Broadcasting compatibility check in NumPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of broadcasting shape check

What is the output of the following code that checks if two arrays can be broadcast together?

NumPy

import numpy as np
shape1 = (3, 1, 5)
shape2 = (1, 4, 5)
result = np.broadcast_shapes(shape1, shape2)
print(result)

A (3, 4, 5)

B (3, 1, 5, 4, 5)

C ValueError: shape mismatch: objects cannot be broadcast to a single shape

D (3, 4)

💡 Hint

Broadcasting compares shapes from the right side, matching dimensions or using 1 to expand.

The shapes (3,1,5) and (1,4,5) broadcast to (3,4,5) because 1 can expand to match the other dimension.

❓ Predict Output

intermediate

Broadcasting compatibility check result

What happens when you try to broadcast these shapes using numpy.broadcast_shapes?

NumPy

import numpy as np
shape1 = (2, 3)
shape2 = (3, 2)
try:
    result = np.broadcast_shapes(shape1, shape2)
except Exception as e:
    result = type(e).__name__
print(result)

A (2, 3, 3, 2)

B ValueError

C (3, 3)

D TypeError

💡 Hint

Broadcasting requires dimensions to be equal or one of them to be 1 from the right side.

Shapes (2,3) and (3,2) are incompatible for broadcasting because their trailing dimensions differ and neither is 1.

❓ data_output

advanced

Resulting shape after broadcasting arrays

Given two arrays with shapes (4, 1, 6) and (3, 6), what is the shape of the result after broadcasting?

NumPy

import numpy as np
arr1 = np.zeros((4, 1, 6))
arr2 = np.zeros((3, 6))
result = np.broadcast(arr1, arr2)
print(result.shape)

A (4, 1, 6, 3, 6)

B (3, 6)

C ValueError

D (4, 3, 6)

💡 Hint

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

The shape (3,6) is treated as (1,3,6) to align with (4,1,6), resulting in (4,3,6).

🔧 Debug

advanced

Identify the broadcasting error

Which option shows the code that will raise a broadcasting error when adding two numpy arrays?

A

import numpy as np
x = np.ones((2, 3))
y = np.ones((3, 2))
result = x + y

B

import numpy as np
x = np.ones((5, 1))
y = np.ones((1, 4))
result = x + y

C

import numpy as np
x = np.ones((3, 1, 2))
y = np.ones((1, 4, 2))
result = x + y

D

import numpy as np
x = np.ones((1, 3))
y = np.ones((3, 1))
result = x + y

💡 Hint

Check if dimensions align from the right or are 1 for broadcasting.

Shapes (2,3) and (3,2) cannot broadcast because their trailing dimensions differ and neither is 1.

🚀 Application

expert

Determine output shape for complex broadcasting

You have arrays with shapes (7, 1, 5, 1) and (1, 3, 1, 4). What is the shape of the result after broadcasting these arrays?

NumPy

import numpy as np
shape1 = (7, 1, 5, 1)
shape2 = (1, 3, 1, 4)
result_shape = np.broadcast_shapes(shape1, shape2)
print(result_shape)

A (7, 1, 5, 4)

B (1, 3, 5, 1)

C (7, 3, 5, 4)

D ValueError

💡 Hint

Broadcasting expands dimensions where one shape has 1 and the other has a size >1.

Each dimension is compared from right to left: 1 vs 4 → 4, 5 vs 1 → 5, 1 vs 3 → 3, 7 vs 1 → 7.

Practice

1. Which of the following pairs of shapes are compatible for broadcasting in NumPy?

easy

A. (1, 2, 3) and (2, 3, 1)

B. (2, 3) and (3, 2)

C. (4, 5) and (4, 5, 1)

D. (3, 1) and (1, 4)

Solution

1. Step 1: Understand broadcasting rules

   Broadcasting compares shapes from right to left. Dimensions must be equal or one must be 1.

2. Step 2: Check each pair

   For (3,1) and (1,4), rightmost dims 1 and 4 are compatible (1 can broadcast to 4), left dims 3 and 1 compatible (1 can broadcast to 3). So compatible.

