Legend placement options in Matplotlib - Time & Space Complexity

Time Complexity: Legend placement options

O(n)

Understanding Time Complexity

We want to understand how the time to place a legend changes as the plot size or number of legend items grows.

How does matplotlib handle legend placement when there are more items or different positions?

Scenario Under Consideration

Analyze the time complexity of this matplotlib legend placement code.

import matplotlib.pyplot as plt

fig, ax = plt.subplots()
for i in range(10):
    ax.plot([0, 1], [i, i], label=f'Line {i}')

ax.legend(loc='upper right')
plt.show()

This code plots 10 lines and places a legend in the upper right corner.

Identify Repeating Operations

Look for loops or repeated steps in legend placement.

• Primary operation: Iterating over legend items to create labels and markers.
• How many times: Once per legend item, here 10 times.

How Execution Grows With Input

As the number of legend items grows, the work to place them grows too.

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

Pattern observation: The operations grow linearly with the number of legend items.

Final Time Complexity

Time Complexity: O(n)

This means the time to place the legend grows in direct proportion to the number of items.

Common Mistake

[X] Wrong: "Legend placement time stays the same no matter how many items there are."

[OK] Correct: Each legend item needs space and drawing, so more items mean more work.

Interview Connect

Understanding how legend placement scales helps you think about plotting performance and user experience as data grows.

Self-Check

What if we changed the legend to be placed outside the plot area? How would that affect the time complexity?