Small multiples (facet grid) in Matplotlib - Time & Space Complexity

Time Complexity: Small multiples (facet grid)

O(n)

Understanding Time Complexity

When creating small multiples with matplotlib, we want to know how the time to draw charts grows as we add more plots.

How does adding more small charts affect the total work matplotlib does?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import matplotlib.pyplot as plt
import numpy as np

fig, axs = plt.subplots(3, 3)
for i, ax in enumerate(axs.flat):
    x = np.linspace(0, 10, 100)
    y = np.sin(x + i)
    ax.plot(x, y)
plt.show()

This code creates a 3 by 3 grid of small plots, each showing a sine wave shifted by a different amount.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Loop over each subplot to draw a line plot.
• How many times: Once for each subplot, here 9 times (3 rows x 3 columns).

How Execution Grows With Input

Each additional small plot adds roughly the same amount of work to draw its line.

Input Size (number of plots)	Approx. Operations
10	10 times the work to draw one plot
100	100 times the work to draw one plot
1000	1000 times the work to draw one plot

Pattern observation: The total work grows directly with the number of small plots.

Final Time Complexity

Time Complexity: O(n)

This means the time to draw all small multiples grows linearly as you add more plots.

Common Mistake

[X] Wrong: "Adding more small plots only slightly increases drawing time because they are small."

[OK] Correct: Each plot still requires its own drawing steps, so total time adds up directly with the number of plots.

Interview Connect

Understanding how drawing many small charts scales helps you design efficient visualizations and explain performance trade-offs clearly.

Self-Check

What if we changed the number of points in each plot from 100 to 1000? How would the time complexity change?

Practice

1. What is the main purpose of using small multiples (facet grid) in matplotlib?

easy

A. To display multiple related charts side by side for easy comparison

B. To create a single large plot with multiple lines

C. To animate a plot over time

D. To change the color scheme of a plot

Solution

1. Step 1: Understand the concept of small multiples

   Small multiples are multiple small charts arranged in a grid to compare different groups or categories easily.

2. Step 2: Identify the purpose in matplotlib

   Matplotlib uses small multiples to show many charts side by side, making it easier to compare data visually.

3. Final Answer:

   To display multiple related charts side by side for easy comparison -> Option A

4. Quick Check:

   Small multiples = multiple charts side by side [OK]

Hint: Small multiples = many small charts for comparison [OK]

Common Mistakes:

• Confusing small multiples with animations
• Thinking it changes colors only
• Assuming it creates one big plot

2. Which of the following is the correct way to create a 2x2 grid of subplots in matplotlib?

easy

A. fig, axes = plt.subplots(4)

B. fig, axes = plt.subplots(1, 4)

C. fig, axes = plt.subplots(2, 2)

D. fig, axes = plt.subplots(2)

Solution

1. Step 1: Recall plt.subplots() syntax

   plt.subplots(rows, columns) creates a grid of subplots with given rows and columns.

2. Step 2: Match the grid size

   To create a 2x2 grid, use plt.subplots(2, 2).

3. Final Answer:

   fig, axes = plt.subplots(2, 2) -> Option C

4. Quick Check:

   plt.subplots(2, 2) = 2 rows and 2 columns [OK]

Hint: Use plt.subplots(rows, columns) for grid size [OK]

Common Mistakes:

• Using single number for grid shape
• Confusing rows and columns
• Missing one dimension in arguments

3. What will be the output of this code snippet?

import matplotlib.pyplot as plt
fig, axes = plt.subplots(1, 3)
data = [1, 2, 3]
for i, ax in enumerate(axes):
    ax.plot([data[i]] * 3)
plt.show()

medium

A. Three line plots each with three points of the same value 1, 2, and 3 respectively

B. A single plot with three lines of values 1, 2, and 3

C. Error because axes is not iterable

D. Three scatter plots with points 1, 2, and 3

Solution

1. Step 1: Understand plt.subplots(1, 3)

   This creates 1 row and 3 columns of subplots, so axes is an array of 3 axes objects.

2. Step 2: Loop plots each subplot

   For each axis, it plots a line with three points all equal to data[i] (1, then 2, then 3).

3. Final Answer:

   Three line plots each with three points of the same value 1, 2, and 3 respectively -> Option A

4. Quick Check:

   Loop over axes plots lines with repeated values [OK]

Hint: Loop over axes to plot each subplot separately [OK]

Common Mistakes:

• Thinking axes is a single plot
• Assuming error due to axes type
• Confusing line plot with scatter plot

4. Identify the error in this code for creating a 2x2 grid of plots:

fig, axes = plt.subplots(2, 2)
for i in range(4):
    axes[i].plot([1, 2, 3])
plt.show()

medium

A. The plot data list is invalid

B. plt.subplots(2, 2) creates only 2 plots, not 4

C. plt.show() is missing

D. axes is a 2D array, so axes[i] indexing causes an error

Solution

1. Step 1: Understand axes shape from plt.subplots(2, 2)

   axes is a 2x2 numpy array of Axes objects, not a flat list.

2. Step 2: Identify indexing error

   axes[i] tries to index a 2D array with one index, causing an error. Correct is axes[row, col] or flatten axes first.

3. Final Answer:

   axes is a 2D array, so axes[i] indexing causes an error -> Option D

4. Quick Check:

   2D axes need two indices or flatten before looping [OK]

Hint: 2D axes need two indices or flatten before indexing [OK]

Common Mistakes:

• Assuming axes is 1D array
• Ignoring error from wrong indexing
• Thinking plt.show() is missing

5. You have a dataset with sales data for 3 regions. How would you create a 1-row, 3-column grid of plots showing sales trends for each region separately using matplotlib?

hard

A. Use plt.plot() three times without subplots

B. Use plt.subplots(1, 3), loop over axes, and plot each region's data on each subplot

C. Use plt.subplots(3, 1) and plot all regions on each subplot

D. Use plt.subplots(1, 1) and plot all regions on the same plot

Solution

1. Step 1: Create a 1x3 grid for three regions

   Use plt.subplots(1, 3) to create one row and three columns of plots.

2. Step 2: Loop over axes and plot each region's data

   Loop through each axis and plot the sales data for each region separately to compare trends side by side.

3. Final Answer:

   Use plt.subplots(1, 3), loop over axes, and plot each region's data on each subplot -> Option B

4. Quick Check:

   One row, three columns, loop to plot each region [OK]

Hint: Create grid then loop axes to plot groups separately [OK]

Common Mistakes:

• Plotting all data on one plot
• Using wrong grid shape
• Not looping over axes