Text placement with ax.text in Matplotlib - Time & Space Complexity

Time Complexity: Text placement with ax.text

O(n)

Understanding Time Complexity

When placing text on a plot using matplotlib's ax.text, it's important to understand how the time to draw grows as we add more text elements.

We want to know how the number of text placements affects the total work matplotlib does.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import matplotlib.pyplot as plt

n = 10
fig, ax = plt.subplots()
for i in range(n):
    ax.text(i, i, f"Point {i}")
plt.show()

This code places n text labels diagonally on a plot, one for each point.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The loop that calls ax.text n times.
• How many times: Exactly n times, once per text label.

How Execution Grows With Input

Each new text label adds a fixed amount of work to draw it on the plot.

Input Size (n)	Approx. Operations
10	10 text placements
100	100 text placements
1000	1000 text placements

Pattern observation: The work grows directly in proportion to the number of text labels added.

Final Time Complexity

Time Complexity: O(n)

This means the time to place text grows linearly as you add more text labels.

Common Mistake

[X] Wrong: "Adding more text labels won't affect performance much because text is simple."

[OK] Correct: Each text label requires drawing and positioning work, so more labels mean more work and longer drawing time.

Interview Connect

Understanding how adding elements like text affects drawing time helps you write efficient plotting code and shows you can think about performance in real tasks.

Self-Check

"What if we added nested loops to place text in a grid of size n by n? How would the time complexity change?"