Array Reversal Techniques in DSA Rust - Time & Space Complexity

Time Complexity: Array Reversal Techniques

O(n)

Understanding Time Complexity

We want to understand how the time it takes to reverse an array changes as the array gets bigger.

How does the number of steps grow when we reverse more items?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

fn reverse_array(arr: &mut [i32]) {
    let mut start = 0;
    let mut end = arr.len().saturating_sub(1);
    while start < end {
        arr.swap(start, end);
        start += 1;
        end -= 1;
    }
}

This code reverses the elements of an array by swapping pairs from the start and end moving towards the center.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Swapping two elements in the array.
• How many times: About half the length of the array (n/2) times.

How Execution Grows With Input

As the array size grows, the number of swaps grows roughly half as fast.

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

Pattern observation: The operations grow linearly with input size, just half as many swaps as elements.

Final Time Complexity

Time Complexity: O(n)

This means the time to reverse the array grows directly in proportion to the number of elements.

Common Mistake

[X] Wrong: "Reversing an array takes constant time because we just swap pairs."

[OK] Correct: Even though each swap is quick, the number of swaps grows with the array size, so total time grows too.

Interview Connect

Understanding how simple loops like this scale helps you explain your code clearly and shows you know how to reason about performance.

Self-Check

"What if we used recursion to reverse the array instead? How would the time complexity change?"

Practice

1. What does reversing an array mean in simple terms?

easy

A. Changing the order of elements so the last becomes first and first becomes last

B. Sorting the array in ascending order

C. Removing duplicate elements from the array

D. Adding new elements to the end of the array

Solution

1. Step 1: Understand array reversal

   Reversing means flipping the order of elements so the last element comes first and the first element goes last.

2. Step 2: Compare with other options

   Sorting arranges elements by value, removing duplicates deletes repeats, and adding elements is insertion, not reversal.

3. Final Answer:

   Changing the order of elements so the last becomes first and first becomes last -> Option A

4. Quick Check:

   Reversal = Flip order [OK]

Hint: Reversal flips order, not sorting or adding [OK]

Common Mistakes:

• Confusing reversal with sorting
• Thinking reversal removes elements
• Mixing reversal with adding elements

2. Which of the following Rust code snippets correctly reverses a mutable array arr in place?

easy

A. arr = arr.reverse();

B. arr.reverse();

C. arr.reverse(&mut arr);

D. reverse(arr);

Solution

1. Step 1: Identify correct method usage

   In Rust, the reverse() method is called directly on a mutable slice or array as arr.reverse(); to reverse it in place.

2. Step 2: Check other options for errors

   arr = arr.reverse(); tries to assign the result of reverse() which returns (), so it's invalid. arr.reverse(&mut arr); passes &mut arr as argument, but reverse() takes no arguments. reverse(arr); calls a function reverse which is undefined.

3. Final Answer:

   arr.reverse(); -> Option B

4. Quick Check:

   Use method directly on mutable array [OK]

Hint: Use arr.reverse() without assignment or arguments [OK]

Common Mistakes:

• Assigning reverse() result to array
• Passing array as argument to reverse()
• Calling undefined reverse function

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

let mut arr = [1, 2, 3, 4, 5];
arr.reverse();
println!("{:?}", arr);

medium

A. [5, 2, 3, 4, 1]

B. [1, 2, 3, 4, 5]

C. [5, 4, 3, 2, 1]

D. Compilation error

Solution

1. Step 1: Understand reverse() effect on array

   The reverse() method reverses the array elements in place, so the order becomes last to first.

2. Step 2: Apply reverse to given array

   Original array is [1, 2, 3, 4, 5]. After reversal, it becomes [5, 4, 3, 2, 1].

3. Final Answer:

   [5, 4, 3, 2, 1] -> Option C

4. Quick Check:

   Reverse flips array order [OK]

Hint: Reverse flips array elements order [OK]

Common Mistakes:

• Expecting original order after reverse
• Thinking reverse sorts array
• Confusing output format

4. Identify the error in this Rust code that tries to reverse an array:

let arr = [10, 20, 30, 40];
arr.reverse();

medium

A. Cannot call reverse() on an immutable array

B. reverse() method does not exist for arrays

C. Missing semicolon after array declaration

D. reverse() requires an argument

Solution

1. Step 1: Check mutability of array

   The array arr is declared immutable by default with let. The reverse() method requires a mutable array.

2. Step 2: Understand method requirements

   To reverse in place, the array must be mutable, declared as let mut arr. Otherwise, calling reverse() causes a compile error.

3. Final Answer:

   Cannot call reverse() on an immutable array -> Option A

4. Quick Check:

   reverse() needs mutable array [OK]

Hint: Make array mutable with 'mut' before reversing [OK]

Common Mistakes:

• Forgetting to add 'mut' to array declaration
• Thinking reverse() needs arguments
• Assuming reverse() is not available for arrays

5. Given a vector vec = vec![1, 2, 3, 4, 5], which code snippet correctly reverses it and returns a new reversed vector without modifying the original?

hard

A. let rev_vec = vec.into_iter().reverse().collect();

B. vec.reverse(); let rev_vec = vec.clone();

C. let rev_vec = vec.reverse();

D. let rev_vec = vec.iter().rev().cloned().collect::();

Solution

1. Step 1: Understand vector reversal without mutation

   To reverse without changing original, use iterator rev() on iter(), clone elements, then collect into new vector.

2. Step 2: Analyze options

   let rev_vec = vec.iter().rev().cloned().collect::(); uses vec.iter().rev().cloned().collect() which creates a new reversed vector. vec.reverse(); let rev_vec = vec.clone(); reverses original vector in place, modifying it. let rev_vec = vec.reverse(); tries to assign reverse() result which is (), invalid. let rev_vec = vec.into_iter().reverse().collect(); uses into_iter() which consumes the original vector, so it doesn't leave the original unmodified.

3. Final Answer:

   let rev_vec = vec.iter().rev().cloned().collect::(); -> Option D

4. Quick Check:

   Use iter().rev().cloned().collect() for new reversed vector [OK]

Hint: Use iter().rev().cloned().collect() for reversed copy [OK]

Common Mistakes:

• Modifying original vector instead of copying
• Assigning reverse() result directly
• Using invalid reverse() on iterator