LineCollection and PolyCollection for speed in Matplotlib - Time & Space Complexity

Time Complexity: LineCollection and PolyCollection for speed

O(n)

Understanding Time Complexity

When drawing many lines or polygons in matplotlib, speed matters a lot.

We want to know how the drawing time grows as we add more shapes.

Scenario Under Consideration

Analyze the time complexity of this matplotlib code using LineCollection.

import matplotlib.pyplot as plt
from matplotlib.collections import LineCollection

n = 100  # Define n before using it
lines = [[(i, 0), (i, 1)] for i in range(n)]
line_collection = LineCollection(lines)
fig, ax = plt.subplots()
ax.add_collection(line_collection)
plt.show()
    

This code creates n vertical lines and draws them all at once using LineCollection.

Identify Repeating Operations

Look for repeated actions that take time as n grows.

• Primary operation: Creating and adding each line segment to the collection.
• How many times: Once per line, so n times.

How Execution Grows With Input

As you add more lines, the work to draw them grows roughly in a straight line.

Input Size (n)	Approx. Operations
10	About 10 line creations and draws
100	About 100 line creations and draws
1000	About 1000 line creations and draws

Pattern observation: The time grows directly with the number of lines.

Final Time Complexity

Time Complexity: O(n)

This means if you double the number of lines, the drawing time roughly doubles.

Common Mistake

[X] Wrong: "Using LineCollection makes drawing time constant no matter how many lines."

[OK] Correct: LineCollection speeds up drawing by batching, but still must process each line once, so time grows with n.

Interview Connect

Understanding how batch drawing affects performance shows you can think about efficiency in real projects.

Self-Check

What if we replaced LineCollection with drawing each line separately using ax.plot? How would the time complexity change?