Multi-dimensional fancy indexing in NumPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of multi-dimensional fancy indexing with arrays

What is the output of the following code snippet using NumPy fancy indexing?

NumPy

import numpy as np
arr = np.array([[10, 20, 30], [40, 50, 60], [70, 80, 90]])
rows = np.array([0, 1, 2])
cols = np.array([2, 1, 0])
result = arr[rows, cols]
print(result)

A [30 50 70]

B [10 50 90]

C [30 40 90]

D [10 20 30]

💡 Hint

Remember that arr[rows, cols] selects elements at positions (rows[i], cols[i]) for each i.

The code selects elements at positions (0,2), (1,1), and (2,0) from the array, which are 30, 50, and 70 respectively.

❓ data_output

intermediate

Shape of result from multi-dimensional fancy indexing

Given the code below, what is the shape of the resulting array 'result'?

NumPy

import numpy as np
arr = np.arange(27).reshape(3,3,3)
rows = np.array([0, 1])
cols = np.array([1, 2])
result = arr[rows, cols]
print(result.shape)

A (2, 2)

B (2, 3)

C (3, 3)

D (3, 2)

💡 Hint

Check how fancy indexing with two arrays affects the shape when indexing a 3D array.

The indexing arr[rows, cols] selects elements at (0,1) and (1,2), each is a 1D array of length 3, so the result shape is (2,3).

🔧 Debug

advanced

Identify the error in multi-dimensional fancy indexing

What error does the following code raise when executed?

NumPy

import numpy as np
arr = np.array([[1, 2], [3, 4]])
rows = np.array([0, 1, 2])
cols = np.array([1, 0, 1])
result = arr[rows, cols]
print(result)

A No error, outputs [2 3 4]

B ValueError: shape mismatch between rows and cols

C TypeError: unsupported operand type(s) for indexing

D IndexError: index 2 is out of bounds for axis 0 with size 2

💡 Hint

Check the size of the array and the indices used for rows.

The array has shape (2,2), so index 2 for rows is out of bounds causing IndexError.

🚀 Application

advanced

Extract diagonal elements using multi-dimensional fancy indexing

Which option correctly extracts the diagonal elements from a 2D NumPy array 'arr' using fancy indexing?

NumPy

import numpy as np
arr = np.array([[5, 6, 7], [8, 9, 10], [11, 12, 13]])

A arr[np.arange(3), np.arange(3)]

B arr[[0,1,2], [2,1,0]]

C arr[:, np.arange(3)]

D arr[np.arange(3), 0]

💡 Hint

Diagonal elements have the same row and column indices.

Using arr[np.arange(3), np.arange(3)] selects elements where row and column indices are equal, which are the diagonal elements.

🧠 Conceptual

expert

Effect of broadcasting in multi-dimensional fancy indexing

Given the code below, what is the shape of 'result' and why?

NumPy

import numpy as np
arr = np.arange(24).reshape(4,6)
rows = np.array([[0], [1], [2]])
cols = np.array([1, 3, 5])
result = arr[rows, cols]
print(result.shape)

A (1, 3) because rows is 2D and cols is 1D, resulting in minimal broadcast

B (4, 6) because fancy indexing returns the original array shape

C (3, 3) because rows and cols broadcast to shape (3,3) and select elements accordingly

D (3,) because rows and cols are flattened before indexing

💡 Hint

Consider how NumPy broadcasts arrays of shapes (3,1) and (3,) for indexing.

rows has shape (3,1) and cols has shape (3,), which broadcast to (3,3). The result shape matches this broadcasted shape.