Custom colormaps in Matplotlib - Time & Space Complexity

Time Complexity: Custom colormaps

O(n)

Understanding Time Complexity

When creating custom colormaps in matplotlib, it is important to understand how the time to generate colors grows as the number of colors increases.

We want to know how the work done changes when we ask for more colors in the colormap.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.colors import LinearSegmentedColormap

colors = [(1, 0, 0), (0, 1, 0), (0, 0, 1)]  # red, green, blue
n_colors = 256
custom_cmap = LinearSegmentedColormap.from_list('custom', colors, N=n_colors)

plt.imshow(np.linspace(0, 1, n_colors).reshape(1, n_colors), aspect='auto', cmap=custom_cmap)
plt.show()
    

This code creates a custom colormap with 256 colors by blending red, green, and blue, then displays it as a gradient.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Generating each of the n_colors colors by interpolating between given base colors.
• How many times: The interpolation runs once for each of the n_colors steps, so n_colors times.

How Execution Grows With Input

As the number of colors requested increases, the time to create the colormap grows roughly in direct proportion.

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

Pattern observation: Doubling the number of colors roughly doubles the work needed to generate them.

Final Time Complexity

Time Complexity: O(n)

This means the time to create the colormap grows linearly with the number of colors you want.

Common Mistake

[X] Wrong: "Creating a colormap with more colors takes the same time as with fewer colors."

[OK] Correct: Each color must be calculated by blending base colors, so more colors mean more calculations and more time.

Interview Connect

Understanding how time grows with input size helps you explain performance when customizing visualizations, a useful skill in data science projects.

Self-Check

What if we changed the colormap creation to use a fixed small number of colors but repeated the display many times? How would the time complexity change?