Vectorization over loops in NumPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of vectorized vs loop sum

What is the output of the following code that sums two arrays using a loop and using vectorization?

NumPy

import numpy as np
arr1 = np.array([1, 2, 3])
arr2 = np.array([4, 5, 6])

# Using loop
result_loop = []
for i in range(len(arr1)):
    result_loop.append(arr1[i] + arr2[i])

# Using vectorization
result_vec = arr1 + arr2

print(result_loop)
print(result_vec.tolist())

A [5, 7, 9]\n[4, 6, 8]

B [5, 7, 9]\n[1, 2, 3, 4, 5, 6]

C [5, 7, 9]\n[5, 7, 9]

D [4, 6, 8]\n[5, 7, 9]

💡 Hint

Think about how element-wise addition works in numpy arrays compared to manual loops.

Both the loop and vectorized code add corresponding elements of the two arrays. The loop creates a list with sums, and vectorization returns a numpy array which is converted to list for printing. Both outputs are the same: [5, 7, 9].

❓ data_output

intermediate

Result shape after vectorized operation

Given two numpy arrays a with shape (3, 1) and b with shape (1, 4), what is the shape of the result after a + b?

NumPy

import numpy as np
a = np.array([[1], [2], [3]])
b = np.array([[10, 20, 30, 40]])
c = a + b
print(c.shape)

A (3, 4)

B (3, 1)

C (1, 4)

D (4, 3)

💡 Hint

Remember numpy broadcasting rules for arrays with different shapes.

Array a has shape (3,1) and b has shape (1,4). Broadcasting expands them to (3,4) each before addition, so the result shape is (3,4).

🔧 Debug

advanced

Identify error in vectorized code

What error does the following code raise?

NumPy

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

A TypeError: unsupported operand type(s) for +: 'numpy.ndarray' and 'str'

B ValueError: operands could not be broadcast together with shapes (3,) (1,)

C SyntaxError: invalid syntax

D No error, output: [5 6 7]

💡 Hint

Think about adding numbers and strings in numpy arrays.

You cannot add a numpy array of integers and a string directly. This raises a TypeError about unsupported operand types.

🚀 Application

advanced

Vectorized calculation of Euclidean distances

You have two sets of points in 2D space stored as numpy arrays A (shape (m, 2)) and B (shape (n, 2)). Which option correctly computes the matrix of Euclidean distances between each point in A and each point in B using vectorization?

NumPy

import numpy as np
A = np.array([[1, 2], [3, 4]])
B = np.array([[5, 6], [7, 8], [9, 10]])

A np.sqrt(((A - B) ** 2).sum(axis=1))

B np.sqrt(((A[:, None, :] - B[None, :, :]) ** 2).sum(axis=2))

C np.linalg.norm(A - B, axis=1)

D np.sum(np.abs(A - B), axis=2)

💡 Hint

Use broadcasting to subtract each point in B from each point in A, then sum squared differences.

Option B uses broadcasting to create a (m, n, 2) array of differences, squares them, sums over coordinates, and takes square root to get Euclidean distances matrix of shape (m, n).

🧠 Conceptual

expert

Why vectorization is faster than loops in numpy?

Which of the following best explains why vectorized operations in numpy are faster than explicit Python loops?

A Vectorized operations use GPU by default to speed up calculations.

B Vectorized operations use multiple CPU cores automatically to parallelize loops.

C Vectorized operations convert data to strings for faster processing.

D Vectorized operations use optimized C code and avoid Python-level loops, reducing overhead.

💡 Hint

Think about what happens under the hood when numpy runs vectorized code.

Numpy vectorized operations run compiled C code internally, avoiding slow Python loops and function calls, which makes them faster. They do not automatically use multiple cores or GPUs.