Common broadcasting patterns in NumPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of broadcasting addition

What is the output of this code snippet 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 the smaller array.

The array arr2 with shape (3,) is broadcast across the rows of arr1 with shape (2,3). Each element in arr2 is added to the corresponding column in arr1.

❓ data_output

intermediate

Shape after broadcasting

Given these arrays, what is the shape of the result after broadcasting and 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 (3, 4)

D (1, 3)

💡 Hint

Check how the shapes (4,1) and (3,) align for broadcasting.

The array arr1 has shape (4,1) and arr2 has shape (3,). NumPy broadcasts arr2 to (1,3), then both arrays broadcast to (4,3).

🔧 Debug

advanced

Identify the broadcasting error

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

NumPy

import numpy as np

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

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

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

C IndexError: index out of bounds

D No error, output is [[2 4] [4 6]]

💡 Hint

Check if the shapes of the arrays can be broadcast together.

The shapes (2,2) and (3,) are incompatible for broadcasting because the trailing dimensions do not match and neither is 1.

❓ visualization

advanced

Visualize broadcasting with reshaping

Which option correctly reshapes arr2 to broadcast with arr1 for element-wise multiplication?

NumPy

import numpy as np
import matplotlib.pyplot as plt

arr1 = np.arange(6).reshape(2,3)
arr2 = np.array([1, 2])

# Reshape arr2 here
arr2_reshaped = ???
result = arr1 * arr2_reshaped
plt.imshow(result)
plt.colorbar()
plt.show()

A arr2.reshape(3,1)

B arr2.reshape(1,2)

C arr2.reshape(2,1)

D arr2.reshape(3,2)

💡 Hint

arr1 shape is (2,3). To multiply, arr2 must broadcast to (2,3).

Reshaping arr2 to (2,1) allows it to broadcast across the 3 columns of arr1, resulting in shape (2,3).

🧠 Conceptual

expert

Broadcasting rules application

Given arrays with shapes (5,1,4) and (1,3,1), what is the shape of their broadcasted result?

A (5, 3, 1)

B (5, 1, 1)

C (1, 3, 4)

D (5, 3, 4)

💡 Hint

Compare dimensions from right to left, applying broadcasting rules.

Broadcasting compares dimensions from right to left: 4 and 1 broadcast to 4; 1 and 3 broadcast to 3; 5 and 1 broadcast to 5. Result shape is (5,3,4).

Practice

1. What does broadcasting in NumPy allow you to do?

easy

A. Perform operations on arrays of different shapes without explicit loops

B. Only add arrays of the exact same shape

C. Convert arrays into lists automatically

D. Sort arrays in ascending order

Solution

1. Step 1: Understand broadcasting concept

   Broadcasting lets NumPy perform element-wise operations on arrays with different shapes by automatically expanding the smaller array.

2. Step 2: Compare options

   Only Perform operations on arrays of different shapes without explicit loops correctly describes this feature. Options A, B, and C describe unrelated behaviors.

3. Final Answer:

   Perform operations on arrays of different shapes without explicit loops -> Option A

4. Quick Check:

   Broadcasting = operations on different shapes [OK]

Hint: Broadcasting means math on different shaped arrays without loops [OK]

Common Mistakes:

• Thinking broadcasting requires arrays to have the same shape
• Confusing broadcasting with sorting or type conversion
• Assuming broadcasting changes array data types

2. Which of the following is the correct way to add a 1D array to each row of a 2D array using broadcasting?

easy

A. result = matrix + vector.T where matrix.shape = (3,4) and vector.shape = (4,)

B. result = matrix + vector where matrix.shape = (3,4) and vector.shape = (3,)

C. result = matrix + vector where matrix.shape = (3,4) and vector.shape = (4,)

D. result = matrix + vector.reshape(3,1) where matrix.shape = (3,4) and vector.shape = (4,)

Solution

1. Step 1: Check shapes for broadcasting

   Adding a 1D array of shape (4,) to each row of a (3,4) matrix works because the vector matches the number of columns.

