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?"

Practice

1. What does boolean indexing in numpy allow you to do?

easy

A. Create a new array filled with zeros

B. Change the data type of an array

C. Sort the array elements in ascending order

D. Select elements from an array using a True/False mask

Solution

1. Step 1: Understand boolean indexing concept

   Boolean indexing uses a True/False array to pick elements from another array.

2. Step 2: Identify the correct operation

   Only Select elements from an array using a True/False mask describes selecting elements based on True/False values.

3. Final Answer:

   Select elements from an array using a True/False mask -> Option D

4. Quick Check:

   Boolean indexing = Select elements [OK]

Hint: Boolean mask picks elements where True appears [OK]

Common Mistakes:

• Confusing boolean indexing with sorting
• Thinking it changes data types
• Assuming it creates new arrays with zeros

2. Which of the following is the correct syntax to select elements greater than 5 from a numpy array arr using boolean indexing?

easy

A. arr[arr < 5]

B. arr > 5[arr]

C. arr[arr > 5]

D. arr.select(arr > 5)

Solution

1. Step 1: Understand boolean indexing syntax

   The correct syntax is to use the array with a boolean mask inside square brackets: arr[condition].

2. Step 2: Check each option

   arr[arr > 5] uses arr[arr > 5], which is correct. Others have wrong order or invalid methods.

3. Final Answer:

   arr[arr > 5] -> Option C

4. Quick Check:

   Correct syntax = arr[condition] [OK]

Hint: Put condition inside brackets after array name [OK]

Common Mistakes:

• Placing condition before array name
• Using invalid methods like select()
• Using wrong comparison operators

3. What is the output of the following code?

import numpy as np
arr = np.array([2, 7, 4, 9, 1])
result = arr[arr % 2 == 1]

medium

A. [7 9 1]

B. [2 4]

C. [7 4 9]

D. [2 7 4 9 1]

Solution

1. Step 1: Understand the condition arr % 2 == 1

   This condition selects elements where the remainder when divided by 2 is 1, i.e., odd numbers.

2. Step 2: Apply condition to array elements

   Elements 7, 9, and 1 are odd, so they are selected.

3. Final Answer:

   [7 9 1] -> Option A

4. Quick Check:

   Odd elements = [7 9 1] [OK]

Hint: Filter with modulo to get odd numbers [OK]

Common Mistakes:

• Selecting even numbers instead
• Confusing modulo operator
• Returning full array instead of filtered

4. The following code has a problem. What is the problem?

import numpy as np
arr = np.array([1, 2, 3, 4])
mask = arr > 2
print(arr[mask == True])

medium

A. mask == True is unnecessary and redundant

B. arr should be converted to list first

C. Comparison operator > is invalid for numpy arrays

D. Square brackets cannot be used for indexing

Solution

1. Step 1: Analyze the boolean mask creation

   mask = arr > 2 creates a boolean array correctly.

2. Step 2: Check the indexing expression

   Using mask == True is redundant since mask is already boolean. It's unnecessary and bad practice.

3. Step 3: Correct usage

   Use arr[mask] directly without comparing mask to True.

4. Final Answer:

   mask == True is unnecessary and redundant -> Option A

5. Quick Check:

   Use boolean mask directly [OK]

Hint: Use mask directly, no need for '== True' [OK]

Common Mistakes:

• Adding '== True' to boolean mask
• Trying to convert numpy array to list for indexing
• Misunderstanding comparison operators

5. Given a numpy array data = np.array([10, 15, 20, 25, 30]), how can you select elements greater than 12 and less than 28 using boolean indexing?

hard

A. data[data > 12 and data < 28]

B. data[(data > 12) & (data < 28)]

C. data[data > 12 | data < 28]

D. data[(data > 12) or (data < 28)]

Solution

1. Step 1: Understand combining conditions with & and parentheses

   In numpy, use & for element-wise AND and wrap each condition in parentheses.

2. Step 2: Check each option

   data[(data > 12) & (data < 28)] correctly uses & (element-wise AND) with parentheses around each condition. Using Python keywords and/or cause errors because they don't work element-wise on arrays. Using | (bitwise OR) selects elements greater than 12 or less than 28, which is wrong here.

3. Final Answer:

   data[(data > 12) & (data < 28)] -> Option B

4. Quick Check:

   Use & with parentheses for AND conditions [OK]

Hint: Use & with parentheses for multiple conditions [OK]

Common Mistakes:

• Using 'and' or 'or' instead of & or |
• Not using parentheses around conditions
• Using | (OR) instead of & (AND) for filtering