Text annotations in Matplotlib - Time & Space Complexity

Time Complexity: Text annotations

O(n)

Understanding Time Complexity

When adding text annotations in matplotlib plots, it's important to know how the time to draw grows as we add more annotations.

We want to understand how the number of annotations affects the drawing time.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import matplotlib.pyplot as plt

fig, ax = plt.subplots()
n = 10  # Define n before using it
for i in range(n):
    ax.text(i, i, f'Point {i}')
plt.show()

This code adds n text annotations to a plot, placing each at coordinates (i, i).

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Adding a text annotation with ax.text() inside a loop.
• How many times: Exactly n times, once per loop iteration.

How Execution Grows With Input

Each annotation is added one after another, so the total work grows directly with the number of annotations.

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

Pattern observation: The work increases steadily and linearly as we add more annotations.

Final Time Complexity

Time Complexity: O(n)

This means the time to add annotations grows in direct proportion to how many annotations you add.

Common Mistake

[X] Wrong: "Adding many annotations happens instantly no matter how many there are."

[OK] Correct: Each annotation requires drawing work, so more annotations take more time, not zero extra time.

Interview Connect

Understanding how adding elements like text annotations scales helps you reason about plot performance and responsiveness in real projects.

Self-Check

"What if we batch all annotations into one call instead of a loop? How would the time complexity change?"