Before-after comparison plots in Matplotlib - Time & Space Complexity

Time Complexity: Before-after comparison plots

O(n)

Understanding Time Complexity

We want to understand how the time to create before-after comparison plots changes as the amount of data grows.

How does the plotting time increase when we add more points to compare?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import matplotlib.pyplot as plt

before = [1, 2, 3, 4, 5]
after = [2, 3, 5, 7, 11]

plt.figure(figsize=(6,4))
plt.plot(before, label='Before')
plt.plot(after, label='After')
plt.legend()
plt.show()

This code plots two lines showing values before and after some change for 5 points.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Plotting each data point for both before and after lists.
• How many times: Once for each point in the data arrays (n times per line).

How Execution Grows With Input

As the number of points increases, the plotting work grows roughly in direct proportion.

Input Size (n)	Approx. Operations
10	Plot about 20 points (10 before + 10 after)
100	Plot about 200 points
1000	Plot about 2000 points

Pattern observation: Doubling the number of points doubles the plotting work.

Final Time Complexity

Time Complexity: O(n)

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

Common Mistake

[X] Wrong: "Plotting two lines takes twice as long as plotting one line, so time complexity is O(2n)."

[OK] Correct: Constants like 2 are ignored in time complexity, so O(2n) is simplified to O(n).

Interview Connect

Understanding how plotting time grows helps you explain performance when working with bigger datasets in real projects.

Self-Check

"What if we added a loop to create multiple before-after plots for different groups? How would the time complexity change?"