Broadcasting rules in NumPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of broadcasting addition

What is the output of this code using NumPy broadcasting?

NumPy

import numpy as np

arr1 = np.array([[1, 2, 3], [4, 5, 6]])
arr2 = np.array([10, 20, 30])
result = arr1 + arr2
print(result)

A

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

B

[[11 12 13]
 [14 15 16]]

C

[[10 20 30]
 [10 20 30]]

D

[[1 2 3 10 20 30]
 [4 5 6 10 20 30]]

💡 Hint

Remember how NumPy adds arrays with compatible shapes by stretching smaller arrays.

The array arr2 with shape (3,) is broadcast across the rows of arr1 with shape (2,3). So each row of arr1 adds the arr2 values element-wise.

❓ data_output

intermediate

Shape after broadcasting multiplication

Given these arrays, what is the shape of the result after multiplication?

NumPy

import numpy as np

arr1 = np.ones((4, 1))
arr2 = np.array([1, 2, 3])
result = arr1 * arr2
print(result.shape)

A (4, 3)

B (4, 1)

C (1, 3)

D (3, 4)

💡 Hint

Broadcasting stretches dimensions of size 1 to match the other array.

arr1 has shape (4,1) and arr2 has shape (3,). NumPy treats arr2 as (1,3) and broadcasts arr1 to (4,3). The result shape is (4,3).

🔧 Debug

advanced

Identify the broadcasting error

Which option shows code that will raise a broadcasting error?

NumPy

import numpy as np

arr1 = np.array([[1, 2], [3, 4]])
arr2 = np.array([1, 2, 3])
result = arr1 + arr2

A arr1 + arr2.reshape(3, 1)

B arr1 + arr2[:2]

C arr1 + arr2

D arr1 + arr2[:2].reshape(2, 1)

💡 Hint

Check if the shapes can be broadcast together.

arr1 shape is (2,2), arr2 shape is (3,). These shapes are incompatible for broadcasting, so option C raises a ValueError.

🧠 Conceptual

advanced

Broadcasting rule for trailing dimensions

Which statement best describes NumPy's broadcasting rule for arrays with different shapes?

A Arrays are compatible if each dimension is equal or one of them is 1, starting from the trailing dimensions.

B Arrays are compatible if the total number of elements is the same.

C Arrays are compatible if their shapes are exactly the same.

D Arrays are compatible only if the smaller array has fewer dimensions than the larger one.

💡 Hint

Think about how NumPy compares shapes from the right side.

NumPy compares shapes from the last dimension backward. Dimensions must be equal or one must be 1 to broadcast.

🚀 Application

expert

Using broadcasting to normalize data

You have a 2D NumPy array 'data' of shape (100, 5) representing 100 samples with 5 features each. You want to subtract the mean of each feature from the data using broadcasting. Which code correctly does this?

A data - data.mean()

B data - data.mean(axis=1)

C data - data.mean(axis=0).reshape(100, 5)

D data - data.mean(axis=0)

💡 Hint

Mean per feature means mean along samples axis.

data.mean(axis=0) computes mean for each feature (column). Subtracting this 1D array broadcasts across rows, centering each feature.

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