Why broadcasting matters in NumPy - Test Your Understanding

Practice - 5 Tasks

1fill in blank

easy

Complete the code to create a numpy array of shape (3, 1).

NumPy

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

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

A.dtype

B.size

C.shape

D.ndim

Attempts:

3 left

💡 Hint

Common Mistakes

Using .size instead of .shape

Trying to call .shape() as a function

The .shape attribute shows the dimensions of the array, which is (3, 1) here.

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 subtraction or multiplication instead of addition

Trying to add arrays with incompatible shapes without broadcasting

Adding arrays with compatible shapes uses broadcasting to add B to each row of A.

3fill in blank

hard

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

NumPy

import numpy as np
x = np.array([[1], [2], [3]])
y = np.array([4, 5, 6])
result = x [1] y
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 aligns dimensions

Multiplying arrays with shapes (3,1) and (3,) uses broadcasting to multiply each element correctly.

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 value

Using wrong condition like len(words) instead of len(word) > 3

The dictionary comprehension maps each word to its length using len(word). The condition len(word) > 3 filters words longer than 3 letters.

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension that maps uppercase words to their lengths if length is greater than 4.

NumPy

words = ['apple', 'bat', 'carrot', 'dog']
[1] = { [2]: [3] for w in words if len(w) > 4 }

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

Aresult

Bw.upper()

Clen(w)

Dword

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'word' instead of 'w.upper()' for keys

Not assigning the comprehension to a variable

The dictionary comprehension creates result mapping each uppercase word w.upper() to its length len(w) for words longer than 4 letters.

Practice

1. What is the main benefit of broadcasting in numpy?

easy

A. It sorts arrays before performing operations

B. It increases the size of arrays automatically

C. It converts arrays into lists for easier processing

D. It allows operations on arrays of different shapes without extra loops

Solution

1. Step 1: Understand broadcasting purpose

   Broadcasting lets numpy perform math on arrays with different shapes without needing explicit loops.

2. Step 2: Compare options

   Only It allows operations on arrays of different shapes without extra loops correctly describes this benefit. Others describe unrelated or incorrect behaviors.

3. Final Answer:

   It allows operations on arrays of different shapes without extra loops -> Option D

4. Quick Check:

   Broadcasting = operations on different shapes [OK]

Hint: Broadcasting means no loops needed for different shaped arrays [OK]

Common Mistakes:

• Thinking broadcasting changes array size
• Confusing broadcasting with sorting or converting types
• Assuming broadcasting creates copies of arrays

2. Which of the following numpy operations correctly uses broadcasting?

easy

A. np.array([1, 2, 3]) + np.array([4, 5])

B. np.array([[1], [2], [3]]) + np.array([4, 5, 6])

C. np.array([1, 2, 3]) + 5

D. np.array([1, 2, 3]) + np.array([[4], [5]])

Solution

1. Step 1: Check each operation for broadcasting rules

   np.array([1, 2, 3]) + np.array([4, 5]) fails because shapes (3,) and (2,) are incompatible. np.array([[1], [2], [3]]) + np.array([4, 5, 6]) works because shapes (3,1) and (3,) broadcast to (3,3). np.array([1, 2, 3]) + 5 works because scalar 5 broadcasts to (3,). np.array([1, 2, 3]) + np.array([[4], [5]]) fails due to incompatible shapes (3,) and (2,1).

2. Step 2: Identify correct broadcasting usage

   Both np.array([[1], [2], [3]]) + np.array([4, 5, 6]) and np.array([1, 2, 3]) + 5 are valid broadcasting operations, but since only one option can be correct, and np.array([[1], [2], [3]]) + np.array([4, 5, 6]) is valid, the question needs correction to avoid multiple correct answers.

3. Final Answer:

   np.array([1, 2, 3]) + 5 -> Option C

4. Quick Check:

   Scalar + array always broadcasts [OK]

Hint: Adding scalar to array always broadcasts correctly [OK]

Common Mistakes:

• Assuming arrays of different lengths always broadcast
• Not recognizing scalar broadcasting
• Confusing shape compatibility rules

3. What is the output of this code?

import numpy as np
A = np.array([[1, 2, 3], [4, 5, 6]])
B = np.array([10, 20, 30])
C = A + B
print(C)

medium

A. [[10 20 30]
[10 20 30]]

B. [[11 22 33]
[14 25 36]]

C. [[11 22 33]
[14 25 36]
[10 20 30]]

D. Error due to shape mismatch

Solution

1. Step 1: Analyze shapes of A and B

   A has shape (2,3), B has shape (3,). B broadcasts across rows of A.

2. Step 2: Perform element-wise addition with broadcasting

   Each row of A adds B element-wise: [1+10, 2+20, 3+30] = [11, 22, 33], [4+10, 5+20, 6+30] = [14, 25, 36].

3. Final Answer:

   [[11 22 33] [14 25 36]] -> Option B

4. Quick Check:

   Broadcasting adds B to each row of A [OK]

Hint: Broadcast 1D array across rows of 2D array for addition [OK]

Common Mistakes:

• Expecting error due to different shapes
• Confusing output shape
• Forgetting broadcasting applies along last axis

4. This code throws an error. What is the problem?

import numpy as np
X = np.array([1, 2, 3])
Y = np.array([[10], [20]])
Z = X + Y
print(Z)

medium

A. Shapes (3,) and (2,1) cannot be broadcast together

B. X and Y must be the same shape exactly

C. You cannot add 1D and 2D arrays

D. The arrays must be converted to lists first

Solution

1. Step 1: Check shapes of X and Y

   X shape is (3,), Y shape is (2,1). Broadcasting requires compatible shapes from right to left.

2. Step 2: Determine broadcasting compatibility

   Comparing dimensions: 3 vs 1 (compatible), but 1 vs 2 (not compatible). So broadcasting fails.

3. Final Answer:

   Shapes (3,) and (2,1) cannot be broadcast together -> Option A

4. Quick Check:

   Broadcasting requires compatible shapes [OK]

Hint: Check shapes from right to left for broadcasting compatibility [OK]

Common Mistakes:

• Thinking 1D and 2D arrays cannot be added at all
• Assuming exact shape match is always needed
• Ignoring broadcasting rules for dimensions

5. You have a 3D array A with shape (2, 3, 4) and a 1D array B with shape (4,). You want to add B to each 2D slice of A along the last axis. Which code correctly uses broadcasting to do this?

hard

A. C = A + B

B. C = A + B.reshape(4, 1)

C. C = A + B.reshape(1, 3)

D. C = A + B.reshape(2, 3, 4)

Solution

1. Step 1: Understand shapes and broadcasting rules

   A shape is (2,3,4), B shape is (4,). Broadcasting aligns from the right, so B broadcasts along last axis of A.

2. Step 2: Evaluate each option's effect

   C = A + B adds B directly, broadcasting B over last axis. C = A + B.reshape(4, 1) reshapes B to (4,1), incompatible with A's shape. C = A + B.reshape(1, 3) reshapes B to (1,3), which does not match A's last two dims. C = A + B.reshape(2, 3, 4) reshapes B to (2,3,4), but B has only 4 elements, so reshape fails.

3. Final Answer:

   C = A + B -> Option A

4. Quick Check:

   1D array matches last axis of 3D array [OK]

Hint: Add 1D array matching last axis directly to 3D array [OK]

Common Mistakes:

• Trying to reshape 1D array incorrectly
• Assuming reshape is needed when broadcasting works
• Confusing axis order in reshaping