Palindrome Detection in DSA Rust - Time & Space Complexity

Time Complexity: Palindrome Detection

O(n)

Understanding Time Complexity

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

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

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

fn is_palindrome(s: &str) -> bool {
    let bytes = s.as_bytes();
    let mut left = 0;
    let mut right = bytes.len().saturating_sub(1);
    while left < right {
        if bytes[left] != bytes[right] {
            return false;
        }
        left += 1;
        right -= 1;
    }
    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 from the start and end of the string.
• How many times: About half the length of the string (n/2) times.

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, just half as many checks.

Final Time Complexity

Time Complexity: O(n)

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

Common Mistake

[X] Wrong: "Checking a palindrome takes constant time because we only compare a few characters."

[OK] Correct: Even though we compare pairs from both ends, the number of comparisons grows with the string length, so it is not constant time.

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 used recursion instead of a loop? How would the time complexity change?"

Practice

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

easy

A. It has all unique characters

B. It contains only vowels

C. It is always an even length string

D. It reads the same forwards and backwards

Solution

1. Step 1: Understand palindrome definition

   A palindrome is a word or phrase that reads the same from left to right and right to left.

2. Step 2: Check options against definition

   Only It reads the same forwards and backwards matches this meaning exactly.

3. Final Answer:

   It reads the same forwards and backwards -> Option D

4. Quick Check:

   Palindrome = Same forwards and backwards [OK]

Hint: Palindrome means mirror reading same both ways [OK]

Common Mistakes:

• Confusing palindrome with unique characters
• Thinking palindrome must be even length
• Assuming palindrome only has vowels

2. Which Rust code snippet correctly checks if a string s is a palindrome?

easy

A. s.reverse() == s

B. s.chars().eq(s.chars().rev())

C. s == s.reverse()

D. s.chars().all(|c| c == s.chars().next().unwrap())

Solution

1. Step 1: Understand Rust string palindrome check

   To check palindrome, compare characters iterator with its reverse iterator.

2. Step 2: Analyze options

   s.chars().eq(s.chars().rev()) uses chars().eq(chars().rev()) which correctly compares forward and backward characters. Options A and C use invalid methods or wrong comparisons. s.chars().all(|c| c == s.chars().next().unwrap()) checks if all characters are same, not palindrome.

3. Final Answer:

   s.chars().eq(s.chars().rev()) -> Option B

4. Quick Check:

   Compare chars iterator with reversed iterator [OK]

Hint: Use chars().eq(chars().rev()) to check palindrome [OK]

Common Mistakes:

• Using reverse() method on &str which does not exist
• Comparing string with reversed string incorrectly
• Checking all chars equal instead of palindrome

3. What is the output of this Rust code?

let s = "racecar";
let result = s.chars().eq(s.chars().rev());
println!("{}", result);

medium

A. true

B. Runtime panic

C. Compilation error

D. false

Solution

1. Step 1: Analyze the string and palindrome check

   The string "racecar" reads the same forwards and backwards, so it is a palindrome.

2. Step 2: Understand the code output

   The code compares characters forward and backward and returns true for palindrome strings. So, it prints true.

3. Final Answer:

   true -> Option A

4. Quick Check:

   "racecar" palindrome check = true [OK]

Hint: Check if string equals its reverse chars [OK]

Common Mistakes:

• Assuming palindrome check returns false for odd length
• Thinking code causes compile or runtime error
• Confusing output with string itself

4. Identify the error in this Rust palindrome check code:

fn is_palindrome(s: &str) -> bool {
    s == s.chars().rev().collect::<String>()
}

medium

A. Cannot compare &str with String directly

B. Missing semicolon after collect

C. chars().rev() does not exist

D. Function return type should be String

Solution

1. Step 1: Understand types in comparison

   The left side is &str, right side is String from collect(). Direct comparison between &str and String is not allowed.

2. Step 2: Fix type mismatch

   Convert left side to String or right side to &str for comparison. For example, use s.to_string() == s.chars().rev().collect::<String>().

3. Final Answer:

   Cannot compare &str with String directly -> Option A

4. Quick Check:

   Type mismatch in comparison causes error [OK]

Hint: Compare same types: &str vs &str or String vs String [OK]

Common Mistakes:

• Ignoring type mismatch error
• Assuming collect needs semicolon inside expression
• Thinking chars().rev() is invalid method

5. You want to detect palindromes ignoring case and spaces in Rust. Which code snippet correctly implements this?

hard

A. let is_pal = s.chars().all(|c| c.is_alphanumeric());

B. let lower = s.to_lowercase();
let is_pal = lower == lower.reverse();

C. let filtered: String = s.chars().filter(|c| !c.is_whitespace()).collect();
let lower = filtered.to_lowercase();
let is_pal = lower.chars().eq(lower.chars().rev());

D. let filtered: String = s.chars().filter(|c| c.is_whitespace()).collect();
let is_pal = filtered == filtered.chars().rev().collect::<String>();

Solution

1. Step 1: Remove spaces and convert to lowercase

   let filtered: String = s.chars().filter(|c| !c.is_whitespace()).collect(); let lower = filtered.to_lowercase(); let is_pal = lower.chars().eq(lower.chars().rev()); filters out whitespace, collects characters, then converts to lowercase string.

2. Step 2: Check palindrome on cleaned string

   It compares characters forward and backward correctly on the cleaned lowercase string.

3. Final Answer:

   let filtered: String = s.chars().filter(|c| !c.is_whitespace()).collect(); let lower = filtered.to_lowercase(); let is_pal = lower.chars().eq(lower.chars().rev()); -> Option C

4. Quick Check:

   Filter spaces + lowercase + compare reversed chars [OK]

Hint: Clean string first: remove spaces, lowercase, then check palindrome [OK]

Common Mistakes:

• Using reverse() method which does not exist
• Filtering only whitespace but not converting case
• Checking all chars alphanumeric instead of palindrome