Arithmetic operations on columns in Pandas - Time & Space Complexity

Time Complexity: Arithmetic operations on columns

O(n)

Understanding Time Complexity

We want to understand how the time to do arithmetic on columns changes as the data grows.

How does the work increase when we have more rows in the table?

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(n),
    'B': range(n, 2*n)
})
df['C'] = df['A'] + df['B']

This code creates two columns with numbers and adds them to make a new column.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Adding each pair of numbers from columns A and B.
• How many times: Once for each row in the DataFrame.

How Execution Grows With Input

As the number of rows grows, the number of additions grows the same way.

Input Size (n)	Approx. Operations
10	10 additions
100	100 additions
1000	1000 additions

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

Final Time Complexity

Time Complexity: O(n)

This means the time to add columns grows in a straight line as the data gets bigger.

Common Mistake

[X] Wrong: "Adding two columns is instant no matter how big the data is."

[OK] Correct: Each row needs one addition, so more rows mean more work and more time.

Interview Connect

Knowing how operations grow with data size helps you explain your code choices clearly and confidently.

Self-Check

"What if we added two columns but only for rows where a condition is true? How would the time complexity change?"