plot() function basics in MATLAB - Time & Space Complexity

Time Complexity: plot() function basics

O(n)

Understanding Time Complexity

Let's see how the time it takes to draw a plot changes as we add more points.

We want to know how the plot() function's work grows when the data size grows.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

x = 1:n;
y = sin(x);
plot(x, y);

This code creates two arrays of length n and plots y versus x.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Creating arrays x and y of length n and plotting all points.
• How many times: The plot function processes each of the n points once.

How Execution Grows With Input

As we add more points, the work to plot grows roughly in direct proportion.

Input Size (n)	Approx. Operations
10	About 10 points processed
100	About 100 points processed
1000	About 1000 points processed

Pattern observation: Doubling the points roughly doubles the work.

Final Time Complexity

Time Complexity: O(n)

This means the time to plot grows linearly with the number of points.

Common Mistake

[X] Wrong: "Plotting many points takes the same time as plotting a few points."

[OK] Correct: Each point adds work, so more points mean more time.

Interview Connect

Understanding how plotting time grows helps you reason about performance when visualizing data.

Self-Check

"What if we plot multiple lines instead of one? How would the time complexity change?"

Practice

1. What does the plot() function do in MATLAB?

easy

A. It calculates the sum of two numbers.

B. It clears the command window.

C. It saves data to a file.

D. It creates a graph to visually display data points.

Solution

1. Step 1: Understand the purpose of plot()

   The plot() function is used to draw graphs in MATLAB, which helps visualize data points.

2. Step 2: Compare with other options

   Options A, C, and D describe unrelated functions like summing numbers, saving files, or clearing the window, which plot() does not do.

3. Final Answer:

   It creates a graph to visually display data points. -> Option D

4. Quick Check:

   plot() = graph display [OK]

Hint: Remember: plot() always draws graphs [OK]

Common Mistakes:

• Confusing plot() with data calculation functions
• Thinking plot() saves files
• Assuming plot() clears the screen

2. Which of the following is the correct syntax to plot y versus x in MATLAB?

easy

A. plot(x:y)

B. plot(y, x)

C. plot(x, y)

D. plot(x + y)

Solution

1. Step 1: Recall the syntax of plot()

   The correct syntax to plot y versus x is plot(x, y), where x and y are vectors of the same length.

2. Step 2: Check other options

   plot(y, x) reverses the order, plotting x versus y, which is incorrect. plot(x:y) uses a colon operator incorrectly. plot(x + y) tries to plot the sum, which is invalid.

3. Final Answer:

   plot(x, y) -> Option C

4. Quick Check:

   plot(x, y) = correct syntax [OK]

Hint: Always put x first, then y in plot() [OK]

Common Mistakes:

• Swapping x and y arguments
• Using colon operator inside plot()
• Trying to plot sums instead of vectors

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

x = 1:3;
y = [2 4 6];
plot(x, y)

medium

A. A plot with points (1,2), (2,4), (3,6) connected by lines.

B. A plot with points (2,1), (4,2), (6,3) connected by lines.

C. An error because x and y have different lengths.

D. A plot with points (1,1), (2,2), (3,3) connected by lines.

Solution

1. Step 1: Analyze vectors x and y

   x is [1 2 3] and y is [2 4 6], both have length 3, so they can be plotted against each other.

2. Step 2: Understand plot output

   The plot will connect points (1,2), (2,4), and (3,6) with lines.

3. Final Answer:

   A plot with points (1,2), (2,4), (3,6) connected by lines. -> Option A

4. Quick Check:

   plot(x, y) = points (1,2), (2,4), (3,6) [OK]

Hint: Match x and y points by position in vectors [OK]

Common Mistakes:

• Mixing up x and y coordinates
• Assuming error due to vector length mismatch
• Confusing point coordinates

4. Identify the error in this MATLAB code:

x = 1:5;
y = [2 4 6];
plot(x, y)

medium

A. Vectors x and y have different lengths causing an error.

B. plot() function is misspelled.

C. x and y must be column vectors, not row vectors.

D. No error; the plot will display correctly.

Solution

1. Step 1: Check lengths of x and y

   x has length 5, y has length 3. plot() requires vectors of equal length.

2. Step 2: Understand consequence

   Because lengths differ, MATLAB will produce an error when trying to plot.

3. Final Answer:

   Vectors x and y have different lengths causing an error. -> Option A

4. Quick Check:

   Equal length vectors needed [OK]

Hint: Ensure x and y vectors have same length before plotting [OK]

Common Mistakes:

• Ignoring vector length mismatch
• Thinking row vs column vector matters here
• Assuming plot() spelling error

5. You want to plot the function y = x^2 for x from -3 to 3 with a red dashed line. Which code correctly does this?

hard

A. x = -3:0.1:3; y = x.^2; plot(x, y, 'blue-')

B. x = -3:0.1:3; y = x.^2; plot(x, y, 'r--')

C. x = -3:0.1:3; y = x^2; plot(y, x, 'r--')

D. x = -3:3; y = x^2; plot(x, y, 'red-dash')

Solution

1. Step 1: Define x and y correctly

   x must be a vector from -3 to 3 with small steps (e.g., 0.1). y = x squared element-wise uses .^2.

2. Step 2: Use correct plot style

   The style string 'r--' means red dashed line. x = -3:0.1:3; y = x.^2; plot(x, y, 'r--') uses this correctly.

3. Step 3: Check other options

   x = -3:3; y = x^2; plot(x, y, 'red-dash') uses invalid syntax for y and style. x = -3:0.1:3; y = x^2; plot(y, x, 'r--') swaps x and y. x = -3:0.1:3; y = x.^2; plot(x, y, 'blue-') uses blue solid line, not red dashed.

4. Final Answer:

   x = -3:0.1:3; y = x.^2; plot(x, y, 'r--') -> Option B

5. Quick Check:

   Element-wise power + 'r--' = red dashed line [OK]

Hint: Use .^ for element-wise power and 'r--' for red dashed line [OK]

Common Mistakes:

• Using ^ instead of .^ for vectors
• Swapping x and y in plot()
• Wrong line style string