Marker size variation in Matplotlib - Time & Space Complexity

Time Complexity: Marker size variation

O(n)

Understanding Time Complexity

When we change marker sizes in a plot, the computer must draw each marker with its own size. We want to understand how the time to draw grows as we add more markers.

How does the drawing time increase when we vary marker sizes for many points?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import matplotlib.pyplot as plt
import numpy as np

x = np.arange(1000)
y = np.random.rand(1000)
sizes = np.linspace(10, 200, 1000)

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

This code plots 1000 points with marker sizes changing from small to large.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Drawing each marker with its specific size.
• How many times: Once for each point, here 1000 times.

How Execution Grows With Input

Each new point adds one more marker to draw, so the total work grows as we add points.

Input Size (n)	Approx. Operations
10	10 marker draws
100	100 marker draws
1000	1000 marker draws

Pattern observation: The drawing time grows directly with the number of points.

Final Time Complexity

Time Complexity: O(n)

This means the time to draw markers grows in a straight line as we add more points.

Common Mistake

[X] Wrong: "Changing marker sizes makes the drawing time grow faster than the number of points."

[OK] Correct: Each marker is drawn once regardless of size; size changes do not multiply the number of drawing steps.

Interview Connect

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

Self-Check

What if we added a loop to redraw each marker multiple times? How would the time complexity change?

Practice

1. What does the s parameter control in the plt.scatter() function in matplotlib?

easy

A. The size of the markers in the scatter plot

B. The color of the markers

C. The shape of the markers

D. The transparency of the markers

Solution

1. Step 1: Understand the role of plt.scatter()

   The plt.scatter() function creates scatter plots where each point can have different visual properties.

2. Step 2: Identify the s parameter purpose

   The s parameter specifically sets the size of each marker in the scatter plot, either as a single value or a list of sizes.

3. Final Answer:

   The size of the markers in the scatter plot -> Option A

4. Quick Check:

   s controls marker size [OK]

Hint: Remember: 's' stands for size in scatter plots [OK]

Common Mistakes:

• Confusing 's' with color or shape parameters
• Thinking 's' controls transparency
• Assuming 's' changes marker style

2. Which of the following is the correct way to set marker sizes to 50 for all points in a scatter plot using matplotlib?

easy

A. plt.scatter(x, y, size=50)

B. plt.scatter(x, y, s=50)

C. plt.scatter(x, y, marker_size=50)

D. plt.scatter(x, y, sizes=50)

Solution

1. Step 1: Recall the parameter name for marker size

   The correct parameter to set marker size in plt.scatter() is s.

2. Step 2: Check the syntax for setting size

   Using s=50 sets all markers to size 50. Other options use incorrect parameter names.

3. Final Answer:

   plt.scatter(x, y, s=50) -> Option B

4. Quick Check:

   Use s for size [OK]

Hint: Use s to set size, not 'size' or 'sizes' [OK]

Common Mistakes:

• Using 'size' or 'sizes' instead of 's'
• Trying to set marker size with 'marker_size'
• Syntax errors from wrong parameter names

3. What will be the output marker sizes for the scatter plot from this code?

import matplotlib.pyplot as plt
x = [1, 2, 3]
y = [4, 5, 6]
sizes = [20, 50, 80]
plt.scatter(x, y, s=sizes)
plt.show()

medium

A. All markers will have size 20

B. Code will raise an error due to wrong size input

C. