Broadcasting rules in NumPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to create a 2D array of shape (3, 4) filled with ones.

NumPy

import numpy as np
arr = np.ones([1])
print(arr.shape)

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

A(3, 4)

B[3, 4]

C3

D3, 4

Attempts:

3 left

💡 Hint

Common Mistakes

Using a list instead of a tuple for the shape.

Passing dimensions without parentheses.

The np.ones function expects a shape tuple, so (3, 4) is correct.

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
A = np.array([[1, 2, 3], [4, 5, 6]])
B = np.array([10, 20, 30])
result = A [1] B
print(result)

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

A+

B*

C-

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using multiplication instead of addition.

Trying to add arrays with incompatible shapes without broadcasting.

Using + adds the 1D array B to each row of A by broadcasting.

3fill in blank

hard

Fix the error in the code to multiply a (3,1) array with a (3,) array using broadcasting.

NumPy

import numpy as np
A = np.array([[1], [2], [3]])
B = np.array([10, 20, 30])
result = A [1] B
print(result)

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

A-

B*

C+

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using addition or subtraction instead of multiplication.

Not understanding how broadcasting works with different shapes.

Multiplying A and B with * uses broadcasting to produce a (3,3) array.

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 = ['apple', 'bat', 'carrot', 'dog']
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 the word itself as the value instead of its length.

Incorrect condition that does not filter properly.

The dictionary comprehension maps each word to its length using len(word), filtering only 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 3.

NumPy

[1] = { [2]: [3] for word in words if len(word) > 3 }

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

Aresult

Bword

Clen(word)

Dword.upper()

Attempts:

3 left

💡 Hint

Common Mistakes

Using the original word as key instead of uppercase.

Swapping keys and values in the dictionary.

Not assigning the dictionary to a variable.

The dictionary comprehension maps each uppercase word.upper() to its length len(word) for words longer than 3 characters, stored in result.

Practice

1. What is the main purpose of broadcasting in NumPy?

easy

A. To create copies of arrays for backup

B. To perform operations on arrays of different shapes by stretching dimensions

C. To sort arrays automatically before calculations

D. To convert arrays into lists for easier processing

Solution

1. Step 1: Understand broadcasting concept

   Broadcasting allows NumPy to perform element-wise operations on arrays with different shapes by stretching dimensions of size 1.

2. Step 2: Compare options with concept

   Only To perform operations on arrays of different shapes by stretching dimensions correctly describes this purpose. Other options describe unrelated actions.

3. Final Answer:

   To perform operations on arrays of different shapes by stretching dimensions -> Option B

4. Quick Check:

   Broadcasting = Stretching dimensions for operations [OK]

Hint: Broadcasting stretches size 1 dims to match shapes [OK]

Common Mistakes:

• Thinking broadcasting copies arrays
• Confusing broadcasting with sorting
• Believing broadcasting converts arrays to lists

2. Which of the following is a valid broadcasting rule in NumPy?

easy

A. Arrays must have the same number of dimensions

B. All dimensions must be equal

C. Dimensions must be exactly equal or one of them must be 1

D. Only 1D arrays can be broadcasted

Solution

1. Step 1: Recall broadcasting rules

   Broadcasting compares shapes from right to left; dimensions must be equal or one must be 1 to stretch.

2. Step 2: Evaluate options

   Dimensions must be exactly equal or one of them must be 1 matches the rule exactly. Options A, B, and D are incorrect because broadcasting allows different dimensions and works beyond 1D arrays.

3. Final Answer:

   Dimensions must be exactly equal or one of them must be 1 -> Option C

4. Quick Check:

   Broadcasting rule = equal or 1 dimension [OK]

Hint: Check if dims are equal or one is 1 [OK]

Common Mistakes:

• Assuming all dims must match exactly
• Believing arrays must have same number of dims
• Thinking broadcasting only works on 1D arrays

3. What is the shape of the result when adding arrays a = np.ones((3,1)) and b = np.ones((1,4)) using broadcasting?

medium

A. (3, 1)

B. (4, 3)

C. (1, 4)

D. (3, 4)

Solution

1. Step 1: Analyze shapes of a and b

   a has shape (3,1), b has shape (1,4). Broadcasting compares from right: 1 vs 4 and 3 vs 1.

2. Step 2: Apply broadcasting rules

   Dimensions 1 and 4 broadcast to 4; 3 and 1 broadcast to 3. Result shape is (3,4).

3. Final Answer:

   (3, 4) -> Option D

4. Quick Check:

   Broadcast (3,1) + (1,4) = (3,4) [OK]

Hint: Match dims right to left, stretch 1 to other size [OK]

Common Mistakes:

• Confusing order of dimensions
• Forgetting to broadcast size 1 dimension
• Swapping dimensions in result shape

4. Consider the code:

import numpy as np
x = np.ones((2,3))
y = np.ones((3,2))
z = x + y

What error will occur and why?

medium

A. ValueError because shapes (2,3) and (3,2) are incompatible for broadcasting

B. TypeError because arrays have different data types

C. No error, result shape is (2,3)

D. SyntaxError due to invalid addition

Solution

1. Step 1: Check shapes of x and y

   x shape is (2,3), y shape is (3,2). Compare dims right to left: 3 vs 2 and 2 vs 3.

2. Step 2: Apply broadcasting rules

   Neither dimension matches or is 1, so broadcasting fails and raises ValueError.

3. Final Answer:

   ValueError because shapes (2,3) and (3,2) are incompatible for broadcasting -> Option A

4. Quick Check:

   Broadcasting fails if dims differ and neither is 1 [OK]

Hint: Broadcast dims must be equal or 1; else error [OK]

Common Mistakes:

• Assuming addition works despite shape mismatch
• Confusing error type as TypeError or SyntaxError
• Ignoring dimension order in shapes

5. You have a 3D array A with shape (4,1,5) and a 2D array B with shape (1,3). You want to add them using broadcasting. What will be the shape of the result?

hard

A. Broadcasting will fail with ValueError

B. (4, 1, 3)

C. (1, 3, 5)

D. (4, 3, 5)

Solution

1. Step 1: Align shapes by adding missing dimension

   A shape is (4,1,5), B shape is (1,3). Treat B as (1,1,3) to match 3D shape.

2. Step 2: Compare dimensions right to left

   For each dim: 5 vs 3 (A's last dim 5, B's last dim 3) - mismatch. This means broadcasting fails.

3. Step 3: Re-examine dimension matching

   Actually, B's shape is (1,3), so when adding to A (4,1,5), B is broadcast to (1,1,3). Compare dims: 5 vs 3 (A's last dim 5, B's last dim 3) - mismatch. NumPy aligns shapes from right: A (4,1,5), B (1,1,3). Last dims 5 and 3 mismatch, so broadcasting fails.

4. Final Answer:

   Broadcasting will fail with ValueError -> Option A

5. Quick Check:

   Mismatch in last dims 5 and 3 causes failure [OK]

Hint: Align dims right to left; mismatch without 1 causes error [OK]

Common Mistakes:

• Assuming missing dims auto-align without prepending
• Ignoring last dimension mismatch
• Thinking broadcasting always works if dims differ