Labels, title, and legend in MATLAB - Time & Space Complexity

Time Complexity: Labels, title, and legend

O(n)

Understanding Time Complexity

We want to understand how the time it takes to add labels, titles, and legends to a plot changes as the plot gets more complex.

How does adding these elements affect the program's running time?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

x = 1:1000;
y = sin(x);
plot(x, y);
title('Sine Wave');
xlabel('X Axis');
ylabel('Y Axis');
legend('sin(x)');

This code plots a sine wave and adds a title, labels for the x and y axes, and a legend.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Plotting the data points (drawing 1000 points).
• How many times: The plot function processes all 1000 points once.
• Adding title, labels, and legend are single operations without loops.

How Execution Grows With Input

Adding labels, title, and legend takes about the same time no matter how many points are plotted.

Input Size (n)	Approx. Operations
10	Plotting 10 points + fixed label/title/legend steps
100	Plotting 100 points + fixed label/title/legend steps
1000	Plotting 1000 points + fixed label/title/legend steps

Pattern observation: Plotting time grows with number of points, but adding labels, title, and legend stays constant.

Final Time Complexity

Time Complexity: O(n)

This means the time grows linearly with the number of points plotted, while adding labels, title, and legend adds only a small fixed time.

Common Mistake

[X] Wrong: "Adding a title or legend makes the program run much slower as data grows."

[OK] Correct: Titles and legends are added once and do not depend on data size, so their time cost stays about the same.

Interview Connect

Understanding which parts of code grow with input size helps you explain performance clearly and shows you can think about efficiency in real projects.

Self-Check

"What if we added a legend entry for every data point? How would the time complexity change?"