Modifying arrays in Javascript - Time & Space Complexity

Time Complexity: Modifying arrays

O(n)

Understanding Time Complexity

When we change items in an array, the time it takes can grow as the array gets bigger.

We want to know how the work needed changes when we add or remove items.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

const arr = [1, 2, 3, 4, 5];

// Add an item at the end
arr.push(6);

// Remove the first item
arr.shift();

// Insert an item at index 2
arr.splice(2, 0, 10);
    

This code adds, removes, and inserts items in an array at different positions.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Moving elements to make space or close gaps when inserting or removing.
• How many times: Depends on how many elements need to shift after the change.

How Execution Grows With Input

When adding at the end, work stays about the same no matter the size.

When removing or inserting near the start, many elements must move, so work grows with array size.

Input Size (n)	Approx. Operations
10	Few to 10 moves
100	Few to 100 moves
1000	Few to 1000 moves

Pattern observation: Inserting or removing at the start or middle means more moves as array grows; adding at the end stays quick.

Final Time Complexity

Time Complexity: O(n)

This means the time to insert or remove items can grow directly with the number of elements in the array.

Common Mistake

[X] Wrong: "Adding or removing items anywhere in an array always takes the same time."

[OK] Correct: Removing or inserting at the start or middle requires shifting many elements, so it takes longer as the array grows.

Interview Connect

Understanding how array changes affect time helps you explain your code choices clearly and shows you know how data structures work behind the scenes.

Self-Check

"What if we used a linked list instead of an array? How would the time complexity for inserting or removing items change?"