contour plots in MATLAB - Time & Space Complexity

Time Complexity: contour plots

O(n^2)

Understanding Time Complexity

When we create contour plots in MATLAB, the program calculates many points to draw lines showing levels of a surface.

We want to understand how the time to draw these plots grows as the data size increases.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

% Create grid points
[x, y] = meshgrid(linspace(-2, 2, n), linspace(-2, 2, n));

% Define function values on grid
z = x.^2 + y.^2;

% Draw contour plot
contour(x, y, z, 10);
    

This code creates a grid of points, computes values for each point, and draws contour lines for 10 levels.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Calculating values for each point in the n-by-n grid.
• How many times: Once for each of the n² points.

How Execution Grows With Input

As the grid size n grows, the number of points grows by n squared, so the work grows quickly.

Input Size (n)	Approx. Operations
10	100
100	10,000
1000	1,000,000

Pattern observation: Doubling n makes the work about four times bigger because we have n by n points.

Final Time Complexity

Time Complexity: O(n^2)

This means the time to create the contour plot grows roughly with the square of the grid size.

Common Mistake

[X] Wrong: "The time grows linearly with n because we just loop once over the data."

[OK] Correct: The data is a grid with n rows and n columns, so the total points are n times n, not just n.

Interview Connect

Understanding how plotting time grows helps you explain performance when working with large data sets or visualizations.

Self-Check

"What if we increased the number of contour levels from 10 to 100? How would the time complexity change?"