Normalized histograms in Matplotlib - Time & Space Complexity

Time Complexity: Normalized histograms

O(n)

Understanding Time Complexity

We want to understand how the time to create a normalized histogram changes as the data size grows.

How does the work increase when we have more data points?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import matplotlib.pyplot as plt
import numpy as np

n = 1000  # example data size

data = np.random.randn(n)  # n data points
plt.hist(data, bins=50, density=True)
plt.show()

This code creates a histogram with 50 bins and normalizes it so the area sums to 1.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Counting how many data points fall into each of the 50 bins.
• 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 grows, the time to count them into bins grows roughly the same.

Input Size (n)	Approx. Operations
10	About 10 checks to place points in bins
100	About 100 checks
1000	About 1000 checks

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

Final Time Complexity

Time Complexity: O(n)

This means the time to create the normalized histogram grows linearly with the number of data points.

Common Mistake

[X] Wrong: "The number of bins affects the time complexity a lot, so more bins means much slower."

[OK] Correct: The number of bins is usually fixed and small compared to data size, so it does not change the main growth pattern.

Interview Connect

Understanding how data size affects histogram creation helps you explain performance in data visualization tasks clearly and confidently.

Self-Check

"What if we increased the number of bins to grow with the data size? How would the time complexity change?"