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?"

Practice

1. Which MATLAB function is used to add a label to the x-axis of a plot?

easy

A. xlabel

B. ylabel

C. title

D. legend

Solution

1. Step 1: Understand axis labeling functions

   In MATLAB, xlabel labels the x-axis, ylabel labels the y-axis, title adds a main heading, and legend explains plot lines.

2. Step 2: Identify the function for x-axis label

   The function xlabel is specifically designed to add a label to the x-axis.

3. Final Answer:

   xlabel -> Option A

4. Quick Check:

   Label x-axis = xlabel [OK]

Hint: Use xlabel for x-axis label, ylabel for y-axis [OK]

Common Mistakes:

• Confusing xlabel with ylabel
• Using title instead of axis labels
• Using legend for axis labels

2. Which of the following is the correct syntax to add a legend to a plot with two lines labeled 'Data1' and 'Data2'?

easy

A. legend{'Data1', 'Data2'}

B. legend = ('Data1', 'Data2')

C. legend['Data1', 'Data2']

D. legend('Data1', 'Data2')

Solution

1. Step 1: Recall correct legend syntax

   In MATLAB, the function legend is called with parentheses and string arguments to label plot lines.

2. Step 2: Identify correct syntax

   The correct syntax uses parentheses and comma-separated strings: legend('Data1', 'Data2'). Other options use invalid assignment or brackets.

3. Final Answer:

   legend('Data1', 'Data2') -> Option D

4. Quick Check:

   legend('labels') uses parentheses [OK]

Hint: Use legend('label1', 'label2') with parentheses [OK]

Common Mistakes:

• Using assignment '=' instead of function call
• Using square or curly brackets
• Missing quotes around labels

3. What will be the title of the plot after running this MATLAB code?

plot(1:5, [2 4 6 8 10]);
title('Sales Over Time');

medium

A. plot(1:5, [2 4 6 8 10])

B. Sales Over Time

C. 1:5

D. No title

Solution

1. Step 1: Understand the title function

   The title function sets the main heading of the plot to the given string.

2. Step 2: Check the given code

   The code calls title('Sales Over Time'), so the plot's title will be exactly 'Sales Over Time'.

3. Final Answer:

   Sales Over Time -> Option B

4. Quick Check:

   title('text') sets plot title [OK]

Hint: title('text') sets the plot's main heading [OK]

Common Mistakes:

• Confusing title with axis labels
• Expecting variable values as title
• No title if title function missing

4. Identify the error in this MATLAB code snippet:

plot(x, y);
xlabel = 'Time';
ylabel('Value');
legend('Line1');

medium

A. Using assignment '=' with xlabel instead of function call

B. Missing ylabel function call

C. legend syntax is incorrect

D. plot function is missing arguments

Solution

1. Step 1: Check xlabel usage

   The code uses xlabel = 'Time'; which assigns a string to variable xlabel instead of calling the function xlabel('Time').

2. Step 2: Verify other lines

   ylabel('Value') and legend('Line1') are correctly called as functions. The plot function has arguments x, y assumed defined.

3. Final Answer:

   Using assignment '=' with xlabel instead of function call -> Option A

4. Quick Check:

   Use xlabel('text'), not xlabel = 'text' [OK]

Hint: Call xlabel as function: xlabel('text'), not assignment [OK]

Common Mistakes:

• Assigning xlabel instead of calling function
• Confusing ylabel syntax
• Incorrect legend usage

5. You have plotted two data sets on the same graph using:

plot(x, y1, '-r', x, y2, '-b');

How do you add a title 'Comparison', label the x-axis as 'Time', the y-axis as 'Value', and add a legend with labels 'Data1' and 'Data2'?

hard

A. title = 'Comparison'; xlabel = 'Time'; ylabel = 'Value'; legend = ('Data1', 'Data2');

B. title('Comparison'); xlabel('Time'); ylabel('Value'); legend(['Data1', 'Data2']);

C. title('Comparison'); xlabel('Time'); ylabel('Value'); legend('Data1', 'Data2');

D. title('Comparison'); xlabel('Time'); ylabel('Value'); legend{'Data1', 'Data2'};

Solution

1. Step 1: Use correct function calls for labels and title

   Functions title, xlabel, and ylabel require parentheses with string arguments.

2. Step 2: Use correct legend syntax

   The legend function takes comma-separated strings inside parentheses, not assignment or brackets.

3. Final Answer:

   title('Comparison'); xlabel('Time'); ylabel('Value'); legend('Data1', 'Data2'); -> Option C

4. Quick Check:

   Use function calls with parentheses for labels and legend [OK]

Hint: Use function calls with parentheses for all labels and legend [OK]

Common Mistakes:

• Assigning strings instead of calling functions
• Using brackets or braces for legend
• Missing quotes around labels