Custom legend entries in Matplotlib - Time & Space Complexity

Time Complexity: Custom legend entries

O(n)

Understanding Time Complexity

We want to understand how the time needed to create custom legend entries in matplotlib changes as the number of legend items grows.

How does adding more custom legend entries affect the drawing time?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import matplotlib.pyplot as plt
from matplotlib.lines import Line2D

custom_lines = [Line2D([0], [0], color='r', lw=4),
                Line2D([0], [0], color='g', lw=4)]
labels = ['Red line', 'Green line']

plt.legend(custom_lines, labels)
plt.show()

This code creates a legend with two custom line entries using matplotlib's Line2D objects.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Creating and adding each custom legend entry to the legend.
• How many times: Once per legend item, so the number of legend items (n) times.

How Execution Grows With Input

As the number of custom legend entries increases, the time to create and render the legend grows roughly in direct proportion.

Input Size (n)	Approx. Operations
10	About 10 legend entry creations and render steps
100	About 100 legend entry creations and render steps
1000	About 1000 legend entry creations and render steps

Pattern observation: The time grows linearly as the number of legend entries increases.

Final Time Complexity

Time Complexity: O(n)

This means the time to create the legend grows directly with the number of custom entries.

Common Mistake

[X] Wrong: "Adding more legend entries does not affect performance much because it's just a small part of the plot."

[OK] Correct: Each legend entry requires separate drawing and layout work, so more entries mean more work and longer rendering time.

Interview Connect

Understanding how UI elements like legends scale helps you reason about performance in data visualization tasks, a useful skill in many data science roles.

Self-Check

"What if we used a single legend entry with multiple labels instead of multiple separate entries? How would the time complexity change?"