Highlight and annotate pattern in Matplotlib - Time & Space Complexity

Time Complexity: Highlight and annotate pattern

O(n)

Understanding Time Complexity

We want to understand how the time to highlight and annotate patterns in a plot changes as the data grows.

How does the work increase when we add more points to highlight or annotate?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import matplotlib.pyplot as plt

x = range(100)
y = [i**2 for i in x]

plt.plot(x, y)

for i in range(len(x)):
    if y[i] > 2000:
        plt.annotate('High', (x[i], y[i]), color='red')

plt.show()

This code plots a curve and adds annotations to points where the y-value is greater than 2000.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Looping through all points to check and annotate.
• How many times: Once for each data point (n times).

How Execution Grows With Input

As the number of points increases, the code checks each point once and may add annotations.

Input Size (n)	Approx. Operations
10	About 10 checks and some annotations
100	About 100 checks and more annotations
1000	About 1000 checks and many annotations

Pattern observation: The work grows roughly in direct proportion to the number of points.

Final Time Complexity

Time Complexity: O(n)

This means the time to highlight and annotate grows linearly as the number of points increases.

Common Mistake

[X] Wrong: "Adding annotations only takes constant time regardless of data size."

[OK] Correct: Each point must be checked and possibly annotated, so time grows with data size.

Interview Connect

Understanding how plotting and annotation scale helps you write efficient data visualizations and explain your reasoning clearly.

Self-Check

"What if we only annotate points above a fixed threshold without checking all points? How would the time complexity change?"