1D and 2D broadcasting in NumPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of 1D and 2D broadcasting addition

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

NumPy

import numpy as np

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

A

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

B

[[11 22 33]
 [21 32 43]
 [31 42 53]]

C

[[10 20 30]
 [11 21 31]
 [12 22 32]]

D

[[1 2 3]
 [10 20 30]
 [11 22 33]]

💡 Hint

Remember how NumPy aligns shapes for broadcasting: the smaller array is stretched along missing dimensions.

The 1D array [1,2,3] is broadcast across each row of the 2D array [[10],[20],[30]]. So each element in arr2 adds to each element in arr1, producing a 3x3 array where each row is arr1 plus the corresponding element of arr2.

❓ data_output

intermediate

Shape of result 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, 1)

B (3, 4)

C (4, 3)

D (1, 3)

💡 Hint

Broadcasting stretches arrays to match each other's shape along missing dimensions.

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

🔧 Debug

advanced

Identify the error in broadcasting shapes

What error will this code raise when trying to add these arrays?

NumPy

import numpy as np

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

A No error, outputs a (2,3) array

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

C IndexError: index out of bounds

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

💡 Hint

Check if the shapes can be aligned for broadcasting.

The shapes (3,) and (2,2) cannot be broadcast because their dimensions do not match or are not 1.

❓ visualization

advanced

Visualize broadcasting result of subtraction

What does the printed array look like after this subtraction with broadcasting?

NumPy

import numpy as np

arr1 = np.array([[5, 10, 15], [20, 25, 30]])
arr2 = np.array([1, 2, 3])
result = arr1 - arr2
print(result)

A

[[ 6 12 18]
 [21 27 33]]

B

[[ 4  8 12]
 [19 23 27]]

C

[[ 4  8 12]
 [ 1  2  3]]

D

[[ 4  8 12]
 [19 23 27]
 [ 4  8 12]]

💡 Hint

Broadcast arr2 across rows of arr1 and subtract element-wise.

arr2 is broadcast across each row of arr1. Subtracting element-wise gives the shown 2x3 array.

🧠 Conceptual

expert

Why does broadcasting fail for these shapes?

Given arrays with shapes (3,1) and (2,3), why does broadcasting fail when trying to add them?

A Because the dimensions are not compatible: 1 and 3 can broadcast, but 3 and 2 cannot.

B Because both arrays have different numbers of dimensions, broadcasting is not allowed.

C Because the arrays have the same total number of elements but different shapes.

D Because broadcasting requires both arrays to have the same shape exactly.

💡 Hint

Broadcasting compares shapes from the right side dimension-wise.

Broadcasting rules require each dimension to be equal or one of them to be 1. Here, the last dimensions 1 and 3 are compatible, but the next dimensions 3 and 2 are not.