Mathematical expressions with LaTeX in Matplotlib - Time & Space Complexity

Time Complexity: Mathematical expressions with LaTeX

O(n)

Understanding Time Complexity

We want to understand how the time to render mathematical expressions with LaTeX in matplotlib changes as the expressions get longer or more complex.

How does the rendering time grow when we add more symbols or formulas?

Scenario Under Consideration

Analyze the time complexity of the following matplotlib code snippet.

import matplotlib.pyplot as plt

expr = r'$\sum_{i=1}^n i^2 = \frac{n(n+1)(2n+1)}{6}$'
plt.text(0.5, 0.5, expr, fontsize=14, ha='center')
plt.axis('off')
plt.show()

This code displays a mathematical formula using LaTeX syntax in a matplotlib plot.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Parsing and rendering each LaTeX symbol and command.
• How many times: Once per symbol or command in the expression.

How Execution Grows With Input

As the length of the LaTeX expression grows, the number of symbols to parse and render grows roughly in a straight line.

Input Size (symbols)	Approx. Operations
10	10
100	100
1000	1000

Pattern observation: The work grows directly with the number of symbols in the expression.

Final Time Complexity

Time Complexity: O(n)

This means the rendering time increases in a straight line as the expression gets longer.

Common Mistake

[X] Wrong: "Rendering a LaTeX expression takes the same time no matter how long it is."

[OK] Correct: Longer expressions have more symbols and commands, so they take more time to parse and draw.

Interview Connect

Understanding how rendering time grows helps you think about performance when showing formulas in plots, a useful skill for clear and efficient data visualization.

Self-Check

"What if we added nested fractions and square roots to the LaTeX expression? How would the time complexity change?"