Logical operations (and, or, not) in NumPy - Time & Space Complexity

Time Complexity: Logical operations (and, or, not)

O(n)

Understanding Time Complexity

We want to understand how the time it takes to do logical operations with numpy arrays changes as the arrays get bigger.

Specifically, how does the work grow when using and, or, and not on arrays?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import numpy as np

arr1 = np.random.choice([True, False], size=1000)
arr2 = np.random.choice([True, False], size=1000)

result_and = np.logical_and(arr1, arr2)
result_or = np.logical_or(arr1, arr2)
result_not = np.logical_not(arr1)

This code creates two arrays of True/False values and applies logical AND, OR, and NOT element-wise.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Element-wise logical operations on arrays.
• How many times: Once for each element in the arrays (n times, where n is array length).

How Execution Grows With Input

As the array size grows, the number of logical checks grows directly with it.

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

Pattern observation: The work grows in a straight line with the input size.

Final Time Complexity

Time Complexity: O(n)

This means the time to do logical operations grows directly with the number of elements.

Common Mistake

[X] Wrong: "Logical operations on arrays are instant and don't depend on size."

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

Interview Connect

Understanding how logical operations scale helps you write efficient code when working with large data sets.

Self-Check

"What if we used nested arrays (2D arrays) instead of 1D? How would the time complexity change?"