Arrow annotations in Matplotlib - Time & Space Complexity

Time Complexity: Arrow annotations

O(n)

Understanding Time Complexity

We want to understand how the time it takes to add arrow annotations in a plot changes as we add more arrows.

How does the number of arrows affect the work matplotlib does?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import matplotlib.pyplot as plt

n = 10  # Define n before using it
fig, ax = plt.subplots()

for i in range(n):
    ax.annotate('', xy=(i, i), xytext=(i-1, i-1), arrowprops=dict(facecolor='blue'))

plt.show()

This code draws n arrows on a plot, each pointing from one point to the next.

Identify Repeating Operations

• Primary operation: Adding an arrow annotation inside the loop.
• How many times: The loop runs n times, so the arrow is added n times.

How Execution Grows With Input

Each arrow is added one after another, so the total work grows as we add more arrows.

Input Size (n)	Approx. Operations
10	10 arrow additions
100	100 arrow additions
1000	1000 arrow additions

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

Final Time Complexity

Time Complexity: O(n)

This means the time to add arrows grows in a straight line as you add more arrows.

Common Mistake

[X] Wrong: "Adding more arrows does not affect the time much because each arrow is simple."

[OK] Correct: Each arrow requires matplotlib to do work to draw and store it, so more arrows mean more work and more time.

Interview Connect

Understanding how adding elements like arrows affects performance helps you write efficient plotting code and explain your reasoning clearly.

Self-Check

"What if we added arrows in nested loops, creating arrows between all pairs of points? How would the time complexity change?"