Bar and histogram plots in MATLAB - Time & Space Complexity

Time Complexity: Bar and histogram plots

O(n)

Understanding Time Complexity

When we create bar or histogram plots in MATLAB, the program processes data to display visual bars. Understanding how the time to create these plots grows with data size helps us know what to expect as data gets bigger.

We want to know: how does the time to draw these plots change when we add more data points?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

    data = randi(100, 1, n);  % Generate n random integers
    figure;
    histogram(data, 10);       % Create histogram with 10 bins
    bar_data = histcounts(data, 10);
    figure;
    bar(bar_data);             % Create bar plot from histogram counts
    

This code generates random data, creates a histogram with fixed bins, then makes a bar plot from the histogram counts.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Counting how many data points fall into each bin (histcounts).
• How many times: Each of the n data points is checked once to find its bin.

How Execution Grows With Input

As the number of data points (n) grows, the program checks each point once to place it in a bin.

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

Pattern observation: The number of operations grows directly with the number of data points.

Final Time Complexity

Time Complexity: O(n)

This means the time to create the histogram and bar plot grows in a straight line as you add more data points.

Common Mistake

[X] Wrong: "The time to create a histogram depends on the number of bins, so more bins always mean much slower plotting."

[OK] Correct: While bins affect some steps, the main work is checking each data point once. The number of bins is usually much smaller and does not multiply the work by n.

Interview Connect

Knowing how data size affects plotting time helps you write efficient code and explain your choices clearly. This skill shows you understand how programs handle data behind the scenes.

Self-Check

"What if we increased the number of bins from 10 to 1000? How would the time complexity change?"

Practice

1. Which of the following best describes the difference between a bar plot and a histogram in MATLAB?

easy

A. Both bar plots and histograms display values for specific categories.

B. Bar plots show data distribution over ranges; histograms display values for specific categories.

C. Both bar plots and histograms show data distribution over ranges.

D. Bar plots display values for specific categories; histograms show data distribution over ranges.

Solution

1. Step 1: Understand bar plot purpose

   Bar plots show values for distinct categories or positions, like sales per month.

2. Step 2: Understand histogram purpose

   Histograms group data into ranges (bins) to show how data spreads, like exam scores distribution.

3. Final Answer:

   Bar plots display values for specific categories; histograms show data distribution over ranges. -> Option D

4. Quick Check:

   Bar = categories, Histogram = ranges [OK]

Hint: Bar = categories, Histogram = data spread [OK]

Common Mistakes:

• Confusing bar plots with histograms
• Thinking both show the same type of data
• Assuming histograms show exact values per category

2. Which MATLAB command correctly creates a bar plot for the vector y = [3, 7, 5]?

easy

A. bar(y)

B. histogram(y)

C. plotbar(y)

D. barplot(y)

Solution

1. Step 1: Identify correct function for bar plot

   The MATLAB function to create a bar plot is bar().

2. Step 2: Check syntax correctness

   Calling bar(y) plots the values in vector y as bars.

3. Final Answer:

   bar(y) -> Option A

4. Quick Check:

   Use bar() for bar plots [OK]

Hint: Use bar() to plot bar charts, histogram() for histograms [OK]

Common Mistakes:

• Using histogram() instead of bar()
• Using non-existent functions like plotbar()
• Incorrect function names or typos

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

data = [1, 2, 2, 3, 3, 3, 4];
histogram(data, 3)

medium

A. An error because histogram requires vector of edges

B. A histogram with 3 bins showing counts of data in ranges covering 1 to 4

C. A bar plot with bars at positions 1, 2, 3, 4

D. A line plot connecting the data points

Solution

1. Step 1: Understand histogram function with bin count

   Calling histogram(data, 3) creates a histogram with 3 bins dividing the data range.

2. Step 2: Analyze data distribution

   Data ranges from 1 to 4, so bins cover intervals like [1-2), [2-3), [3-4]. Counts show how many values fall in each bin.

3. Final Answer:

   A histogram with 3 bins showing counts of data in ranges covering 1 to 4 -> Option B

4. Quick Check:

   histogram(data, bins) = bins count [OK]

Hint: histogram(data, n) makes n bins for data spread [OK]

Common Mistakes:

• Confusing histogram with bar plot output
• Expecting exact bars at data points
• Thinking histogram needs edges vector always

4. The following MATLAB code is intended to create a bar plot of y = [4, 6, 8], but it produces an error. What is the error?

bar y

medium

A. Incorrect function name; should be histogram

B. Vector y is not defined

C. Missing parentheses around the vector argument

D. bar function cannot plot vectors

Solution

1. Step 1: Check syntax of bar function call

   The correct syntax requires parentheses: bar(y).

2. Step 2: Identify cause of error

   Writing bar y without parentheses causes MATLAB syntax error.

3. Final Answer:

   Missing parentheses around the vector argument -> Option C

4. Quick Check:

   Function calls need parentheses [OK]

Hint: Always use parentheses when calling functions [OK]

Common Mistakes:

• Omitting parentheses in function calls
• Confusing bar with histogram function
• Assuming vector y is undefined without checking

5. You have a dataset of exam scores: scores = [55, 70, 70, 85, 90, 90, 90, 100]. You want to create a histogram with bins of width 10 (like 50-59, 60-69, etc.). Which MATLAB command correctly creates this histogram?

hard

A. histogram(scores, 'BinWidth', 10)

B. bar(scores, 10)

C. histogram(scores, 10)

D. bar(scores, 'BinWidth', 10)

Solution

1. Step 1: Understand how to set bin width in histogram

   Use histogram(data, 'BinWidth', value) to specify bin size.

2. Step 2: Check options for correct syntax

   histogram(scores, 'BinWidth', 10) uses correct syntax to set bin width to 10 for scores.

3. Step 3: Identify incorrect options

   Options B and D use bar function incorrectly; C sets number of bins, not width.

4. Final Answer:

   histogram(scores, 'BinWidth', 10) -> Option A

5. Quick Check:

   Use 'BinWidth' to set histogram bin size [OK]

Hint: Use 'BinWidth' property to set histogram bin size [OK]

Common Mistakes:

• Using bar instead of histogram for bin width
• Passing number instead of 'BinWidth' name-value pair
• Confusing bin count with bin width