Array initialization in C - Time & Space Complexity

Time Complexity: Array initialization

O(n)

Understanding Time Complexity

When we create and fill an array, the time it takes depends on how many items we add.

We want to know how the work grows as the array size grows.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

int arr[1000];
for (int i = 0; i < 1000; i++) {
    arr[i] = 0;
}
    

This code sets each element of an array with 1000 items to zero.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Setting each array element to zero inside the loop.
• How many times: Exactly 1000 times, once for each element.

How Execution Grows With Input

As the array size grows, the number of steps grows the same way.

Input Size (n)	Approx. Operations
10	10 steps
100	100 steps
1000	1000 steps

Pattern observation: Doubling the array size doubles the work needed.

Final Time Complexity

Time Complexity: O(n)

This means the time to initialize grows directly with the number of elements.

Common Mistake

[X] Wrong: "Initializing an array is instant no matter the size."

[OK] Correct: Each element must be set one by one, so bigger arrays take more time.

Interview Connect

Understanding how array initialization scales helps you explain performance in real code.

Self-Check

"What if we initialize the array with a fixed value using a library function? How would the time complexity change?"