Multiple plots (hold on) in MATLAB - Time & Space Complexity

Time Complexity: Multiple plots (hold on)

O(n)

Understanding Time Complexity

When we use multiple plots with hold on in MATLAB, we add several drawing steps. We want to understand how the time to draw grows as we add more plots.

How does the time needed change when we plot more lines on the same figure?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

x = linspace(0, 2*pi, 1000);
hold on;
for k = 1:n
    y = sin(k*x);
    plot(x, y);
end
hold off;

This code plots n sine waves on the same figure, each with 1000 points.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The for loop runs n times, each time calling plot to draw a line.
• How many times: The loop repeats exactly n times, once per sine wave.

How Execution Grows With Input

Each additional plot adds a similar amount of work because it draws another line with 1000 points.

Input Size (n)	Approx. Operations
10	10 plot calls, each drawing 1000 points
100	100 plot calls, each drawing 1000 points
1000	1000 plot calls, each drawing 1000 points

Pattern observation: The total work grows directly with the number of plots n. Doubling n roughly doubles the drawing time.

Final Time Complexity

Time Complexity: O(n)

This means the time to draw grows in a straight line with the number of plots you add.

Common Mistake

[X] Wrong: "Adding more plots won't affect the time much because the points are fixed at 1000."

[OK] Correct: Each plot call still draws all 1000 points, so more plots mean more total points drawn, increasing time linearly.

Interview Connect

Understanding how repeated drawing commands affect performance helps you write efficient visualization code and shows you can think about how work grows with input size.

Self-Check

What if we increased the number of points per plot from 1000 to 10,000? How would the time complexity change?

Practice

1. What does the hold on command do in MATLAB plotting?

easy

A. Clears the current figure before plotting new data.

B. Allows multiple plots to be drawn on the same figure without erasing previous plots.

C. Saves the current plot to a file.

D. Changes the color of the plot lines automatically.

Solution

1. Step 1: Understand the purpose of hold on

   The hold on command tells MATLAB to keep the current plot and add new plots on top of it.

2. Step 2: Compare with other options

   Other commands like hold off or default plotting clear the figure before new plots, so they do not allow multiple plots together.

3. Final Answer:

   Allows multiple plots to be drawn on the same figure without erasing previous plots. -> Option B

4. Quick Check:

   hold on = multiple plots on one figure [OK]

Hint: Remember: hold on means keep adding plots [OK]

Common Mistakes:

• Thinking hold on clears the figure
• Confusing hold on with saving plots
• Assuming hold on changes plot colors

2. Which of the following is the correct way to plot two lines on the same figure in MATLAB?

easy

A. plot(x1, y1); hold on; plot(x2, y2); hold off;

B. hold on; plot(x1, y1); hold off; plot(x2, y2);

C. plot(x1, y1); plot(x2, y2);

D. plot(x1, y1); hold off; plot(x2, y2);

Solution

1. Step 1: Identify the correct sequence to keep multiple plots

   Using hold on after the first plot keeps it visible for the second plot.

2. Step 2: Confirm proper use of hold off

   Calling hold off after plotting both lines resets plotting behavior for future plots.

3. Final Answer:

   plot(x1, y1); hold on; plot(x2, y2); hold off; -> Option A

4. Quick Check:

   Use hold on between plots to combine them [OK]

Hint: Use hold on right after first plot to add more [OK]

Common Mistakes:

• Not using hold on before second plot
• Using hold off too early
• Plotting without hold on clears previous plot

3. What will be the output of the following MATLAB code?

t = 0:0.1:1;
plot(t, t);
hold on;
plot(t, t.^2);

medium

A. Two plots will appear: a straight line and a curve on the same figure.

B. Only the plot of t vs t^2 will be shown.

C. An error will occur because hold on is used incorrectly.

D. Only the plot of t vs t will be shown.

Solution

1. Step 1: Analyze the first plot command

   The first plot draws a straight line y = t on the figure.

2. Step 2: Understand the effect of hold on and second plot

   Using hold on keeps the first plot visible, so the second plot y = t^2 is drawn on the same figure as a curve.

3. Final Answer:

   Two plots will appear: a straight line and a curve on the same figure. -> Option A

4. Quick Check:

   hold on keeps previous plot, so both appear [OK]

Hint: hold on keeps old plots visible for new ones [OK]

Common Mistakes:

• Thinking only last plot shows
• Assuming hold on causes error
• Confusing plot commands order

4. Identify the error in this MATLAB code that tries to plot two lines on the same figure:

plot(x, y1)
hold off
plot(x, y2)

medium

A. There is no error; the code works correctly.

B. The variable x is not defined.

C. hold off should be called before the first plot.

D. hold off should be replaced with hold on to keep both plots visible.

Solution

1. Step 1: Understand the effect of hold off

   Calling hold off resets plotting to clear the figure before the next plot.

2. Step 2: Identify correct command to keep plots

   To keep both plots visible, hold on should be used instead of hold off.

3. Final Answer:

   hold off should be replaced with hold on to keep both plots visible. -> Option D

4. Quick Check:

   Use hold on to combine plots, not hold off [OK]

Hint: hold off clears plots; use hold on to keep them [OK]

Common Mistakes:

• Using hold off instead of hold on
• Thinking hold off adds plots
• Ignoring hold commands altogether

5. You want to plot three different data sets on the same figure with different colors and then reset plotting to default for future plots. Which sequence of commands is correct?

hard

A. plot(x1, y1, 'r'); plot(x2, y2, 'g'); plot(x3, y3, 'b'); hold on; hold off;

B. hold on; plot(x1, y1, 'r'); plot(x2, y2, 'g'); plot(x3, y3, 'b');

C. plot(x1, y1, 'r'); hold on; plot(x2, y2, 'g'); plot(x3, y3, 'b'); hold off;

D. plot(x1, y1, 'r'); hold off; plot(x2, y2, 'g'); hold on; plot(x3, y3, 'b');

Solution

1. Step 1: Use hold on after first plot to combine multiple plots

   After plotting the first data set, hold on keeps the figure active for additional plots.

2. Step 2: Plot all data sets with specified colors and then reset with hold off

   Plotting the second and third data sets adds them to the same figure. Calling hold off resets plotting behavior for future plots.

3. Final Answer:

   plot(x1, y1, 'r'); hold on; plot(x2, y2, 'g'); plot(x3, y3, 'b'); hold off; -> Option C

4. Quick Check:

   hold on after first plot, hold off after last plot [OK]

Hint: hold on after first plot, hold off after last [OK]

Common Mistakes:

• Not calling hold off after multiple plots
• Calling hold on before first plot
• Mixing hold on and hold off incorrectly