Colormaps (sequential, diverging, qualitative) in Matplotlib - Time & Space Complexity

Time Complexity: Colormaps (sequential, diverging, qualitative)

O(n)

Understanding Time Complexity

When using colormaps in matplotlib, it is important to understand how the time to apply colors grows as the data size increases.

We want to know how the coloring process scales when we have more data points to display.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import matplotlib.pyplot as plt
import numpy as np

# Create data
n = 1000
values = np.random.rand(n)

# Create scatter plot with a colormap
plt.scatter(range(n), values, c=values, cmap='viridis')
plt.colorbar()
plt.show()

This code creates a scatter plot of 1000 points, coloring each point using a sequential colormap based on its value.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Assigning a color to each data point based on its value.
• How many times: Once for each of the n data points (here, 1000 times).

How Execution Grows With Input

As the number of data points increases, the number of color assignments grows proportionally.

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

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

Final Time Complexity

Time Complexity: O(n)

This means the time to apply colors grows directly in proportion to the number of points you want to color.

Common Mistake

[X] Wrong: "Applying a colormap takes the same time no matter how many points there are."

[OK] Correct: Each point needs its color calculated and assigned, so more points mean more work.

Interview Connect

Understanding how operations scale with data size helps you write efficient visualizations and explain your choices clearly in discussions.

Self-Check

"What if we used a colormap on a 2D image array instead of a 1D list? How would the time complexity change?"