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.