apply() with lambda functions in Pandas - Time & Space Complexity

Time Complexity: apply() with lambda functions

O(n)

Understanding Time Complexity

We want to understand how the time needed to run apply() with lambda functions changes as the data grows.

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

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import pandas as pd

df = pd.DataFrame({'A': range(1000)})
df['B'] = df['A'].apply(lambda x: x * 2)

This code creates a column 'B' by doubling each value in column 'A' using apply() with a lambda function.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The lambda function is called once for each row in column 'A'.
• How many times: Exactly as many times as there are rows in the DataFrame.

How Execution Grows With Input

As the number of rows increases, the total work grows in direct proportion.

Input Size (n)	Approx. Operations
10	10 calls to lambda
100	100 calls to lambda
1000	1000 calls to lambda

Pattern observation: Doubling the input size doubles the number of lambda calls and total work.

Final Time Complexity

Time Complexity: O(n)

This means the time needed grows linearly with the number of rows in the DataFrame.

Common Mistake

[X] Wrong: "Using apply() with a lambda is always slow because it loops over the data multiple times."

[OK] Correct: The lambda function is called once per row, so the loop happens only once. The time grows linearly, not more.

Interview Connect

Understanding how apply() scales helps you explain your data processing choices clearly and confidently.

Self-Check

"What if we replaced the lambda with a vectorized operation instead? How would the time complexity change?"