Array operations (append, insert, remove) in Swift - Time & Space Complexity

Time Complexity: Array operations (append, insert, remove)

O(1) for append, O(n) for insert and remove

Understanding Time Complexity

When working with arrays, it's important to know how fast operations like adding or removing items happen.

We want to understand how the time to do these operations changes as the array grows.

Scenario Under Consideration

Analyze the time complexity of these common array operations in Swift.

var numbers = [1, 2, 3, 4, 5]
numbers.append(6)          // Add at the end
numbers.insert(0, at: 0)  // Insert at the start
numbers.remove(at: 2)     // Remove from middle
    

This code shows adding, inserting, and removing elements in an array.

Identify Repeating Operations

Look at what happens inside each operation:

• Primary operation: Moving elements to make space or fill gaps.
• How many times: Depends on position: appending moves none, inserting/removing near start moves many.

How Execution Grows With Input

As the array gets bigger, the cost changes differently for each operation.

Input Size (n)	Append	Insert at start	Remove from middle
10	~1 operation	~10 operations	~8 operations
100	~1 operation	~100 operations	~50 operations
1000	~1 operation	~1000 operations	~500 operations

Pattern observation: Appending stays fast, but inserting or removing near the start or middle grows with array size.

Final Time Complexity

Time Complexity: O(1) for append, O(n) for insert and remove

This means adding at the end is quick no matter the size, but inserting or removing inside takes longer as the array grows.

Common Mistake

[X] Wrong: "All array operations take the same time regardless of position."

[OK] Correct: Because inserting or removing inside requires shifting many elements, which takes more time as the array grows.

Interview Connect

Understanding these differences helps you explain why some operations are faster and shows you know how data structures work under the hood.

Self-Check

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