3. Final Answer:

   (3, 1) and (1, 4) are compatible -> Option D

4. Quick Check:

   Broadcast dims right to left, 1 can expand [OK]

Hint: Check shapes from right; 1 or equal dims broadcast [OK]

Common Mistakes:

• Assuming all different shapes are compatible
• Not comparing dimensions from right to left
• Ignoring that 1 can broadcast to any size

2. Which of the following is the correct way to check broadcasting compatibility of shapes (2, 3) and (3,) using NumPy?

easy

A. numpy.broadcast_shapes((2, 3), (3,))

B. numpy.broadcast((2, 3), (3,))

C. numpy.broadcast_shapes([2, 3], 3)

D. numpy.broadcast((2, 3), (3))

Solution

1. Step 1: Identify the correct function

   NumPy provides numpy.broadcast_shapes to check shape compatibility, which takes tuples as shape arguments.

2. Step 2: Check argument types

   numpy.broadcast_shapes((2, 3), (3,)) uses numpy.broadcast_shapes with tuples, which is correct. numpy.broadcast_shapes([2, 3], 3) uses a scalar for the second argument, which is invalid for this function.

3. Final Answer:

   numpy.broadcast_shapes((2, 3), (3,)) -> Option A

4. Quick Check:

   Use numpy.broadcast_shapes with tuples [OK]

Hint: Use numpy.broadcast_shapes with tuples for shape check [OK]

Common Mistakes:

• Using numpy.broadcast instead of numpy.broadcast_shapes
• Passing scalars instead of sequences
• Missing parentheses or wrong argument types

3. What will be the output of the following code?

import numpy as np
shape = np.broadcast_shapes((4, 1, 3), (1, 5, 3))
print(shape)

medium

A. (4, 1, 3)

B. (4, 5, 3)

C. (1, 5, 3)

D. ValueError: shapes not compatible

Solution

1. Step 1: Compare shapes dimension-wise from right

   Rightmost dims: 3 and 3 match. Next dims: 1 and 5, 1 broadcasts to 5. Leftmost dims: 4 and 1, 1 broadcasts to 4.

2. Step 2: Determine broadcasted shape

   Broadcasted shape is (4, 5, 3) combining max of each dimension.

3. Final Answer:

   (4, 5, 3) -> Option B

4. Quick Check:

   Broadcast dims max or 1 expands [OK]

Hint: Broadcast dims take max or 1 expands to max [OK]

Common Mistakes:

• Confusing which dimension broadcasts to which
• Expecting error when shapes are compatible
• Mixing up order of dimensions

4. The following code throws an error. What is the cause?

import numpy as np
np.broadcast_shapes((3, 2), (2, 3))

medium

A. Shapes are not compatible for broadcasting

B. Function broadcast_shapes does not exist

C. Tuples must be of same length

D. Missing import statement

Solution

1. Step 1: Check broadcasting rules for shapes (3, 2) and (2, 3)

   Compare from right: 2 vs 3 are different and neither is 1, so incompatible.

2. Step 2: Confirm error cause

   Since shapes cannot broadcast, numpy.broadcast_shapes raises ValueError.

3. Final Answer:

   Shapes are not compatible for broadcasting -> Option A

4. Quick Check:

   Broadcast dims must be equal or 1 [OK]

Hint: Check dims right to left; mismatch without 1 causes error [OK]

Common Mistakes:

• Thinking function is missing or typo
• Assuming tuples must be same length
• Ignoring broadcasting dimension rules

5. You have arrays with shapes (7, 1, 5) and (1, 3, 1). You want to add them using broadcasting. What will be the resulting shape?

hard

A. (1, 3, 5)

B. (7, 1, 1)

C. (7, 3, 5)

D. Cannot broadcast these shapes

Solution

1. Step 1: Compare shapes from right to left

   Right dims: 5 and 1, 1 broadcasts to 5. Middle dims: 1 and 3, 1 broadcasts to 3. Left dims: 7 and 1, 1 broadcasts to 7.

2. Step 2: Combine broadcasted dimensions

   Resulting shape is (7, 3, 5) taking max of each dimension.

3. Final Answer:

   (7, 3, 5) -> Option C

4. Quick Check:

   Broadcast dims max or 1 expands [OK]

Hint: Broadcast dims max or 1 expands to max [OK]

Common Mistakes:

• Mixing up dimension order
• Assuming shapes must be identical
• Forgetting 1 can broadcast to any size