Broadcasting rules in Data Analysis Python - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of adding arrays with broadcasting

What is the output of this Python code using NumPy broadcasting?

Data Analysis Python

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 Raises ValueError due to shape mismatch

C

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

D

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

💡 Hint

Remember how NumPy broadcasts a 1D array to match the shape of a 2D array when adding.

The 1D array [10, 20, 30] is broadcasted to each row of the 2D array arr1, so each element in arr1's rows is added to the corresponding element in arr2.

❓ data_output

intermediate

Shape after broadcasting in multiplication

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

Data Analysis Python

import numpy as np

arr1 = np.ones((3, 1, 4))
arr2 = np.ones((1, 5, 1))
result = arr1 * arr2
print(result.shape)

A (3, 1, 5, 4)

B (3, 5, 4)

C (1, 5, 4)

D Raises ValueError due to incompatible shapes

💡 Hint

Broadcasting aligns dimensions from the right and expands dimensions of size 1.

The shapes (3,1,4) and (1,5,1) broadcast to (3,5,4) by expanding the singleton dimensions.

🔧 Debug

advanced

Identify the broadcasting error

What error does this code raise and why?

Data Analysis Python

import numpy as np

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

A Output: [[2 4 6] [4 6 8]]

B TypeError: unsupported operand type(s) for +: 'int' and 'list'

C ValueError: operands could not be broadcast together with shapes (3,) (2,2)

D Output: [[2 4] [4 6] [4 6]]

💡 Hint

Check if the shapes of the arrays can be broadcasted according to the rules.

The shapes (3,) and (2,2) cannot be broadcasted because their dimensions are incompatible from the right side.

❓ visualization

advanced

Visualize broadcasting with arrays

Which option correctly describes the broadcasting process when adding these arrays?

Data Analysis Python

import numpy as np

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

A arr2 is reshaped to (1,3) and broadcasted to (3,3), arr1 is broadcasted to (3,3), result shape is (3,3)

B arr1 is broadcasted to (3,3), arr2 is broadcasted to (3,3), result shape is (3,3)

C Raises ValueError due to incompatible shapes (3,1) and (3,)

D arr2 is broadcasted to (3,1), arr1 remains (3,1), result shape is (3,1)

💡 Hint

Remember that a 1D array of shape (3,) can be treated as (1,3) for broadcasting with (3,1).

arr2 is treated as shape (1,3) and broadcasted to (3,3). arr1 is broadcasted from (3,1) to (3,3). The result shape is (3,3).

🧠 Conceptual

expert

Understanding broadcasting rules with multiple dimensions

Given arrays with shapes (4,1,3,1) and (1,5,1,7), what is the resulting shape after broadcasting?

A (4, 1, 3, 7)

B (1, 5, 3, 1)

C Raises ValueError due to incompatible shapes

D (4, 5, 3, 7)

💡 Hint

Broadcasting compares dimensions from right to left, expanding singleton dimensions or matching equal sizes.

Each dimension is compared: 1 vs 7 → 7, 3 vs 1 → 3, 1 vs 5 → 5, 4 vs 1 → 4. Result shape is (4,5,3,7).