Boolean type in NumPy - Time & Space Complexity

Time Complexity: Boolean type

O(n)

Understanding Time Complexity

We want to understand how fast operations with Boolean arrays run in numpy.

How does the time needed change when the array gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import numpy as np

arr = np.random.choice([True, False], size=1000)
result = np.sum(arr)

This code creates a Boolean array and counts how many True values it has.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Checking each element in the Boolean array to count True values.
• How many times: Once for every element in the array.

How Execution Grows With Input

As the array gets bigger, the time to count True values grows in a straight line.

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

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

Final Time Complexity

Time Complexity: O(n)

This means the time grows directly with the number of elements in the array.

Common Mistake

[X] Wrong: "Counting True values is instant and does not depend on array size."

[OK] Correct: The code must check each element once, so bigger arrays take more time.

Interview Connect

Knowing how Boolean operations scale helps you explain performance clearly and shows you understand data handling basics.

Self-Check

"What if we used a numpy function that stops early when a True is found? How would the time complexity change?"

Practice

1. What does the bool type in numpy represent?

easy

A. Values that are either True or False

B. Integer numbers only

C. Floating point numbers

D. Text strings

Solution

1. Step 1: Understand the boolean type meaning

   The boolean type stores only two possible values: True or False.

2. Step 2: Compare with other types

   Integer, float, and string types store numbers or text, not boolean values.

3. Final Answer:

   Values that are either True or False -> Option A

4. Quick Check:

   Boolean type = True/False [OK]

Hint: Boolean means True or False only [OK]

Common Mistakes:

• Confusing boolean with integer or float
• Thinking boolean stores text
• Assuming boolean can store multiple values

2. Which of the following is the correct way to create a numpy boolean array?

easy

A. np.array([1, 0, 1], dtype=str)

B. np.array([True, False, True], dtype=bool)

C. np.array([True, False, True], dtype=int)

D. np.array(['True', 'False'], dtype=bool)

Solution

1. Step 1: Check dtype for boolean array

   To create a boolean array, use dtype=bool with True/False values.

2. Step 2: Validate options

   np.array([True, False, True], dtype=bool) uses correct dtype and values. np.array([1, 0, 1], dtype=str) uses string dtype, not boolean. np.array([True, False, True], dtype=int) uses int dtype. np.array(['True', 'False'], dtype=bool) uses strings 'True', 'False' which are not boolean values.

3. Final Answer:

   np.array([True, False, True], dtype=bool) -> Option B

4. Quick Check:

   Boolean array needs dtype=bool [OK]

Hint: Use dtype=bool with True/False values [OK]

Common Mistakes:

• Using string values instead of boolean
• Setting wrong dtype like int or str
• Confusing True/False strings with boolean

3. What is the output of this code?

import numpy as np
arr = np.array([1, 2, 3, 4, 5])
mask = arr > 3
print(mask)

medium

A. [3 4 5]

B. [True True True False False]

C. [False False False True True]

D. [1 1 1 0 0]

Solution

1. Step 1: Evaluate the condition arr > 3

   For each element in arr, check if it is greater than 3: 1>3 False, 2>3 False, 3>3 False, 4>3 True, 5>3 True.

2. Step 2: Understand the mask output

   The mask is a boolean array showing True where condition is met, False otherwise: [False False False True True].

3. Final Answer:

   [False False False True True] -> Option C

4. Quick Check:

   Condition mask = [False False False True True] [OK]

Hint: Compare array with condition to get boolean mask [OK]

Common Mistakes:

• Confusing boolean mask with integer 1/0
• Expecting filtered values instead of mask
• Mixing up True and False positions

4. Find the error in this code snippet:

import numpy as np
arr = np.array([10, 20, 30])
mask = arr = 20
print(mask)

medium

A. print statement syntax error

B. Missing import statement for numpy

C. Array elements are not boolean

D. Using '=' instead of '==' for comparison

Solution

1. Step 1: Identify the assignment vs comparison

   The code uses 'mask = arr = 20' which assigns 20 to arr and mask, not a comparison.

2. Step 2: Correct the comparison operator

   To create a boolean mask, use 'mask = arr == 20' to compare each element with 20.

3. Final Answer:

   Using '=' instead of '==' for comparison -> Option D

4. Quick Check:

   Use '==' for comparison, '=' is assignment [OK]

Hint: Use '==' to compare, not '=' assignment [OK]

Common Mistakes:

• Using single '=' instead of '=='
• Confusing assignment with comparison
• Expecting boolean mask but getting int

5. Given a numpy array data = np.array([5, 10, 15, 20, 25]), how can you use a boolean mask to select only values greater than 12 and less than 22?

hard

A. mask = (data > 12) & (data < 22); result = data[mask]

B. mask = data > 12 or data < 22; result = data[mask]

C. mask = data > 12 and data < 22; result = data[mask]

D. mask = (data > 12) | (data < 22); result = data[mask]

Solution

1. Step 1: Create correct boolean mask with logical AND

   To select values greater than 12 and less than 22, use element-wise AND: (data > 12) & (data < 22).

2. Step 2: Apply mask to data array

   Use the mask to index data: data[mask] returns values meeting both conditions.

3. Final Answer:

   mask = (data > 12) & (data < 22); result = data[mask] -> Option A

4. Quick Check:

   Use '&' for element-wise AND in numpy [OK]

Hint: Use '&' for AND, '|' for OR in numpy boolean masks [OK]

Common Mistakes:

• Using 'and' or 'or' instead of '&' or '|'
• Forgetting parentheses around conditions
• Using '|' (OR) instead of '&' (AND) for both conditions