Array Deletion at Beginning in DSA Rust - Time & Space Complexity

Time Complexity: Array Deletion at Beginning

O(n)

Understanding Time Complexity

We want to understand how long it takes to remove the first item from an array.

How does the work grow when the array gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

fn delete_first(arr: &mut Vec<i32>) {
    if !arr.is_empty() {
        arr.remove(0);
    }
}
    

This code removes the first element from a dynamic array if it is not empty.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Shifting all elements after the first one to the left by one position.
• How many times: For an array of size n, this shift happens n-1 times.

How Execution Grows With Input

When the array size grows, the number of elements to shift grows almost the same.

Input Size (n)	Approx. Operations
10	9 shifts
100	99 shifts
1000	999 shifts

Pattern observation: The work grows roughly in a straight line with the array size.

Final Time Complexity

Time Complexity: O(n)

This means the time to delete the first element grows linearly with the number of elements in the array.

Common Mistake

[X] Wrong: "Removing the first element is always fast because it's just one item."

[OK] Correct: Because all other elements must move to fill the gap, the work depends on the array size.

Interview Connect

Knowing this helps you explain why some data structures are better for front deletions, showing your understanding of efficiency.

Self-Check

"What if we used a linked list instead of an array? How would the time complexity change?"

Practice

1. What happens when you delete the first element from an array in Rust using remove(0)?

easy

A. The array elements remain unchanged.

B. The last element is removed instead of the first.

C. The array becomes empty regardless of its original size.

D. The first element is removed and all other elements shift left by one position.

Solution

1. Step 1: Understand remove(0) method

   The remove(0) method removes the element at index 0, which is the first element in the array.

2. Step 2: Effect on array elements

   After removal, all elements to the right shift left by one to fill the gap, reducing the array length by one.

3. Final Answer:

   The first element is removed and all other elements shift left by one position. -> Option D

4. Quick Check:

   Deleting at start shifts elements left [OK]

Hint: Deleting at index 0 shifts all elements left by one [OK]

Common Mistakes:

• Thinking last element is removed instead of first
• Assuming array size stays the same
• Believing elements do not shift after deletion

2. Which of the following Rust code snippets correctly deletes the first element from a vector v?

easy

A. v.remove(0);

B. v.delete(0);

C. v.pop_front();

D. v.shift();

Solution

1. Step 1: Identify correct Rust method for deletion at index

   Rust vectors use remove(index) to delete element at a specific position.

2. Step 2: Check other options for validity

   delete, pop_front, and shift are not valid Rust vector methods.

3. Final Answer:

   v.remove(0); -> Option A

4. Quick Check:

   Use remove(0) to delete first element [OK]

Hint: Use remove(0) to delete first element in Rust vector [OK]

Common Mistakes:

• Using non-existent methods like pop_front or shift
• Confusing Rust with other languages' syntax
• Trying to use delete which is invalid in Rust

3. What is the output of the following Rust code?

let mut v = vec![10, 20, 30, 40];
v.remove(0);
println!("{:?}", v);

medium

A. [20, 30, 40]

B. [10, 20, 30, 40]

C. [30, 40]

D. [40]

Solution

1. Step 1: Initial vector elements

   The vector v starts as [10, 20, 30, 40].

2. Step 2: Remove first element

   v.remove(0) removes 10, shifting remaining elements left.

3. Step 3: Resulting vector

   After removal, v becomes [20, 30, 40].

4. Final Answer:

   [20, 30, 40] -> Option A

5. Quick Check:

   Remove first element shifts left [OK]

Hint: Removing index 0 drops first element, shifts others left [OK]

Common Mistakes:

• Expecting original vector unchanged
• Thinking multiple elements removed
• Confusing output format

4. Identify the error in this Rust code that tries to delete the first element of a vector:

let mut v = vec![1, 2, 3];
v.remove();

medium

A. Cannot remove elements from a vector.

B. Missing index argument in remove method.

C. remove method does not exist for vectors.

D. Vector cannot be mutable.

Solution

1. Step 1: Check method signature

   The remove method requires an index argument specifying which element to remove.

2. Step 2: Identify missing argument

   The code calls v.remove() without any index, causing a compile error.

3. Final Answer:

   Missing index argument in remove method. -> Option B

4. Quick Check:

   remove needs index argument [OK]

Hint: Always provide index to remove method [OK]

Common Mistakes:

• Calling remove without index
• Thinking remove works like pop() without arguments
• Assuming vector immutability causes error

5. Given a vector v = vec![5, 10, 15, 20, 25], write Rust code to delete the first two elements and print the resulting vector. What will be the output?

hard

A. [5, 10, 15]

B. [10, 15, 20, 25]

C. [15, 20, 25]

D. [20, 25]

Solution

1. Step 1: Remove first element twice

   Calling v.remove(0) twice removes elements at index 0 each time, first 5 then 10.

2. Step 2: Resulting vector after removals

   After removals, vector becomes [15, 20, 25].

3. Final Answer:

   [15, 20, 25] -> Option C

4. Quick Check:

   Two removals at index 0 drop first two elements [OK]

Hint: Remove index 0 repeatedly to delete from start [OK]

Common Mistakes:

• Removing only once instead of twice
• Removing wrong indices after first removal
• Expecting original vector unchanged