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.

Practice

1. What does broadcasting in NumPy allow you to do with arrays of different shapes?

easy

A. Only add arrays if they have the exact same shape

B. Sort arrays in ascending order

C. Convert arrays into lists automatically

D. Perform element-wise operations without manually reshaping arrays

Solution

1. Step 1: Understand broadcasting concept

   Broadcasting lets NumPy perform math on arrays with different shapes by stretching smaller arrays.

2. Step 2: Identify what broadcasting enables

   This means you can do element-wise operations without manually reshaping arrays to the same shape.

3. Final Answer:

   Perform element-wise operations without manually reshaping arrays -> Option D

4. Quick Check:

   Broadcasting = element-wise operations on different shapes [OK]

Hint: Broadcasting stretches smaller arrays to match bigger ones [OK]

Common Mistakes:

• Thinking arrays must have the same shape to operate
• Confusing broadcasting with sorting or reshaping
• Assuming broadcasting copies data

2. Which of the following is the correct way to add a 1D array b = np.array([1, 2, 3]) to each row of a 2D array a with shape (4, 3)?

easy

A. a + b

B. a + b.T

C. a + b.reshape(3, 1)

D. a + b.reshape(1, 4)

Solution

1. Step 1: Check shapes of arrays

   Array a has shape (4, 3), and b has shape (3,). Adding a + b broadcasts b across rows.

2. Step 2: Understand broadcasting rules

   Since b matches the number of columns, it adds to each row correctly without reshaping.

3. Final Answer:

   a + b -> Option A

4. Quick Check:

   1D array added across rows = a + b [OK]

Hint: Add 1D array directly if its length matches columns [OK]

Common Mistakes:

• Trying to transpose 1D array which has no effect
• Reshaping to wrong dimensions causing errors
• Confusing rows and columns in shapes

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])
result = a + b
print(result)

medium

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

B. [[11 12 13]
[14 15 16]]

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

D. Error due to shape mismatch

Solution

1. Step 1: Analyze shapes and operation

   a shape is (2,3), b shape is (3,). Adding broadcasts b across rows.

2. Step 2: Calculate element-wise addition

   Row 1: [1+10, 2+20, 3+30] = [11, 22, 33]
   Row 2: [4+10, 5+20, 6+30] = [14, 25, 36]

3. Final Answer:

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

4. Quick Check:

   Broadcast add across rows = [[11 22 33], [14 25 36]] [OK]

Hint: Add 1D array to 2D rows matches columns [OK]

Common Mistakes:

• Expecting error due to different shapes
• Adding element-wise without broadcasting
• Confusing rows and columns in addition

4. Identify the error in this code snippet:

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

medium

A. Using wrong operator for addition

B. Syntax error in array creation

C. Shapes of a and b are incompatible for broadcasting

D. No error, code runs fine

Solution

1. Step 1: Check shapes of arrays

   a shape is (3, 2), b shape is (3,). They differ in second dimension.

2. Step 2: Understand broadcasting rules

   Broadcasting requires trailing dimensions to match or be 1. Here, 2 != 3, so addition fails.

3. Final Answer:

   Shapes of a and b are incompatible for broadcasting -> Option C

4. Quick Check:

   Shape mismatch causes broadcasting error [OK]

Hint: Check trailing dimensions match or are 1 for broadcasting [OK]

Common Mistakes:

• Assuming any shapes can broadcast
• Ignoring dimension order in arrays
• Thinking 1D arrays always broadcast to 2D

5. You have a 2D array data of shape (5, 4) representing 5 samples with 4 features each. You want to subtract the mean of each feature (given as a 1D array mean_vals of length 4) from the corresponding feature column in data. Which code correctly applies broadcasting to do this?

hard

A. data - mean_vals.reshape(4, 1)

B. data - mean_vals

C. data - mean_vals.reshape(1, 5)

D. data - mean_vals.T

Solution

1. Step 1: Understand shapes and operation

   data shape is (5, 4), mean_vals shape is (4,). Subtracting mean_vals from data broadcasts mean_vals across rows.

2. Step 2: Confirm correct broadcasting

   Since mean_vals length matches columns, data - mean_vals subtracts feature-wise means correctly.

3. Final Answer:

   data - mean_vals -> Option B

4. Quick Check:

   Subtract 1D array from 2D rows = data - mean_vals [OK]

Hint: Subtract 1D array matching columns directly [OK]

Common Mistakes:

• Reshaping mean_vals incorrectly causing errors
• Transposing 1D array which has no effect
• Trying to subtract mean_vals across wrong axis