Vector vs raster output decision in Matplotlib - Performance Comparison

Time Complexity: Vector vs raster output decision

O(n)

Understanding Time Complexity

When creating plots with matplotlib, choosing vector or raster output affects how long saving the image takes.

We want to know how the time to save grows as the plot gets more complex.

Scenario Under Consideration

Analyze the time complexity of saving a plot as vector or raster.

import matplotlib.pyplot as plt
import numpy as np

x = np.linspace(0, 10, 1000)
y = np.sin(x)

plt.plot(x, y)
plt.savefig('plot_output.pdf', dpi=300, format='pdf')  # vector output
plt.savefig('plot_output.png', dpi=300)           # raster output

This code plots a sine wave and saves it as vector (PDF) and raster (PNG) images.

Identify Repeating Operations

Look at what repeats when saving the plot.

• Primary operation: Processing each data point to draw lines and shapes.
• How many times: Once per data point (1000 points here).

How Execution Grows With Input

Saving time grows as the number of points increases.

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

Pattern observation: The work grows directly with the number of points.

Final Time Complexity

Time Complexity: O(n)

This means saving time increases linearly as the plot gets more detailed.

Common Mistake

[X] Wrong: "Vector output is always faster to save than raster output."

[OK] Correct: Vector files store instructions for each point, so saving can take longer as points increase, unlike raster which saves pixels directly.

Interview Connect

Understanding how output choice affects saving time helps you explain trade-offs clearly in real projects.

Self-Check

What if we increased the plot complexity by adding many more lines? How would the time complexity change?