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).

Practice

1. What does broadcasting do when working with arrays of different shapes in Python's NumPy?

easy

A. It stretches smaller arrays to match the shape of larger arrays without copying data.

B. It copies smaller arrays to make them the same size as larger arrays.

C. It only works if arrays have exactly the same shape.

D. It deletes extra elements from larger arrays to match smaller ones.

Solution

1. Step 1: Understand broadcasting concept

   Broadcasting allows operations on arrays with different shapes by stretching the smaller array.

2. Step 2: Identify how broadcasting works

   It does not copy data but virtually stretches the smaller array to match the larger one.

3. Final Answer:

   It stretches smaller arrays to match the shape of larger arrays without copying data. -> Option A

4. Quick Check:

   Broadcasting = stretching without copying [OK]

Hint: Broadcasting stretches smaller arrays without copying data [OK]

Common Mistakes:

• Thinking broadcasting copies data
• Believing arrays must have same shape
• Assuming larger arrays get shrunk

2. Which of the following code snippets correctly applies broadcasting to add a 1D array to each row of a 2D array in NumPy?

easy

A. result = arr2d + arr1d[:, np.newaxis]

B. result = arr2d.flatten() + arr1d

C. result = arr2d + arr1d.reshape(-1, 1)

D. result = arr2d + arr1d

Solution

1. Step 1: Understand shapes of arrays

   arr2d is 2D (m,n), arr1d is 1D (n,). Adding arr1d directly to arr2d adds arr1d to each row by broadcasting.

2. Step 2: Check reshaping effects

   Reshaping arr1d to column vector (A,C) causes shape incompatibility (m,n) + (n,1); flattening arr2d (D) leads to incompatible 1D shapes.

3. Final Answer:

   result = arr2d + arr1d -> Option D

4. Quick Check:

   Direct addition broadcasts 1D to rows [OK]

Hint: Add 1D array directly to 2D to broadcast rows [OK]

Common Mistakes:

• Reshaping 1D array to column vector
• Flattening the 2D array arr2d
• Confusing row vs column broadcasting

3. What is the output of the following code?

import numpy as np
arr1 = np.array([[1, 2, 3], [4, 5, 6]])
arr2 = np.array([10, 20, 30])
result = arr1 + arr2
print(result)

medium

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

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

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

D. Error due to shape mismatch

Solution

1. Step 1: Identify shapes of arrays

   arr1 shape is (2,3), arr2 shape is (3,). Broadcasting stretches arr2 to (2,3).

2. Step 2: Perform element-wise addition

   Add each element of arr2 to corresponding column in arr1: [[1+10,2+20,3+30],[4+10,5+20,6+30]].

3. Final Answer:

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

4. Quick Check:

   Broadcasting adds arr2 to each row [OK]

Hint: Broadcast 1D array across rows for addition [OK]

Common Mistakes:

• Expecting error due to shape difference
• Confusing addition with multiplication
• Misreading output shape

4. The following code throws a ValueError. What is the main reason?

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

medium

A. arr1 should be 1D to add with arr2.

B. arr2 must be reshaped to (2,1) before addition.

C. Shapes (2,2) and (3,) are incompatible for broadcasting.

D. Addition operator '+' cannot be used with arrays.

Solution

1. Step 1: Check shapes of arrays

   arr1 shape is (2,2), arr2 shape is (3,). Broadcasting requires trailing dimensions to be equal or 1.

2. Step 2: Identify broadcasting rule violation

   Last dimensions 2 and 3 differ and neither is 1, so broadcasting fails causing ValueError.

3. Final Answer:

   Shapes (2,2) and (3,) are incompatible for broadcasting. -> Option C

4. Quick Check:

   Broadcasting needs compatible trailing dimensions [OK]

Hint: Check trailing dimensions for broadcasting compatibility [OK]

Common Mistakes:

• Assuming any shapes can broadcast
• Thinking reshaping arr2 fixes without correct shape
• Believing '+' can't add arrays

5. You have a 3D array arr3d with shape (2, 3, 4) and a 1D array arr1d with shape (4,). You want to add arr1d to each 2D slice of arr3d along the last axis. Which code correctly uses broadcasting to do this?

hard

A. result = arr3d + arr1d.reshape(2, 3, 4)

B. result = arr3d + arr1d.reshape(1, 1, 4)

C. result = arr3d + arr1d.reshape(4, 1, 1)

D. result = arr3d + arr1d.reshape(1, 4, 1)

Solution

1. Step 1: Understand shapes and broadcasting rules

   arr3d shape is (2,3,4), arr1d shape is (4,). To add along last axis, arr1d must broadcast to (1,1,4).

2. Step 2: Reshape arr1d for correct broadcasting

   Reshape arr1d to (1,1,4) so it broadcasts across first two dimensions and aligns with last dimension.

3. Step 3: Confirm addition

   Addition with arr3d + arr1d.reshape(1,1,4) works correctly by broadcasting arr1d along first two axes.

4. Final Answer:

   result = arr3d + arr1d.reshape(1, 1, 4) -> Option B

5. Quick Check:

   Reshape 1D to (1,1,last_dim) for 3D broadcasting [OK]

Hint: Reshape 1D to (1,1,last_dim) to add along last axis [OK]

Common Mistakes:

• Not reshaping arr1d or wrong reshape shape
• Confusing axis order in reshape
• Assuming direct addition always works