Color mapping with colorbar in Matplotlib - Time & Space Complexity

Time Complexity: Color mapping with colorbar

O(n)

Understanding Time Complexity

We want to understand how the time needed to create a color map with a colorbar changes as we increase the data size.

How does the work grow when we add more points to the plot?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import matplotlib.pyplot as plt
import numpy as np

n = 1000
x = np.random.rand(n)
y = np.random.rand(n)
z = np.random.rand(n)

plt.scatter(x, y, c=z, cmap='viridis')
plt.colorbar()
plt.show()

This code creates a scatter plot of n points colored by values in z, then adds a colorbar to explain the colors.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Plotting each of the n points with a color based on z.
• How many times: Once for each of the n points.

How Execution Grows With Input

As we add more points, the plotting work grows roughly in direct proportion to the number of points.

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

Pattern observation: Doubling the points roughly doubles the work needed to plot and color them.

Final Time Complexity

Time Complexity: O(n)

This means the time to create the colored scatter plot with colorbar grows linearly with the number of points.

Common Mistake

[X] Wrong: "Adding a colorbar makes the time grow much faster than the points plotted."

[OK] Correct: The colorbar is created once and does not depend on the number of points, so it adds a small fixed cost, not a growing one.

Interview Connect

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

Self-Check

What if we changed the scatter plot to a heatmap with a fixed grid size? How would the time complexity change?