Broadcasting performance implications in NumPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to create a 2D array of shape (3, 3) filled with ones using NumPy.

NumPy

import numpy as np
arr = np.[1]((3, 3))

Drag options to blanks, or click blank then click option'

Azeros

Bones

Cempty

Dfull

Attempts:

3 left

💡 Hint

Common Mistakes

Using np.zeros creates an array of zeros, not ones.

Using np.empty creates uninitialized values.

The np.ones function creates an array filled with ones. This is useful to test broadcasting performance with non-zero values.

2fill in blank

medium

Complete the code to add a 1D array to each row of a 2D array using broadcasting.

NumPy

import numpy as np
arr2d = np.ones((3, 3))
arr1d = np.array([1, 2, 3])
result = arr2d [1] arr1d

Drag options to blanks, or click blank then click option'

A+

B*

C-

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using '*' multiplies instead of adding.

Using '-' subtracts instead of adding.

Using the + operator adds the 1D array to each row of the 2D array by broadcasting.

3fill in blank

hard

Fix the error in the code to correctly broadcast a 1D array to a 2D array for multiplication.

NumPy

import numpy as np
arr2d = np.ones((3, 3))
arr1d = np.array([1, 2, 3])
result = arr2d * arr1d.[1]((3, 1))

Drag options to blanks, or click blank then click option'

Areshape

Bflatten

Ctranspose

Dravel

Attempts:

3 left

💡 Hint

Common Mistakes

Using flatten or ravel returns a 1D array, no shape change.

Using transpose on 1D array has no effect.

Using reshape changes the shape of arr1d to (3,1) so it broadcasts correctly with arr2d.

4fill in blank

hard

Fill both blanks to create a dictionary comprehension that maps words to their lengths only if length is greater than 3.

NumPy

words = ['data', 'science', 'ai', 'ml']
lengths = {word: [1] for word in words if [2]

Drag options to blanks, or click blank then click option'

Alen(word)

Blen(word) > 3

Cword

Dlen(words)

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'word' as value instead of length.

Using 'len(words)' which is total words, not per word.

The dictionary comprehension uses len(word) as the value and filters words with length greater than 3.

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension that maps uppercase words to their lengths only if length is greater than 2.

NumPy

words = ['cat', 'dog', 'a', 'bird']
result = { [1]: [2] for w in words if [3] }

Drag options to blanks, or click blank then click option'

Aw.upper()

Blen(w)

Clen(w) > 2

Dw.lower()

Attempts:

3 left

💡 Hint

Common Mistakes

Using w.lower() instead of uppercase.

Filtering with wrong length condition.

The comprehension maps the uppercase version of each word to its length, filtering words longer than 2 characters.

Practice

1. What is the main benefit of using broadcasting in NumPy?

easy

A. It slows down calculations to save memory.

B. It automatically converts arrays to lists for easier processing.

C. It allows operations on arrays of different shapes without explicit loops.

D. It increases the size of arrays to match the largest array.

Solution

1. Step 1: Understand broadcasting purpose

   Broadcasting lets NumPy perform element-wise operations on arrays with different shapes without needing explicit loops.

2. Step 2: Compare options

   Only It allows operations on arrays of different shapes without explicit loops. correctly describes this benefit. Options A, B, and C are incorrect or misleading.

3. Final Answer:

   It allows operations on arrays of different shapes without explicit loops. -> Option C

4. Quick Check:

   Broadcasting = fast array ops [OK]

Hint: Broadcasting = math on different shaped arrays fast [OK]

Common Mistakes:

• Thinking broadcasting changes array sizes permanently
• Confusing broadcasting with converting arrays to lists
• Assuming broadcasting slows down calculations

2. Which of the following is the correct syntax to add a 1D array b to each row of a 2D array a using broadcasting?

easy

A. a * b

B. a.T + b

C. a + b.reshape(-1, 1)

D. a + b

Solution

1. Step 1: Understand shapes for broadcasting

   If a is 2D with shape (m, n) and b is 1D with shape (n,), adding a + b broadcasts b across rows.

