed equals original [OK]

Common Mistakes:

• Confusing palindrome with unique characters
• Thinking palindrome means only vowels
• Assuming empty string is always palindrome

2. Which of the following C# code snippets correctly checks if a string s is a palindrome?

easy

A. return s.Length == 0;

B. return s == s.ToUpper();

C. return s == new string(s.Reverse().ToArray());

D. return s[0] == s[s.Length];

Solution

1. Step 1: Understand palindrome check logic

   To check palindrome, compare string with its reversed version.

2. Step 2: Analyze each option

   return s == new string(s.Reverse().ToArray()); reverses string and compares correctly. return s == s.ToUpper(); compares uppercase, not palindrome. return s.Length == 0; checks empty string only. return s[0] == s[s.Length]; accesses invalid index (out of range).

3. Final Answer:

   return s == new string(s.Reverse().ToArray()); -> Option C

4. Quick Check:

   Reverse and compare = return s == new string(s.Reverse().ToArray()); [OK]

Hint: Reverse string and compare to original [OK]

Common Mistakes:

• Using wrong index causing out of range error
• Comparing uppercase instead of reversed string
• Checking only empty string

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

string s = "level";
bool isPalindrome = s == new string(s.Reverse().ToArray());
Console.WriteLine(isPalindrome);

medium

A. True

B. False

C. Compilation error

D. Runtime exception

Solution

1. Step 1: Reverse the string "level"

   Reversed string is "level", same as original.

2. Step 2: Compare original and reversed strings

   Since both are equal, isPalindrome is true, so Console.WriteLine prints True.

3. Final Answer:

   True -> Option A

4. Quick Check:

   "level" reversed = "level" [OK]

Hint: Check if reversed string equals original [OK]

Common Mistakes:

• Assuming output is False for palindromes
• Confusing compilation error due to Reverse()
• Thinking runtime exception occurs

4. Identify the error in this palindrome check code and select the fix:

string s = "test";
bool isPalindrome = true;
for (int i = 0; i <= s.Length / 2; i++)
{
    if (s[i] != s[s.Length - i])
    {
        isPalindrome = false;
        break;
    }
}
Console.WriteLine(isPalindrome);

medium

A. Remove the break statement

B. Change loop condition to i < s.Length

C. Initialize isPalindrome to false

D. Change s.Length - i to s.Length - i - 1

Solution

1. Step 1: Identify index error in character comparison

   String indices go from 0 to s.Length - 1, so s[s.Length - i] is out of range when i=0.

2. Step 2: Fix index to s.Length - i - 1

   This correctly accesses the mirrored character from the end.

3. Final Answer:

   Change s.Length - i to s.Length - i - 1 -> Option D

4. Quick Check:

   Correct index fixes out of range error [OK]

Hint: Remember last index is length minus one [OK]

Common Mistakes:

• Using s.Length - i instead of s.Length - i - 1
• Looping beyond half the string length
• Removing break causing unnecessary checks

5. You want to detect if a string is a palindrome ignoring case and spaces. Which code snippet correctly implements this in C#?

hard

A. string clean = new string(s.Where(char.IsLetterOrDigit).ToArray()).ToLower();
bool isPal = clean == new string(clean.Reverse().ToArray());

B. string clean = s.Replace(" ", "");
bool isPal = clean == clean.ToUpper();

C. bool isPal = s == new string(s.Reverse().ToArray());

D. bool isPal = s.ToLower() == s.ToUpper();

Solution

1. Step 1: Clean string by removing non-letter/digit and convert to lowercase

   string clean = new string(s.Where(char.IsLetterOrDigit).ToArray()).ToLower(); bool isPal = clean == new string(clean.Reverse().ToArray()); uses Where with char.IsLetterOrDigit and ToLower to normalize string.

2. Step 2: Reverse cleaned string and compare

   string clean = new string(s.Where(char.IsLetterOrDigit).ToArray()).ToLower(); bool isPal = clean == new string(clean.Reverse().ToArray()); reverses cleaned string and compares correctly for palindrome ignoring case and spaces.

3. Final Answer:

   string clean = new string(s.Where(char.IsLetterOrDigit).ToArray()).ToLower(); bool isPal = clean == new string(clean.Reverse().ToArray()); -> Option A

4. Quick Check:

   Normalize then reverse and compare = string clean = new string(s.Where(char.IsLetterOrDigit).ToArray()).ToLower(); bool isPal = clean == new string(clean.Reverse().ToArray()); [OK]

Hint: Remove spaces and lowercase before checking palindrome [OK]

Common Mistakes:

• Not removing spaces or punctuation
• Comparing original string without normalization
• Using uppercase comparison incorrectly