Small multiples (facet grid) in Matplotlib - Time & Space Complexity

Time Complexity: Small multiples (facet grid)

O(n)

Understanding Time Complexity

When creating small multiples with matplotlib, we want to know how the time to draw charts grows as we add more plots.

How does adding more small charts affect the total work matplotlib does?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import matplotlib.pyplot as plt
import numpy as np

fig, axs = plt.subplots(3, 3)
for i, ax in enumerate(axs.flat):
    x = np.linspace(0, 10, 100)
    y = np.sin(x + i)
    ax.plot(x, y)
plt.show()

This code creates a 3 by 3 grid of small plots, each showing a sine wave shifted by a different amount.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Loop over each subplot to draw a line plot.
• How many times: Once for each subplot, here 9 times (3 rows x 3 columns).

How Execution Grows With Input

Each additional small plot adds roughly the same amount of work to draw its line.

Input Size (number of plots)	Approx. Operations
10	10 times the work to draw one plot
100	100 times the work to draw one plot
1000	1000 times the work to draw one plot

Pattern observation: The total work grows directly with the number of small plots.

Final Time Complexity

Time Complexity: O(n)

This means the time to draw all small multiples grows linearly as you add more plots.

Common Mistake

[X] Wrong: "Adding more small plots only slightly increases drawing time because they are small."

[OK] Correct: Each plot still requires its own drawing steps, so total time adds up directly with the number of plots.

Interview Connect

Understanding how drawing many small charts scales helps you design efficient visualizations and explain performance trade-offs clearly.

Self-Check

What if we changed the number of points in each plot from 100 to 1000? How would the time complexity change?