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?"