Mplcursors for hover labels in Matplotlib - Time & Space Complexity

Time Complexity: Mplcursors for hover labels

O(n)

Understanding Time Complexity

When using mplcursors to add hover labels on plots, it's important to understand how the time to respond grows as the number of points increases.

We want to know how the hover label updates scale with more data points.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import matplotlib.pyplot as plt
import mplcursors

n = 100  # Define n before using it
fig, ax = plt.subplots()
points = ax.scatter(range(n), range(n))
mplcursors.cursor(points)
plt.show()

This code creates a scatter plot with n points and enables hover labels using mplcursors.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Checking mouse position against each of the n points to detect hover.
• How many times: This check happens every time the mouse moves over the plot area.

How Execution Grows With Input

As the number of points n increases, the system checks more points for hover detection.

Input Size (n)	Approx. Operations per Hover
10	10 checks
100	100 checks
1000	1000 checks

Pattern observation: The number of checks grows linearly with the number of points.

Final Time Complexity

Time Complexity: O(n)

This means the time to detect which point is hovered grows directly with the number of points.

Common Mistake

[X] Wrong: "Hover detection time stays the same no matter how many points are plotted."

[OK] Correct: Each point must be checked to see if the mouse is over it, so more points mean more checks and longer detection time.

Interview Connect

Understanding how interactive plot features scale helps you design responsive visualizations and shows you can think about user experience and performance together.

Self-Check

What if we changed from scatter points to a heatmap? How would the time complexity of hover detection change?