NumPy and scientific computing ecosystem - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of NumPy broadcasting with different shapes

What is the output of the following code snippet?

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 Raises ValueError due to shape mismatch

C

[[10 20 30]
 [10 20 30]]

D

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

💡 Hint

Recall how NumPy broadcasts arrays with compatible shapes.

NumPy broadcasts the 1D array arr2 across the rows of arr1, adding element-wise. The shapes (2,3) and (3,) are compatible for broadcasting.

❓ data_output

intermediate

Shape and size of a reshaped NumPy array

Given the code below, what are the shape and size of the array 'reshaped'?

NumPy

import numpy as np

arr = np.arange(24)
reshaped = arr.reshape(2, 3, 4)
print(reshaped.shape, reshaped.size)

A (2, 3, 4) 24

B (3, 4, 2) 24

C (2, 4, 3) 12

D (24,) 24

💡 Hint

The reshape method changes the shape but does not change the total number of elements.

The array is reshaped into dimensions 2 by 3 by 4, keeping the total size 24 (2*3*4).

🔧 Debug

advanced

Identify the error in NumPy matrix multiplication

What error will the following code raise when executed?

NumPy

import numpy as np

A = np.array([[1, 2], [3, 4]])
B = np.array([5, 6, 7])
C = np.dot(A, B)
print(C)

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

B No error, output: [17 39]

C IndexError: index out of bounds

D ValueError: shapes (2,2) and (3,) not aligned: 2 (dim 1) != 3 (dim 0)

💡 Hint

Check the shapes of the arrays before matrix multiplication.

Matrix multiplication requires the inner dimensions to match. Here, A is (2,2) and B is (3,), so they cannot be multiplied.

❓ visualization

advanced

Plotting a 2D Gaussian distribution using NumPy and Matplotlib

Which option produces a correct 2D heatmap of a Gaussian distribution centered at (0,0)?

NumPy

import numpy as np
import matplotlib.pyplot as plt

x = np.linspace(-3, 3, 100)
y = np.linspace(-3, 3, 100)
X, Y = np.meshgrid(x, y)
Z = np.exp(-(X**2 + Y**2))
plt.imshow(Z, extent=[-3,3,-3,3], origin='lower')
plt.colorbar()
plt.show()

A Raises NameError due to undefined variable Z

B Displays a checkerboard pattern with random colors

C Displays a smooth circular heatmap with highest intensity at center

D Displays a flat image with uniform color

💡 Hint

The Gaussian function decreases smoothly from the center.

The code computes a 2D Gaussian and plots it as a heatmap with highest intensity at the center (0,0).

🧠 Conceptual

expert

Understanding memory layout in NumPy arrays

Which statement about NumPy array memory layout is TRUE?

A Fortran-contiguous arrays store rows sequentially, while C-contiguous arrays store columns sequentially.

B C-contiguous arrays store rows sequentially in memory, while Fortran-contiguous arrays store columns sequentially.

C NumPy arrays always store data in column-major order regardless of flags.

D Memory layout does not affect performance in NumPy operations.

💡 Hint

Think about how C and Fortran languages store multi-dimensional arrays.

C-contiguous means row-major order (rows stored one after another). Fortran-contiguous means column-major order (columns stored one after another). This affects performance in some operations.