Feature engineering basics in Pandas - Time & Space Complexity

Time Complexity: Feature engineering basics

O(n)

Understanding Time Complexity

When creating new features from data, it is important to know how the time to do this grows as the data gets bigger.

We want to understand how the work needed changes when we add more rows or columns.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import pandas as pd

n = 10  # Example value for n

df = pd.DataFrame({
    'A': range(1, n+1),
    'B': range(n, 0, -1)
})

df['C'] = df['A'] + df['B']
df['D'] = df['A'] * 2

This code creates two new columns by adding and multiplying existing columns for each row.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Adding and multiplying values for each row in the DataFrame.
• How many times: Once per row, so n times where n is the number of rows.

How Execution Grows With Input

As the number of rows grows, the number of operations grows roughly the same amount.

Input Size (n)	Approx. Operations
10	About 20 (2 operations per row)
100	About 200
1000	About 2000

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

Final Time Complexity

Time Complexity: O(n)

This means the time to create new features grows in a straight line as the data size grows.

Common Mistake

[X] Wrong: "Creating new features takes the same time no matter how big the data is."

[OK] Correct: Each row needs to be processed, so more rows mean more work and more time.

Interview Connect

Understanding how feature creation scales helps you explain your data preparation steps clearly and shows you know how to handle bigger datasets.

Self-Check

"What if we created new features using pairs of rows instead of single rows? How would the time complexity change?"

Practice

1. What is the main purpose of feature engineering in pandas?

easy

A. To create new useful columns from existing data

B. To delete unnecessary rows from the dataset

C. To change the data type of columns

D. To visualize data using charts

Solution

1. Step 1: Understand feature engineering definition

   Feature engineering means creating new columns that help models learn better.

2. Step 2: Compare options with definition

   Only To create new useful columns from existing data matches the purpose of creating new useful columns from existing data.

3. Final Answer:

   To create new useful columns from existing data -> Option A

4. Quick Check:

   Feature engineering = create new columns [OK]

Hint: Feature engineering = making new columns from old data [OK]

Common Mistakes:

• Confusing feature engineering with data cleaning
• Thinking it only changes data types
• Mixing it up with data visualization

2. Which of the following is the correct way to create a new column total as sum of columns 2a and 2b in a pandas DataFrame df?

easy

A. df['total'] <- df['2a'] + df['2b']

B. df.total = df.2a + df.2b

C. df['total'] == df['2a'] + df['2b']

D. df['total'] = df['2a'] + df['2b']

Solution

1. Step 1: Recall pandas syntax for new column

   Use df['new_col'] = expression to create new columns.

2. Step 2: Check each option

   df['total'] = df['2a'] + df['2b'] uses correct syntax. df.total = df.2a + df.2b misses brackets, A uses wrong operator, D uses comparison operator.

3. Final Answer:

   df['total'] = df['2a'] + df['2b'] -> Option D

4. Quick Check:

   New column = df['col'] = ... [OK]

Hint: Use df['col'] = ... to add new columns [OK]

Common Mistakes:

• Using == instead of = for assignment
• Using <- which is not Python syntax
• Accessing columns without brackets

3. Given the DataFrame df below, what will be the output of df['age_group'] after this code?

import pandas as pd
df = pd.DataFrame({'age': [15, 22, 37, 45]})
df['age_group'] = pd.cut(df['age'], bins=[0, 18, 35, 60], labels=['child', 'young_adult', 'adult'])

medium

A. [child, young_adult, young_adult, adult]

B. [child, child, young_adult, adult]

C. [child, young_adult, adult, adult]

D. [child, young_adult, adult, young_adult]

Solution

1. Step 1: Understand pd.cut bins and labels

   Bins: 0-18 = child, 18-35 = young_adult, 35-60 = adult.

2. Step 2: Assign each age to bin

   15 -> child, 22 -> young_adult, 37 -> adult, 45 -> adult.

3. Final Answer:

   [child, young_adult, adult, adult] -> Option C

4. Quick Check:

   Age 37 and 45 fall in adult bin [OK]

Hint: Match values to bins to find labels [OK]

Common Mistakes:

• Misunderstanding bin edges (inclusive/exclusive)
• Assigning wrong labels to ages
• Confusing order of labels

4. What is wrong with this code to create a new column year from a datetime column date in DataFrame df?

df['year'] = df['date'].year

medium

A. There is no error; the code is correct

B. You must use dt.year to access year from datetime column

C. You should use df.year = df.date.year instead

D. The column date must be converted to string first

Solution

1. Step 1: Recall how to extract year from datetime column

   Use df['date'].dt.year to get year from pandas datetime column.

2. Step 2: Identify error in code

   Code uses df['date'].year which is invalid; .year is not attribute of Series.

3. Final Answer:

   You must use dt.year to access year from datetime column -> Option B

4. Quick Check:

   Use df['date'].dt.year for datetime year [OK]

Hint: Use .dt accessor for datetime column parts [OK]

Common Mistakes:

• Using .year directly on Series instead of .dt.year
• Converting datetime to string unnecessarily
• Assigning to df.year instead of df['year']

5. You have a DataFrame df with columns height_cm and weight_kg. You want to create a new feature bmi using the formula bmi = weight_kg / (height_m)^2, where height in meters is height_cm divided by 100. Which code correctly creates the bmi column?

hard

A. df['bmi'] = df['weight_kg'] / (df['height_cm'] / 100) ** 2

B. df['bmi'] = df['weight_kg'] / df['height_cm'] ** 2 / 10000

C. df['bmi'] = df['weight_kg'] * (df['height_cm'] / 100) ** 2

D. df['bmi'] = df['weight_kg'] / (df['height_cm'] * 100) ** 2

Solution

1. Step 1: Convert height from cm to meters

   Height in meters = height_cm / 100.

2. Step 2: Apply BMI formula correctly

   BMI = weight_kg / (height_m)^2 = weight_kg / (height_cm / 100)^2.

3. Step 3: Check each option

   df['bmi'] = df['weight_kg'] / (df['height_cm'] / 100) ** 2 matches formula exactly. Others have wrong operations or units.

4. Final Answer:

   df['bmi'] = df['weight_kg'] / (df['height_cm'] / 100) ** 2 -> Option A

5. Quick Check:

   BMI formula with height in meters = weight / height² [OK]

Hint: Divide height_cm by 100 before squaring for BMI [OK]

Common Mistakes:

• Forgetting to convert cm to meters
• Multiplying instead of dividing
• Incorrect order of operations