applymap() for DataFrame-wide operations in Pandas - Time & Space Complexity

Time Complexity: applymap() for DataFrame-wide operations

O(n x m)

Understanding Time Complexity

We want to understand how the time to run applymap() changes as the DataFrame gets bigger.

How does the number of cells affect the work done?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import pandas as pd
import numpy as np

n, m = 10, 10  # example sizes

df = pd.DataFrame(np.random.randint(0, 100, size=(n, m)))

result = df.applymap(lambda x: x * 2)

This code doubles every number in the DataFrame using applymap().

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Applying the function to each cell in the DataFrame.
• How many times: Once for every cell, so total cells = rows x columns.

How Execution Grows With Input

As the DataFrame grows, the work grows with the number of cells.

Input Size (rows x columns)	Approx. Operations
10 x 10 = 100	100 function calls
100 x 100 = 10,000	10,000 function calls
1000 x 1000 = 1,000,000	1,000,000 function calls

Pattern observation: The number of operations grows directly with the total number of cells.

Final Time Complexity

Time Complexity: O(n x m)

This means the time grows proportionally to the total number of cells in the DataFrame.

Common Mistake

[X] Wrong: "applymap() runs in constant time regardless of DataFrame size."

[OK] Correct: The function runs once per cell, so more cells mean more work and more time.

Interview Connect

Knowing how applymap() scales helps you explain performance when working with large tables.

Self-Check

What if we changed applymap() to apply() on columns? How would the time complexity change?