Adding and removing categories in Pandas - Time & Space Complexity

Time Complexity: Adding and removing categories

O(n + k)

Understanding Time Complexity

We want to understand how the time needed changes when we add or remove categories in a pandas categorical column.

How does the work grow as the number of categories or data size grows?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import pandas as pd

# Create a categorical column
cat = pd.Categorical(["a", "b", "a", "c"])

# Add a new category
cat = cat.add_categories(["d"])

# Remove a category
cat = cat.remove_categories(["b"])

This code creates a categorical column, then adds a new category, and finally removes an existing category.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Updating the internal categories list and mapping data to new categories.
• How many times: The operations scan through the categories and sometimes the data values once each.

How Execution Grows With Input

When adding or removing categories, pandas updates the list of categories and may check data values to adjust mappings.

Input Size (n)	Approx. Operations
10 categories, 1000 data points	Operations scale with categories and data size, roughly scanning categories and data once.
100 categories, 10,000 data points	Operations increase roughly 10 times, scanning more categories and data.
1000 categories, 100,000 data points	Operations increase roughly 100 times, scanning all categories and data.

Pattern observation: The work grows roughly linearly with the number of categories and data points.

Final Time Complexity

Time Complexity: O(n + k)

This means the time grows linearly with the number of data points (n) plus the number of categories (k).

Common Mistake

[X] Wrong: "Adding or removing categories is instant and does not depend on data size."

[OK] Correct: Pandas must update category mappings and sometimes check all data points, so time depends on both categories and data size.

Interview Connect

Understanding how operations scale with data size and categories helps you explain performance in real data tasks clearly and confidently.

Self-Check

"What if we add multiple categories at once instead of one by one? How would the time complexity change?"

Practice

1. What does the add_categories() method do in pandas categorical data?

easy

A. It converts a column to a categorical type.

B. It removes categories from a categorical column.

C. It adds new possible categories to an existing categorical column.

D. It renames existing categories in a categorical column.

Solution

1. Step 1: Understand the purpose of add_categories()

   This method is used to add new possible categories to a pandas categorical column without changing existing data.

2. Step 2: Differentiate from other methods

   Unlike remove_categories() which removes categories, add_categories() only adds new ones.

3. Final Answer:

   It adds new possible categories to an existing categorical column. -> Option C

4. Quick Check:

   add_categories() adds categories [OK]

Hint: Remember: add_categories adds new options, doesn't remove [OK]

Common Mistakes:

• Confusing add_categories with remove_categories
• Thinking it changes existing data values
• Assuming it renames categories

2. Which of the following is the correct syntax to remove categories from a pandas categorical column named df['color']?

easy

A. df['color'].remove_categories(['red', 'blue'])

B. df['color'].drop_categories(['red', 'blue'])

C. df['color'].delete_categories(['red', 'blue'])

D. df['color'].pop_categories(['red', 'blue'])

Solution

1. Step 1: Recall the correct method name

   The pandas method to remove categories is remove_categories().

2. Step 2: Match the syntax with the method

   df['color'].remove_categories(['red', 'blue']) uses remove_categories() correctly on the categorical column.

3. Final Answer:

   df['color'].remove_categories(['red', 'blue']) -> Option A

4. Quick Check:

   Use remove_categories() to remove categories [OK]

Hint: Remember method name is remove_categories, not drop or delete [OK]

Common Mistakes:

• Using non-existent methods like drop_categories
• Confusing remove_categories with add_categories
• Trying to remove categories with pop or delete

3. Given the code:

import pandas as pd
cat = pd.Categorical(['apple', 'banana', 'apple'], categories=['apple', 'banana', 'cherry'])
cat2 = cat.remove_categories(['banana'])
print(cat2)

What will be the output?

medium

A. [apple, NaN, apple]
Categories (2, object): [apple, cherry]

B. [apple, banana, apple]
Categories (2, object): [apple, cherry]

C. [apple, NaN, apple]
Categories (3, object): [apple, banana, cherry]

D. [apple, banana, apple]
Categories (3, object): [apple, banana, cherry]

Solution

1. Step 1: Understand remove_categories effect on data

   Removing 'banana' category replaces all 'banana' values with NaN and removes 'banana' from categories.

2. Step 2: Analyze the printed output

   Values become ['apple', NaN, 'apple'] and categories become ['apple', 'cherry'] with length 2.

3. Final Answer:

   [apple, NaN, apple] Categories (2, object): [apple, cherry] -> Option A

4. Quick Check:

   Removed category replaced by NaN [OK]

Hint: Removing category replaces values with NaN [OK]

Common Mistakes:

• Expecting removed category values to stay unchanged
• Thinking categories length remains same
• Confusing categories list after removal

4. Consider this code snippet:

import pandas as pd
cat = pd.Categorical(['dog', 'cat', 'bird'], categories=['dog', 'cat', 'bird'])
cat = cat.add_categories('fish')
cat = cat.remove_categories('cat')

What is the error in this code?

medium

A. Categorical cannot have more than 3 categories.

B. add_categories cannot add a single category.

C. You cannot chain add_categories and remove_categories.

D. remove_categories expects a list, not a string.

Solution

1. Step 1: Check method argument types

   remove_categories() requires a list or iterable of categories to remove, not a single string.

2. Step 2: Identify the error cause

   Passing 'cat' as a string causes a TypeError or unexpected behavior.

3. Final Answer:

   remove_categories expects a list, not a string. -> Option D

4. Quick Check:

   Pass list to remove_categories [OK]

Hint: Always pass list to remove_categories, not single string [OK]

Common Mistakes:

• Passing single string instead of list to remove_categories
• Thinking add_categories can't add one item
• Assuming chaining methods is invalid

5. You have a pandas categorical column df['status'] with categories ['new', 'in_progress', 'done']. You want to add a new category 'archived' and remove 'new' without losing data for other rows. Which sequence of commands achieves this correctly?

hard

A. df['status'] = df['status'].remove_categories(['new'])
df['status'].add_categories(['archived'])

B. df['status'] = df['status'].add_categories(['archived'])
df['status'] = df['status'].remove_categories(['new'])

C. df['status'].remove_categories(['new'])
df['status'].add_categories(['archived'])

D. df['status'].add_categories('archived')
df['status'].remove_categories('new')

Solution

1. Step 1: Add new category before removing

   Adding 'archived' first ensures it exists as a valid category before removal.

2. Step 2: Remove 'new' category properly

   Removing 'new' replaces its values with NaN, so do this after adding new category and assign back to column.

3. Step 3: Assign results back to the column

   Both methods return new categorical objects, so assign back to df['status'].

4. Final Answer:

   df['status'] = df['status'].add_categories(['archived']) df['status'] = df['status'].remove_categories(['new']) -> Option B

5. Quick Check:

   Add then remove, assign back [OK]

Hint: Add categories first, then remove, assign back [OK]

Common Mistakes:

• Removing category before adding new one
• Not assigning back to the DataFrame column
• Passing string instead of list to methods