Negative indexing in NumPy - Step-by-Step Execution

Concept Flow - Negative indexing

Start with array

↓

Choose index

↓

Is index negative?

No→Access element at index

Yes↓

Convert negative index to positive: length + index

↓

Access element at converted index

↓

Return element

Negative indexing means counting from the end of the array. If index is negative, add array length to get the positive index.

Execution Sample

NumPy

import numpy as np
arr = np.array([10, 20, 30, 40, 50])
print(arr[-1])
print(arr[-3])

Access elements from the end of the array using negative indexes.

Execution Table

Step	Index Used	Is Negative?	Converted Index	Element Accessed	Output
1	-1	Yes	5 + (-1) = 4	arr[4]	50
2	-3	Yes	5 + (-3) = 2	arr[2]	30
3	End	N/A	N/A	N/A	Execution ends

💡 All negative indexes converted and elements accessed; execution ends.

Variable Tracker

Variable	Start	After Step 1	After Step 2	Final
arr	[10, 20, 30, 40, 50]	[10, 20, 30, 40, 50]	[10, 20, 30, 40, 50]	[10, 20, 30, 40, 50]
index	N/A	-1	-3	N/A
converted_index	N/A	4	2	N/A
output	N/A	50	30	N/A

Key Moments - 2 Insights

Why do we add the array length to a negative index?

Because negative indexes count from the end, adding the array length converts them to the correct positive index (see execution_table steps 1 and 2).

What happens if the negative index is -1?

It accesses the last element because converted index is length - 1 (step 1 in execution_table).

Visual Quiz - 3 Questions

Look at the execution_table, what element does arr[-3] access?

A 20

B 30

C 40

D 50

💡 Hint

Check row 2 in execution_table where index -3 converts to 2 and accesses arr[2].

At which step does the negative index -1 get converted to a positive index?

A Step 1

B Step 2

C Step 3

D No conversion needed

💡 Hint

See execution_table row 1 where index -1 is converted to 4.

If the array length was 6 instead of 5, what would arr[-1] access?

A arr[4]

B arr[1]

C arr[5]

D arr[0]

💡 Hint

Negative index -1 converts to length + (-1), so 6 + (-1) = 5.

Concept Snapshot

Negative indexing in numpy:
- Use negative numbers to count from the end.
- Negative index i means access element at length + i.
- Example: arr[-1] is last element.
- Useful to quickly access elements from the back.
- Works like arr[len(arr) + index].

Full Transcript

Negative indexing lets you access elements from the end of a numpy array. When you use a negative index, numpy adds the array length to that index to find the correct position. For example, arr[-1] accesses the last element because it converts to arr[length - 1]. This is helpful to quickly get elements from the back without counting from zero. The execution steps show how negative indexes are converted and used to access elements.