Plotting multiple lines in Matplotlib - Time & Space Complexity

Time Complexity: Plotting multiple lines

O(n)

Understanding Time Complexity

When plotting multiple lines with matplotlib, it's important to understand how the time to draw grows as we add more lines.

We want to know how the plotting time changes when we increase the number of lines.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import matplotlib.pyplot as plt
import numpy as np

x = np.linspace(0, 10, 100)
for i in range(50):
    y = np.sin(x + i)
    plt.plot(x, y)
plt.show()

This code plots 50 sine waves, each shifted by a different amount, on the same graph.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The loop that calls plt.plot() 50 times to draw each line.
• How many times: Once for each line, so 50 times in this example.

How Execution Grows With Input

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

Input Size (n)	Approx. Operations
10	10 plot calls
100	100 plot calls
1000	1000 plot calls

Pattern observation: The work grows linearly as the number of lines increases.

Final Time Complexity

Time Complexity: O(n)

This means the time to plot grows directly in proportion to the number of lines you draw.

Common Mistake

[X] Wrong: "Plotting multiple lines is almost as fast as plotting one line because the data points are the same."

[OK] Correct: Each line requires a separate draw call and rendering, so the time adds up with each new line.

Interview Connect

Understanding how plotting time grows helps you write efficient visualization code and explain performance in real projects.

Self-Check

"What if we plotted all lines using a single call with multiple y arrays? How would the time complexity change?"