Polar axes in Matplotlib - Time & Space Complexity

Time Complexity: Polar axes

O(n)

Understanding Time Complexity

We want to understand how the time to draw a polar plot changes as we add more data points.

How does the plotting time grow when the input size increases?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import matplotlib.pyplot as plt
import numpy as np

n = 100  # Define n
# Create data
theta = np.linspace(0, 2 * np.pi, n)
r = np.abs(np.sin(5 * theta))

# Create polar plot
fig, ax = plt.subplots(subplot_kw={'projection': 'polar'})
ax.plot(theta, r)
plt.show()

This code creates a polar plot with n points, plotting radius r against angle theta.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Calculating and plotting n points on the polar axes.
• How many times: Once for each of the n points in the arrays theta and r.

How Execution Grows With Input

As we increase the number of points, the time to compute and draw grows roughly in direct proportion.

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

Pattern observation: Doubling the points roughly doubles the work needed to plot.

Final Time Complexity

Time Complexity: O(n)

This means the time to create the polar plot grows linearly with the number of points.

Common Mistake

[X] Wrong: "Adding more points won't affect the plotting time much because it's just one plot."

[OK] Correct: Each point requires calculation and drawing, so more points mean more work and longer plotting time.

Interview Connect

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

Self-Check

What if we changed the plot to scatter points instead of a line plot? How would the time complexity change?