Boolean indexing in NumPy - Time & Space Complexity

Time Complexity: Boolean indexing

O(n)

Understanding Time Complexity

We want to understand how the time it takes to select data using boolean indexing changes as the data size grows.

How does the work grow when we filter arrays with conditions?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import numpy as np

arr = np.arange(1000)
mask = arr % 2 == 0
filtered = arr[mask]

This code creates an array, makes a mask for even numbers, and selects those numbers using boolean indexing.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Checking each element against the condition (arr % 2 == 0) and then selecting elements based on the mask.
• How many times: Once for each element in the array, so n times where n is the array size.

How Execution Grows With Input

As the array size grows, the number of checks and selections grows roughly the same way.

Input Size (n)	Approx. Operations
10	About 10 checks and selections
100	About 100 checks and selections
1000	About 1000 checks and selections

Pattern observation: The work grows directly with the size of the input array.

Final Time Complexity

Time Complexity: O(n)

This means the time to filter grows in a straight line as the array gets bigger.

Common Mistake

[X] Wrong: "Boolean indexing is instant no matter the array size because it just picks elements."

[OK] Correct: Actually, it must check each element to decide if it fits the condition, so it takes longer with bigger arrays.

Interview Connect

Understanding how filtering data scales helps you write efficient code and explain your choices clearly in real projects and interviews.

Self-Check

"What if we used multiple conditions combined with & or | in the mask? How would the time complexity change?"