Category codes and labels in Pandas - Time & Space Complexity

Time Complexity: Category codes and labels

O(n)

Understanding Time Complexity

We want to understand how the time needed to get category codes and labels changes as the data grows.

How does the work grow when we have more data rows?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import pandas as pd

# Create a categorical column
cats = pd.Categorical(['apple', 'banana', 'apple', 'orange', 'banana'])

# Get the integer codes for categories
codes = cats.codes

# Get the category labels
labels = cats.categories

This code creates a categorical data column, then extracts the integer codes and the category labels.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Assigning codes to each data row by matching its category.
• How many times: Once for each row in the data (n times).

How Execution Grows With Input

As the number of rows grows, the work to assign codes grows roughly the same amount.

Input Size (n)	Approx. Operations
10	About 10 code assignments
100	About 100 code assignments
1000	About 1000 code assignments

Pattern observation: The work grows directly with the number of rows.

Final Time Complexity

Time Complexity: O(n)

This means the time to get codes grows in a straight line as the data gets bigger.

Common Mistake

[X] Wrong: "Getting category codes is instant no matter how big the data is."

[OK] Correct: Even though categories are fixed, assigning codes must check each row, so time grows with data size.

Interview Connect

Understanding how category codes work helps you explain data processing speed clearly, a useful skill in real projects and interviews.

Self-Check

"What if we had many more unique categories? How would that affect the time complexity of getting codes?"

Practice

1. What does cat.codes show in a pandas categorical Series?

easy

A. The data type of the Series

B. The numeric codes representing each category

C. The count of each category

D. The text labels of the categories

Solution

1. Step 1: Understand what cat.codes returns

   cat.codes gives the integer codes for each category in the Series, replacing repeated text with numbers.

2. Step 2: Differentiate from cat.categories

   cat.categories shows the text labels, not the codes.

3. Final Answer:

   The numeric codes representing each category -> Option B

4. Quick Check:

   cat.codes = numeric codes [OK]

Hint: Remember: codes are numbers, categories are labels [OK]

Common Mistakes:

• Confusing codes with category labels
• Thinking codes show counts
• Assuming codes show data type

2. Which of the following is the correct way to access the category labels of a pandas categorical Series s?

easy

A. s.cat.categories

B. s.cat.codes

C. s.categories

D. s.cat.labels

Solution

1. Step 1: Recall the attribute for category labels

   The category labels are accessed via cat.categories on the Series.

2. Step 2: Check the options for correct syntax

   s.cat.categories is the correct syntax; s.categories is invalid, and cat.labels does not exist.

3. Final Answer:

   s.cat.categories -> Option A

4. Quick Check:

   Category labels = s.cat.categories [OK]

Hint: Use cat.categories to get labels, not just categories [OK]

Common Mistakes:

• Using s.categories instead of s.cat.categories
• Confusing cat.codes with labels
• Trying to use non-existent cat.labels

3. Given the code:

import pandas as pd
s = pd.Series(['apple', 'banana', 'apple', 'orange'], dtype='category')
print(s.cat.codes.tolist())

What is the output?

medium

A. [0, 1, 0, 2]

B. [1, 2, 1, 3]

C. [0, 0, 1, 2]

D. [1, 0, 1, 2]

Solution

1. Step 1: Identify categories and their order

   Categories are sorted alphabetically by default: ['apple', 'banana', 'orange'] with codes 0,1,2 respectively.

2. Step 2: Map each value to its code

   'apple' -> 0, 'banana' -> 1, 'apple' -> 0, 'orange' -> 2, so the list is [0, 1, 0, 2].

3. Final Answer:

   [0, 1, 0, 2] -> Option A

4. Quick Check:

   Alphabetical categories -> codes match [OK]

Hint: Categories sorted alphabetically by default [OK]

Common Mistakes:

• Assuming codes start at 1 instead of 0
• Ignoring alphabetical sorting of categories
• Mixing up category order

4. Which of the following is correct about this code snippet?

import pandas as pd
s = pd.Series(['cat', 'dog', 'cat'], dtype='category')
s.cat.categories = ['dog', 'cat']
print(s.cat.codes.tolist())

medium

A. You cannot assign new categories with different order directly

B. The categories list must be sorted alphabetically

C. You must convert Series to string before assigning categories

D. The code will run without errors and print [0, 1, 0]

Solution

1. Step 1: Understand category assignment rules

   Assigning to cat.categories redefines the labels for existing codes without changing the codes or raising errors, as long as new list has same length and unique values.

2. Step 2: Trace execution

   Original categories ['cat', 'dog'], codes [0,1,0]. New ['dog', 'cat'] same length/unique, codes unchanged, prints [0, 1, 0].

3. Final Answer:

   The code will run without errors and print [0, 1, 0] -> Option D

4. Quick Check:

   New categories redefine code labels, codes unchanged [OK]

Hint: Reassigning cat.categories changes labels but keeps codes intact [OK]

Common Mistakes:

• Thinking reordering causes ValueError
• Expecting codes to adjust to new order like [1, 0, 1]
• Assuming categories must stay alphabetical

5. You have a pandas categorical Series s with categories ['low', 'medium', 'high']. You want to rename the categories to ['L', 'M', 'H'] without changing the data. Which code correctly returns the renamed Series?

hard

A. s.cat.categories = ['L', 'M', 'H']

B. s.cat.categories.rename(['L', 'M', 'H'])

C. s.cat.rename_categories(['L', 'M', 'H'])

D. s.rename_categories(['L', 'M', 'H'])

Solution

1. Step 1: Understand how to rename categories

   The method cat.rename_categories() returns a new Series with renamed categories without changing data codes.

2. Step 2: Check other options for correctness

   Direct assignment to cat.categories works but can cause errors if not careful; cat.categories.rename() is invalid; rename_categories() is not a Series method.

3. Final Answer:

   s.cat.rename_categories(['L', 'M', 'H']) -> Option C

4. Quick Check:

   Use cat.rename_categories() to rename safely [OK]

Hint: Use cat.rename_categories() to rename categories safely [OK]

Common Mistakes:

• Trying to rename categories by invalid methods
• Directly assigning categories without matching length
• Confusing Series methods with cat accessor methods