eval() for expression evaluation in Pandas - Time & Space Complexity

Time Complexity: eval() for expression evaluation

O(n)

Understanding Time Complexity

We want to understand how the time needed to evaluate expressions with pandas eval() changes as the data size grows.

How does the work done by eval() scale when we use it on bigger data?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import pandas as pd

n = 10  # example size

df = pd.DataFrame({
    'A': range(n),
    'B': range(n, 2*n)
})

result = pd.eval('df.A + df.B')

This code creates a DataFrame with two columns and uses pd.eval() to add these columns element-wise.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Element-wise addition of two columns using eval().
• How many times: Once for each row in the DataFrame, so n times.

How Execution Grows With Input

As the number of rows n increases, the number of additions grows linearly.

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

Pattern observation: Doubling the input size roughly doubles the work done.

Final Time Complexity

Time Complexity: O(n)

This means the time to evaluate the expression grows in direct proportion to the number of rows.

Common Mistake

[X] Wrong: "Using eval() makes the operation constant time because it's optimized internally."

[OK] Correct: Even though eval() can be faster than normal Python loops, it still processes each row once, so the time grows with data size.

Interview Connect

Understanding how eval() scales helps you explain performance choices clearly and shows you know how data size affects computation time.

Self-Check

What if we changed the expression to multiply columns instead of adding? How would the time complexity change?