Avoiding broadcasting mistakes in NumPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

What is the output of this NumPy code?

Consider the following code snippet using NumPy arrays. What will be the shape of the result array c?

NumPy

import numpy as np

a = np.array([[1, 2, 3], [4, 5, 6]])
b = np.array([10, 20])
c = a + b

A Raises a ValueError

B (2, 2)

C (3, 2)

D (2, 3)

💡 Hint

Check the shapes of the arrays before addition and how broadcasting rules apply.

The array a has shape (2, 3) and b has shape (2,). NumPy tries to broadcast b to match a. But (2,) cannot be broadcast to (2,3) because the second dimension sizes differ and one is not 1. This causes a ValueError.

❓ data_output

intermediate

What is the resulting array after broadcasting?

Given the arrays below, what is the output of c after the addition?

NumPy

import numpy as np

a = np.array([[1], [2], [3]])
b = np.array([10, 20, 30])
c = a + b

A Raises a ValueError

B

[[11 12 13]
 [21 22 23]
 [31 32 33]]

C

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

D

[[11 21 31]
 [12 22 32]
 [13 23 33]]

💡 Hint

Remember how broadcasting works when one array has shape (3,1) and the other (3,).

Array a has shape (3,1) and b has shape (3,). NumPy broadcasts b to (1,3) and then broadcasts both to (3,3). The addition sums each element of a with each element of b along the second axis.

🔧 Debug

advanced

Why does this broadcasting cause an error?

Examine the code below. Why does the addition raise an error?

NumPy

import numpy as np

x = np.ones((4, 1, 3))
y = np.ones((3, 4))
z = x + y

A The arrays have different numbers of dimensions causing a ValueError

B The arrays have different data types causing a TypeError

C Shapes (4,1,3) and (3,4) are incompatible because trailing dimensions don't match and none is 1

D The arrays have the same shape so no error occurs

💡 Hint

Check how NumPy aligns shapes from the right when broadcasting.

NumPy compares shapes from the right: (4,1,3) and (3,4) align as (4,1,3) and ( ,3,4). The last dimensions 3 and 4 differ and neither is 1, so broadcasting fails with a ValueError.

❓ visualization

advanced

Visualize broadcasting shapes

Which option correctly shows the broadcasted shapes of arrays a and b before addition?

NumPy

import numpy as np

a = np.ones((2, 1, 4))
b = np.ones((1, 3, 1))
c = a + b
print(c.shape)

A (2, 3, 4)

B (2, 1, 4)

C (1, 3, 1)

D Raises a ValueError

💡 Hint

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

Shapes (2,1,4) and (1,3,1) broadcast to (2,3,4). Dimensions 1 expand to match the other array's size.

🧠 Conceptual

expert

Which broadcasting rule explains this behavior?

Given arrays a with shape (5, 1, 7) and b with shape (1, 3, 1), which NumPy broadcasting rule allows their addition?

A Broadcasting requires both arrays to have the same total number of elements

B Arrays must have the same number of dimensions to broadcast

C Broadcasting only works if one array is 1D and the other is 2D

D Dimensions are compared from right to left; sizes must be equal or one must be 1 to broadcast

💡 Hint

Think about how NumPy compares dimensions when broadcasting.

NumPy compares array shapes from right to left. For each dimension, sizes must be equal or one must be 1. This allows arrays of different shapes to be broadcast together.