Negative indexing in NumPy - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is negative indexing in numpy arrays?

Negative indexing means counting elements from the end of the array instead of the start. For example, -1 refers to the last element, -2 to the second last, and so on.

beginner

How do you access the last element of a numpy array using negative indexing?

Use array[-1] to get the last element of the numpy array.

beginner

What will array[-3] return in a numpy array?

It returns the third element from the end of the array.

intermediate

Can negative indexing be used with slicing in numpy? Give an example.

Yes. For example, array[-3:-1] returns a slice starting from the third last element up to (but not including) the second last element.

intermediate

Why is negative indexing useful in data science with numpy?

It allows easy access to elements from the end without needing to know the array length. This is helpful for tasks like getting recent data points or last values.

What does array[-1] return in a numpy array?

A The first element

B The last element

C The middle element

D An error

Negative index -1 always points to the last element in a numpy array.

If array = np.array([10, 20, 30, 40]), what is array[-2]?

A 30

B 20

C 40

D 10

array[-2] accesses the second last element, which is 30.

Which slice uses negative indexing to get the last three elements of array?

A array[3:]

B array[:3]

C array[-3:]

D array[:-3]

array[-3:] slices from the third last element to the end.

What happens if you use array[-len(array)-1] in numpy?

A IndexError

B Returns the first element

C Returns the last element

D Returns None

Negative indices less than -len(array) cause an IndexError.

Why might negative indexing be preferred over positive indexing?

A It is faster

B It avoids errors

C It uses less memory

D It allows easy access from the end without knowing length

Negative indexing lets you access elements from the end without calculating array length.

Explain how negative indexing works in numpy arrays and give an example.

Think about how you count backwards from the last element.

Describe a real-life situation where negative indexing in numpy would be helpful.

Imagine you want the last few days of sales data.

Practice

1. What does negative indexing in a numpy array allow you to do?

easy

A. Sort the array in descending order

B. Access elements starting from the end of the array

C. Change the size of the array

D. Access elements only at the beginning of the array

Solution

1. Step 1: Understand negative indexing concept

   Negative indexing means counting elements from the end of the array, starting at -1 for the last element.

2. Step 2: Compare options with concept

   Only Access elements starting from the end of the array correctly describes accessing elements from the end using negative indexes.

3. Final Answer:

   Access elements starting from the end of the array -> Option B

4. Quick Check:

   Negative indexing = Access from end [OK]

Hint: Negative index -1 means last element [OK]

Common Mistakes:

• Thinking negative index changes array size
• Confusing negative indexing with sorting
• Assuming negative index accesses start only at beginning

2. Which of the following is the correct syntax to get the last element of a numpy array arr using negative indexing?

easy

A. arr[0]

B. arr[1]

C. arr[-0]

D. arr[-1]

Solution

1. Step 1: Recall negative index for last element

   In numpy, -1 is used to access the last element of an array.

2. Step 2: Check each option

   arr[-1] uses arr[-1] which correctly accesses the last element. Others do not.

3. Final Answer:

   arr[-1] -> Option D

4. Quick Check:

   Last element = arr[-1] [OK]

Hint: Use arr[-1] for last element [OK]

Common Mistakes:

• Using arr[-0] which is same as arr[0]
• Using positive index 1 which is second element
• Confusing zero index with negative zero

3. Given the numpy array arr = np.array([10, 20, 30, 40, 50]), what is the output of arr[-3]?

medium

A. 20

B. 40

C. 30

D. 50

Solution

1. Step 1: Understand negative index -3

   Negative index -3 means counting from the end: last is -1 (50), second last -2 (40), third last -3 (30).

2. Step 2: Identify element at index -3

   The element at arr[-3] is 30.

3. Final Answer:

   30 -> Option C

4. Quick Check:

   arr[-3] = 30 [OK]

Hint: Count backward: -1 last, -2 second last, -3 third last [OK]

Common Mistakes:

• Counting negative index from start instead of end
• Mixing up index -3 with positive index 3
• Off-by-one errors in counting

4. Consider the code snippet:

import numpy as np
arr = np.array([5, 10, 15, 20])
print(arr[-5])

What is the error in this code?

medium

A. IndexError: index -5 is out of bounds for axis 0 with size 4

B. SyntaxError due to negative index

C. Prints 5

D. Prints 20

Solution

1. Step 1: Check array size and index used

   Array has 4 elements, valid negative indexes are -1 to -4.

2. Step 2: Understand index -5 usage

   Index -5 is outside valid range, causing IndexError.

3. Final Answer:

   IndexError: index -5 is out of bounds for axis 0 with size 4 -> Option A

4. Quick Check:

   Negative index out of range = IndexError [OK]

Hint: Negative index must be >= -array length [OK]

Common Mistakes:

• Assuming negative index wraps around infinitely
• Thinking negative index causes syntax error
• Expecting last element instead of error

5. You have a 2D numpy array arr = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]). What does arr[-1, -2] return?

hard

A. 8

B. 7

C. 6

D. 9

Solution

1. Step 1: Understand negative indexing in 2D arrays

   For rows, -1 means last row: [7, 8, 9]. For columns, -2 means second last column.

2. Step 2: Identify element at arr[-1, -2]

   Last row is [7, 8, 9], second last column is element 8.

3. Final Answer:

   8 -> Option A

4. Quick Check:

   arr[-1, -2] = 8 [OK]

Hint: Negative indexes count from end in each dimension [OK]

Common Mistakes:

• Mixing row and column indexes
• Using positive indexes instead of negative
• Confusing which axis negative index applies to