Cumulative histograms in Matplotlib - Time & Space Complexity

Time Complexity: Cumulative histograms

O(n)

Understanding Time Complexity

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

How does the number of data points affect the work matplotlib does to draw the histogram?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import matplotlib.pyplot as plt
import numpy as np

data = np.random.randn(1000)
plt.hist(data, bins=50, cumulative=True)
plt.show()

This code creates a cumulative histogram from 1000 random data points divided into 50 bins.

Identify Repeating Operations

• Primary operation: Counting how many data points fall into each bin.
• 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 increases, the work to count them into bins grows roughly in direct proportion.

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

Pattern observation: Doubling the data roughly doubles the counting work.

Final Time Complexity

Time Complexity: O(n)

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

Common Mistake

[X] Wrong: "The number of bins affects the time complexity more than the number of data points."

[OK] Correct: The bins are fixed and small compared to data size; the main work is checking each data point once, so data size dominates time.

Interview Connect

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

Self-Check

"What if we increased the number of bins significantly? How would the time complexity change?"