Figure size and DPI in Matplotlib - Time & Space Complexity

Time Complexity: Figure size and DPI

O(width x height x dpi²)

Understanding Time Complexity

We want to understand how changing figure size and DPI affects the time matplotlib takes to create a figure.

How does the work grow when we increase these settings?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import matplotlib.pyplot as plt

fig = plt.figure(figsize=(width, height), dpi=dpi)
ax = fig.add_subplot(111)
ax.plot(data_x, data_y)
plt.show()

This code creates a figure with a given size and resolution, then plots data on it.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Drawing pixels on the figure canvas based on size and DPI.
• How many times: Number of pixels = width x height x dpi² (because DPI scales pixels per inch).

How Execution Grows With Input

As figure size or DPI increases, the number of pixels to draw grows, making rendering take longer.

Input Size (width x height x dpi²)	Approx. Operations
10 x 10 x 50²	~250,000
20 x 20 x 100²	~4,000,000
30 x 30 x 200²	~36,000,000

Pattern observation: Operations grow roughly with the square of DPI and linearly with figure size.

Final Time Complexity

Time Complexity: O(width x height x dpi²)

This means the time to draw the figure grows with the area times the square of the DPI setting.

Common Mistake

[X] Wrong: "Increasing DPI only slightly increases drawing time because it's just a setting."

[OK] Correct: Higher DPI means many more pixels to draw, so time grows much faster than expected.

Interview Connect

Understanding how figure size and DPI affect rendering time helps you explain performance in data visualization tasks clearly and confidently.

Self-Check

"What if we keep figure size fixed but double the DPI? How would the time complexity change?"