np.full() for custom-filled arrays in NumPy - Time & Space Complexity

Time Complexity: np.full() for custom-filled arrays

O(n)

Understanding Time Complexity

We want to understand how the time needed to create an array filled with a specific value changes as the array size grows.

How does the work increase when we ask numpy to fill bigger arrays?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import numpy as np

# Create a 1D array of size n filled with the value 7
n = 1000
arr = np.full(n, 7)

This code creates a numpy array of length n, filling every element with the number 7.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Filling each element of the array with the given value.
• How many times: Exactly once for each element, so n times.

How Execution Grows With Input

As the array size grows, the time to fill it grows in direct proportion.

Input Size (n)	Approx. Operations
10	10 fill operations
100	100 fill operations
1000	1000 fill operations

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

Final Time Complexity

Time Complexity: O(n)

This means the time to create and fill the array grows linearly with the number of elements.

Common Mistake

[X] Wrong: "np.full() fills the array instantly regardless of size because it uses a shortcut."

[OK] Correct: Even though numpy is fast, it must still set each element, so time grows with array size.

Interview Connect

Understanding how array creation scales helps you reason about data preparation speed, a key skill in data science and coding interviews.

Self-Check

What if we changed np.full() to create a 2D array of size n by m? How would the time complexity change?