Array Insertion at End in DSA Rust - Time & Space Complexity

Time Complexity: Array Insertion at End

O(1) amortized

Understanding Time Complexity

We want to understand how long it takes to add an item at the end of an array.

How does the time needed change as the array grows bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

fn insert_at_end(arr: &mut Vec<i32>, value: i32) {
    arr.push(value);
}

This code adds a new value at the end of a dynamic array (vector).

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Adding one element at the end of the array.
• How many times: Once per insertion call.

How Execution Grows With Input

Adding one element usually takes the same short time, no matter the array size.

Input Size (n)	Approx. Operations
10	1 (simple add)
100	1 (simple add)
1000	1 (simple add)

Pattern observation: Most insertions take constant time, but sometimes resizing the array takes longer.

Final Time Complexity

Time Complexity: O(1) amortized

This means adding an element at the end usually takes the same short time, regardless of array size.

Common Mistake

[X] Wrong: "Adding at the end always takes longer as the array grows."

[OK] Correct: Most insertions are quick because arrays reserve extra space. Only sometimes, when full, the array resizes, which takes longer.

Interview Connect

Knowing this helps you explain why dynamic arrays are efficient for adding items at the end, a common operation in many programs.

Self-Check

"What if we changed the array to a linked list? How would the time complexity of insertion at the end change?"

Practice

1. What does inserting an element at the end of an array mean in simple terms?

easy

A. Sorting the array in ascending order

B. Removing the first item from the array

C. Replacing the first item in the array

D. Adding a new item after the last existing item in the array

Solution

1. Step 1: Understand array structure

   An array is a list of items stored in order, starting from the first to the last.

2. Step 2: Define insertion at the end

   Inserting at the end means placing a new item right after the last item, extending the array by one.

3. Final Answer:

   Adding a new item after the last existing item in the array -> Option D

4. Quick Check:

   Insert at end = Add after last [OK]

Hint: Think: new item goes after the last one [OK]

Common Mistakes:

• Confusing insertion at end with removal
• Thinking insertion replaces an item
• Mixing insertion with sorting

2. Which Rust code snippet correctly inserts the value 10 at the end of a mutable vector named vec?

easy

A. vec.push(10);

B. vec.insert(0, 10);

C. vec[vec.len()] = 10;

D. vec.append(10);

Solution

1. Step 1: Identify correct method to add at end

   In Rust, push adds an element to the end of a vector.

2. Step 2: Check other options

   insert(0, 10) adds at start, vec[vec.len()] = 10 causes error (index out of bounds), append(10) is invalid syntax.

3. Final Answer:

   vec.push(10); -> Option A

4. Quick Check:

   Use push() to add at end [OK]

Hint: Use push() to add at the end of a vector [OK]

Common Mistakes:

• Using insert with wrong index
• Trying to assign to vec[vec.len()] directly
• Using append with a single value

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

let mut numbers = vec![1, 2, 3];
numbers.push(4);
println!("{:?}", numbers);

medium

A. [1, 2, 3]

B. [4, 1, 2, 3]

C. [1, 2, 3, 4]

D. Compilation error

Solution

1. Step 1: Understand initial vector

   The vector numbers starts as [1, 2, 3].

2. Step 2: Apply push operation

   numbers.push(4) adds 4 at the end, making it [1, 2, 3, 4].

3. Final Answer:

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

4. Quick Check:

   push(4) adds 4 at end [OK]

Hint: push() adds element at the end [OK]

Common Mistakes:

• Thinking push adds at start
• Expecting original vector unchanged
• Confusing output format

4. Identify the error in this Rust code that tries to insert 5 at the end of a vector:

let numbers = vec![1, 2, 3];
numbers.push(5);

medium

A. Cannot push because vector is immutable

B. push method does not exist for vectors

C. Syntax error in push call

D. No error, code runs fine

Solution

1. Step 1: Check vector mutability

   The vector numbers is declared without mut, so it is immutable.

2. Step 2: Understand push requirements

   push requires the vector to be mutable to add elements.

3. Final Answer:

   Cannot push because vector is immutable -> Option A

4. Quick Check:

   push needs mutable vector [OK]

Hint: Declare vector as mutable to push [OK]

Common Mistakes:

• Forgetting to add mut keyword
• Assuming push works on immutable vectors
• Misreading error as syntax problem

5. Given a vector vec with elements [2, 4, 6], write Rust code to insert the number 8 at the end and then remove the first element. What will be the final vector?

hard

A. [2, 4, 6, 8]

B. [4, 6, 8]

C. [8, 2, 4, 6]

D. [2, 4, 8]

Solution

1. Step 1: Insert 8 at the end

   Using vec.push(8), vector becomes [2, 4, 6, 8].

2. Step 2: Remove the first element

   Using vec.remove(0), removes 2, vector becomes [4, 6, 8].

3. Final Answer:

   [4, 6, 8] -> Option B

4. Quick Check:

   push then remove first = [4,6,8] [OK]

Hint: Push adds end, remove(0) deletes first [OK]

Common Mistakes:

• Removing last instead of first element
• Not updating vector after push
• Confusing remove index