2. Step 2: Check options

   a + b correctly adds b to each row. a.T + b transposes a causing incompatible shapes. a * b multiplies instead of adds. a + b.reshape(-1, 1) reshapes b incorrectly for row-wise addition.

3. Final Answer:

   a + b -> Option D

4. Quick Check:

   1D add to rows = a + b [OK]

Hint: Add 1D array directly to 2D for row-wise addition [OK]

Common Mistakes:

• Transposing the wrong array leading to shape mismatch
• Confusing addition with multiplication
• Incorrectly reshaping array for broadcasting

3. What will be the output shape of the following code?

import numpy as np
x = np.ones((1000, 1))
y = np.arange(1000)
z = x + y

medium

A. (1000,)

B. (1000, 1000)

C. (1, 1000)

D. (1000, 1)

Solution

1. Step 1: Analyze shapes of x and y

   x has shape (1000, 1), y has shape (1000,). Broadcasting expands y to (1, 1000).

2. Step 2: Determine resulting shape after broadcasting

   Broadcasting rules expand x to (1000, 1000) and y to (1000, 1000), so z shape is (1000, 1000).

3. Final Answer:

   (1000, 1000) -> Option B

4. Quick Check:

   Broadcast shapes = (1000, 1) + (1, 1000) = (1000, 1000) [OK]

Hint: Broadcast dims expand to max shape in each axis [OK]

Common Mistakes:

• Assuming output shape matches smaller array
• Ignoring broadcasting rules for 1D arrays
• Confusing shape (1000,) with (1, 1000)

4. Identify the error in this code snippet that uses broadcasting:

import numpy as np
x = np.array([1, 2, 3])
y = np.array([[1], [2], [3]])
z = x + y.T

medium

A. Broadcasting works fine; no error here.

B. Shapes are incompatible for broadcasting due to transpose.

C. Using transpose on 1D array causes syntax error.

D. Addition operator is invalid for NumPy arrays.

Solution

1. Step 1: Check shapes of x and y.T

   x shape is (3,), y shape is (3,1), so y.T shape is (1,3).

2. Step 2: Analyze broadcasting compatibility

   Adding (3,) and (1,3): NumPy pads (3,) to (1,3), dimensions align (1=1, 3=3), broadcasting works fine; no error.

3. Final Answer:

   Broadcasting works fine; no error here. -> Option A

4. Quick Check:

   (3,) + (1,3) = compatible [OK]

Hint: Check shapes after transpose before adding arrays [OK]

Common Mistakes:

• Thinking transpose causes shape incompatibility
• Ignoring broadcasting rules for 1D arrays
• Thinking addition operator is invalid for arrays

5. You have a large 2D array A of shape (10000, 500) and a 1D array b of shape (500,). You want to add b to each row of A. Which approach is best for performance and memory?

hard

A. Use A + b directly to leverage broadcasting.

B. Use a Python loop to add b to each row of A.

C. Reshape b to (500, 1) and add to A.

D. Convert A and b to lists and use list comprehension.

Solution

1. Step 1: Consider broadcasting efficiency

   Using A + b leverages NumPy's optimized broadcasting, which is fast and memory efficient.

2. Step 2: Compare other methods

   Python loops (Use a Python loop to add b to each row of A.) are slow for large arrays. Reshaping b to (500,1) (Reshape b to (500, 1) and add to A.) mismatches dimensions for row-wise addition. Converting to lists (Convert A and b to lists and use list comprehension.) loses NumPy speed and uses more memory.

3. Final Answer:

   Use A + b directly to leverage broadcasting. -> Option A

4. Quick Check:

   Broadcasting is fastest for large arrays [OK]

Hint: Broadcasting beats loops for big arrays [OK]

Common Mistakes:

• Using slow Python loops for large data
• Incorrectly reshaping arrays for addition
• Converting arrays to lists losing performance