Animation basics in MATLAB - Time & Space Complexity

Time Complexity: Animation basics

O(n)

Understanding Time Complexity

When creating animations in MATLAB, it is important to know how the time to update frames grows as the animation runs.

We want to understand how the number of steps affects the total time taken to show the animation.

Scenario Under Consideration

Analyze the time complexity of the following animation code snippet.

nFrames = 100;
for k = 1:nFrames
    plot(sin(0:0.1:k));
    drawnow;
end

This code draws a sine wave that grows with each frame, updating the plot 100 times.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The for-loop runs the plot and draw commands repeatedly.
• How many times: Exactly nFrames times, once per frame.

How Execution Grows With Input

Each frame requires drawing and updating the plot once, so total work grows with the number of frames.

Input Size (nFrames)	Approx. Operations
10	10 plot updates
100	100 plot updates
1000	1000 plot updates

Pattern observation: The total work grows directly in proportion to the number of frames.

Final Time Complexity

Time Complexity: O(n)

This means the time to complete the animation grows linearly with the number of frames.

Common Mistake

[X] Wrong: "The animation time stays the same no matter how many frames I have."

[OK] Correct: Each frame requires drawing and updating, so more frames mean more work and more time.

Interview Connect

Understanding how animation time grows helps you write smooth animations and shows you can think about performance in real projects.

Self-Check

"What if we added a nested loop inside the frame loop to update multiple plots per frame? How would the time complexity change?"