Why histograms show distributions in Matplotlib - Performance Analysis

Time Complexity: Why histograms show distributions

O(n)

Understanding Time Complexity

We want to understand how the time to create a histogram changes as we add more data points.

How does the work grow when the input data size grows?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import matplotlib.pyplot as plt
import numpy as np

n = 1000  # example number of data points

data = np.random.randn(n)  # n data points
plt.hist(data, bins=10)
plt.show()

This code creates a histogram with 10 bins from n random data points.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Assigning each of the n data points to one of the 10 bins.
• How many times: Once for each data point, so n times.

How Execution Grows With Input

As we add more data points, the number of operations grows roughly the same as the number of points.

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

Pattern observation: The work grows linearly with the number of data points.

Final Time Complexity

Time Complexity: O(n)

This means the time to build the histogram grows directly with the number of data points.

Common Mistake

[X] Wrong: "The number of bins affects the time complexity a lot."

[OK] Correct: The number of bins is usually fixed and small, so it does not grow with input size and does not affect the main time cost.

Interview Connect

Understanding how histogram creation scales helps you explain data visualization performance clearly and confidently.

Self-Check

"What if the number of bins grew with the number of data points? How would the time complexity change?"