2. Step 2: Evaluate options

   result = matrix + vector where matrix.shape = (3,4) and vector.shape = (4,) matches this pattern. result = matrix + vector where matrix.shape = (3,4) and vector.shape = (3,) tries to add a (3,) vector to (3,4) matrix which fails. result = matrix + vector.T where matrix.shape = (3,4) and vector.shape = (4,) uses transpose incorrectly. result = matrix + vector.reshape(3,1) where matrix.shape = (3,4) and vector.shape = (4,) reshapes vector wrongly.

3. Final Answer:

   result = matrix + vector where matrix.shape = (3,4) and vector.shape = (4,) -> Option C

4. Quick Check:

   Vector shape matches columns for row-wise addition [OK]

Hint: Add vector matching columns to matrix rows for broadcasting [OK]

Common Mistakes:

• Using vector shape matching rows instead of columns
• Trying to transpose 1D vector which has no effect
• Reshaping vector incorrectly before addition

3. What is the output of the following code?

import numpy as np
A = np.array([[1, 2, 3], [4, 5, 6]])
B = np.array([10, 20, 30])
C = A + B
print(C)

medium

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

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

C. [[10 20 30]
[10 20 30]]

D. ValueError due to shape mismatch

Solution

1. Step 1: Understand shapes of A and B

   A has shape (2,3), B has shape (3,). B will broadcast across rows of A.

2. Step 2: Perform element-wise addition

   Each row of A adds B: [1+10, 2+20, 3+30] = [11, 22, 33], [4+10, 5+20, 6+30] = [14, 25, 36].

3. Final Answer:

   [[11 22 33] [14 25 36]] -> Option A

4. Quick Check:

   Broadcast adds vector to each matrix row [OK]

Hint: Add vector to each matrix row when vector shape matches columns [OK]

Common Mistakes:

• Expecting an extra row in output
• Confusing broadcasting with stacking arrays
• Thinking shape mismatch causes error here

4. Identify the error in this code snippet:

import numpy as np
X = np.array([[1, 2], [3, 4], [5, 6]])
y = np.array([10, 20, 30])
result = X + y

medium

A. y should be reshaped to (3,1) before addition

B. No error, code runs fine

C. X and y must have the same number of columns

D. Shapes (3,2) and (3,) cannot broadcast together

Solution

1. Step 1: Check shapes of X and y

   X shape is (3,2), y shape is (3,). Broadcasting rules require trailing dimensions to match or be 1.

2. Step 2: Analyze broadcasting compatibility

   Here, last dims are 2 (X) and 1 (y) after broadcasting rules, so y broadcasts along columns. The addition works without error.

3. Final Answer:

   No error, code runs fine -> Option B

4. Quick Check:

   Broadcasting allows (3,2) + (3,) by treating (3,) as (3,1) [OK]

Hint: Trailing dimensions must match or be 1 for broadcasting [OK]

Common Mistakes:

• Assuming broadcasting works if first dims match
• Not checking trailing dimension compatibility
• Thinking reshaping y to (3,1) fixes addition here

5. Given a 2D array M of shape (4,3) and a 1D array v of shape (4,), how can you add v to each column of M using broadcasting?

hard

A. M + v.T

B. M + v

C. M + v.reshape(1,4)

D. M + v.reshape(4,1)

Solution

1. Step 1: Understand shapes and desired operation

   M is (4,3), v is (4,). To add v to each column, v must be reshaped to (4,1) to broadcast along columns.

2. Step 2: Check each option

   M + v.reshape(4,1) reshapes v to (4,1), allowing broadcasting with M (4,3). M + v tries to add (4,) to (4,3) which broadcasts incorrectly. M + v.reshape(1,4) reshapes v to (1,4), incompatible. M + v.T uses transpose on 1D array which has no effect.

3. Final Answer:

   M + v.reshape(4,1) -> Option D

4. Quick Check:

   Reshape vector to (rows,1) to add to columns [OK]

Hint: Reshape vector to (rows,1) to add to matrix columns [OK]

Common Mistakes:

• Adding vector without reshaping when shapes differ
• Using reshape(1, rows) instead of (rows,1)
• Assuming transpose changes 1D array shape