Valid Palindrome Two Pointer in DSA Python - Time & Space Complexity

Time Complexity: Valid Palindrome Two Pointer

O(n)

Understanding Time Complexity

We want to know how the time taken to check if a string is a palindrome grows as the string gets longer.

Specifically, how many steps does the two-pointer method take as input size increases?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

def is_palindrome(s: str) -> bool:
    left, right = 0, len(s) - 1
    while left < right:
        if s[left] != s[right]:
            return False
        left += 1
        right -= 1
    return True

This code checks if a string reads the same forwards and backwards using two pointers moving towards the center.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Comparing characters at two positions in the string.
• How many times: At most, half the length of the string (n/2) times.

How Execution Grows With Input

As the string length grows, 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 grows directly in proportion to the string length.

Common Mistake

[X] Wrong: "The two-pointer method checks every character twice, so it takes O(2n) time."

[OK] Correct: The method compares pairs from both ends simultaneously, so it only needs about n/2 comparisons, which is still O(n) because constants are ignored.

Interview Connect

Understanding this simple linear time check helps build confidence for string problems and shows you can reason about efficient scanning techniques.

Self-Check

"What if we ignored non-alphanumeric characters and spaces? How would the time complexity change?"

Practice

1. What does the two-pointer technique check when verifying if a string is a palindrome?

easy

A. It counts the number of vowels in the string

B. It compares characters from the start and end moving towards the center

C. It reverses the string and compares with the original

D. It sorts the characters and checks if sorted string equals original

Solution

1. Step 1: Understand two-pointer technique

   Two pointers start at the beginning and end of the string.

2. Step 2: Compare characters moving inward

   Characters at both pointers are compared; pointers move closer if equal.

3. Final Answer:

   It compares characters from the start and end moving towards the center -> Option B

4. Quick Check:

   Two-pointer palindrome check = comparing ends [OK]

Hint: Compare characters from both ends moving inward [OK]

Common Mistakes:

• Thinking it reverses the string
• Checking only vowels or sorting characters
• Using one pointer only

2. Which of the following is the correct syntax to initialize two pointers for a palindrome check in Python?

easy

A. left = 1; right = len(s)

B. left = -1; right = len(s) + 1

C. left = len(s); right = 0

D. left = 0; right = len(s) - 1

Solution

1. Step 1: Identify pointer start positions

   Left pointer starts at 0 (first character), right pointer at last index (length - 1).

2. Step 2: Check syntax correctness

   left = 0; right = len(s) - 1 correctly sets left=0 and right=len(s)-1 for valid indexing.

3. Final Answer:

   left = 0; right = len(s) - 1 -> Option D

4. Quick Check:

   Start pointers at 0 and last index [OK]

Hint: Start left at 0 and right at length minus one [OK]

Common Mistakes:

• Starting right pointer at length (out of range)
• Starting left pointer at 1 (skips first char)
• Using negative or invalid indices

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

def is_palindrome(s):
    left, right = 0, len(s) - 1
    while left < right:
        if s[left] != s[right]:
            return False
        left += 1
        right -= 1
    return True

print(is_palindrome('racecar'))
print(is_palindrome('hello'))

medium

A. True\nTrue

B. False\nTrue

C. True\nFalse

D. False\nFalse

Solution

1. Step 1: Check 'racecar' palindrome

   Characters match from both ends, so returns True.

2. Step 2: Check 'hello' palindrome

   Characters differ ('h' != 'o'), returns False.

3. Final Answer:

   True\nFalse -> Option C

4. Quick Check:

   'racecar' palindrome = True, 'hello' not = False [OK]

Hint: Check characters from ends; mismatch means False [OK]

Common Mistakes:

• Assuming 'hello' is palindrome
• Returning True without full check
• Mixing up True/False outputs

4. Find the error in this palindrome check code:

def check_palindrome(s):
    left, right = 0, len(s)
    while left < right:
        if s[left] != s[right]:
            return False
        left += 1
        right -= 1
    return True

medium

A. right should be initialized as len(s) - 1

B. left should start at 1

C. The while condition should be left <= right

D. The function should return False at the end

Solution

1. Step 1: Check pointer initialization

   Right pointer is set to len(s), which is out of string index range.

2. Step 2: Correct pointer initialization

   Right should be len(s) - 1 to point to last character index.

3. Final Answer:

   right should be initialized as len(s) - 1 -> Option A

4. Quick Check:

   Right pointer must be last index, not length [OK]

Hint: Right pointer = length minus one, not length [OK]

Common Mistakes:

• Using len(s) as index causes IndexError
• Changing left pointer start incorrectly
• Incorrect loop condition

5. Given the string s = "A man, a plan, a canal: Panama", which modification is needed in the two-pointer palindrome check to correctly identify it as a palindrome?

hard

A. Ignore non-alphanumeric characters and case during comparison

B. Reverse the string and compare directly

C. Only compare vowels in the string

D. Convert string to uppercase and compare characters directly

Solution

1. Step 1: Understand input complexity

   String contains spaces, commas, and mixed case which affect direct comparison.

2. Step 2: Modify comparison logic

   Skip non-alphanumeric characters and compare lowercase versions to ignore case and symbols.

3. Step 3: Why other options fail

   Reversing or uppercase alone won't ignore spaces/punctuation; vowels only is incorrect.

4. Final Answer:

   Ignore non-alphanumeric characters and case during comparison -> Option A

5. Quick Check:

   Clean string and ignore case for palindrome check [OK]

Hint: Skip symbols and compare lowercase chars [OK]

Common Mistakes:

• Not ignoring punctuation and spaces
• Only changing case without skipping symbols
• Comparing vowels only