Bubble charts concept in Matplotlib - Time & Space Complexity

Time Complexity: Bubble charts concept

O(n)

Understanding Time Complexity

We want to understand how the time to draw a bubble chart changes as we add more bubbles.

How does the number of bubbles affect the work matplotlib does?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import matplotlib.pyplot as plt

x = [1, 2, 3, 4, 5]
y = [5, 4, 3, 2, 1]
sizes = [100, 200, 300, 400, 500]

plt.scatter(x, y, s=sizes)
plt.show()

This code draws a bubble chart with 5 bubbles, each sized differently.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Drawing each bubble on the chart.
• How many times: Once for each bubble in the data arrays.

How Execution Grows With Input

As we add more bubbles, matplotlib draws more circles one by one.

Input Size (n)	Approx. Operations
10	10 drawing steps
100	100 drawing steps
1000	1000 drawing steps

Pattern observation: The work grows directly with the number of bubbles.

Final Time Complexity

Time Complexity: O(n)

This means the time to draw the chart grows in a straight line as you add more bubbles.

Common Mistake

[X] Wrong: "Drawing many bubbles happens instantly no matter how many there are."

[OK] Correct: Each bubble needs to be drawn separately, so more bubbles mean more work and more time.

Interview Connect

Knowing how drawing time grows helps you understand performance when visualizing large data sets.

Self-Check

"What if we added animation to the bubbles? How would that affect the time complexity?"

Practice

1. What does the size of bubbles represent in a bubble chart created with matplotlib?

easy

A. The color of the bubbles

B. A third data value representing magnitude or quantity

C. The x-axis position

D. The y-axis position

Solution

1. Step 1: Understand bubble chart data dimensions

   A bubble chart shows data points with x and y coordinates plus a size dimension.

2. Step 2: Identify what bubble size represents

   The size of each bubble encodes a third data value, like quantity or magnitude.

3. Final Answer:

   A third data value representing magnitude or quantity -> Option B

4. Quick Check:

   Bubble size = third data value [OK]

Hint: Bubble size shows extra data beyond x and y [OK]

Common Mistakes:

• Confusing size with color
• Thinking size is x or y position
• Ignoring the third data dimension

2. Which matplotlib function parameter controls the bubble sizes in a bubble chart?

easy

A. size

B. bubble_size

C. radius

D. s

Solution

1. Step 1: Recall plt.scatter parameters

   The plt.scatter function uses s to set bubble sizes.

2. Step 2: Confirm correct parameter name

   Other options like size or radius are not valid parameters for bubble size in plt.scatter.

3. Final Answer:

   s -> Option D

4. Quick Check:

   plt.scatter(x, y, s=...) sets bubble size [OK]

Hint: Use 's' parameter for bubble sizes in plt.scatter [OK]

Common Mistakes:

• Using 'size' instead of 's'
• Trying 'radius' which is invalid
• Confusing with color parameter

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

import matplotlib.pyplot as plt
x = [1, 2, 3]
y = [4, 5, 6]
sizes = [100, 200, 300]
plt.scatter(x, y, s=sizes)
plt.show()

medium

A. A syntax error due to incorrect parameter

B. A scatter plot with all bubbles the same size

C. A scatter plot with three bubbles sized 100, 200, and 300 respectively

D. A scatter plot with bubbles sized 1, 2, and 3

Solution

1. Step 1: Analyze the code parameters

   The code uses plt.scatter with x, y coordinates and s=sizes where sizes are [100, 200, 300].

2. Step 2: Understand bubble size mapping

   Each bubble size corresponds to the values in the sizes list, so bubbles will have sizes 100, 200, and 300.

3. Final Answer:

   A scatter plot with three bubbles sized 100, 200, and 300 respectively -> Option C

4. Quick Check:

   Bubble sizes match 's' list values [OK]

Hint: Bubble sizes come from the 's' list values [OK]

Common Mistakes:

• Assuming all bubbles have same size
• Confusing sizes with x or y values
• Expecting syntax error incorrectly

4. Identify the error in this bubble chart code:

import matplotlib.pyplot as plt
x = [1, 2, 3]
y = [4, 5, 6]
sizes = [100, 200]
plt.scatter(x, y, s=sizes)
plt.show()

medium

A. The sizes list length does not match x and y lengths

B. The parameter 's' is misspelled

C. x and y must be strings, not lists

D. plt.scatter cannot plot more than two points

Solution

1. Step 1: Check lengths of x, y, and sizes

   x and y have 3 elements each, but sizes has only 2 elements.

2. Step 2: Understand size array length requirement

   The sizes array must match the number of points to assign size to each bubble.

3. Final Answer:

   The sizes list length does not match x and y lengths -> Option A

4. Quick Check:

   Sizes length must equal x and y length [OK]

Hint: Sizes array length must match x and y arrays [OK]

Common Mistakes:

• Ignoring size list length mismatch
• Thinking 's' parameter is misspelled
• Believing x and y must be strings

5. You want to create a bubble chart where bubble sizes represent sales volume, but sales data has zeros and very large values. Which approach is best to make the chart readable?

hard

A. Normalize sales data and apply a size scaling factor

B. Use raw sales values directly as sizes

C. Set all bubble sizes to a fixed constant

D. Use sales data as x-axis values instead

Solution

1. Step 1: Understand impact of raw sizes

   Using raw sales values with zeros and large numbers causes bubbles too small or too large, making chart unreadable.

2. Step 2: Normalize and scale sizes

   Normalizing sales data (e.g., min-max scaling) and applying a size factor keeps bubbles proportional and visible.

3. Step 3: Evaluate other options

   Fixed sizes lose data meaning; using sales as x-axis changes chart type and loses size info.

4. Final Answer:

   Normalize sales data and apply a size scaling factor -> Option A

5. Quick Check:

   Normalize and scale sizes for readability [OK]

Hint: Normalize and scale sizes to handle zeros and extremes [OK]

Common Mistakes:

• Using raw sizes causing unreadable bubbles
• Fixing all sizes losing data info
• Misusing sales data as axis instead of size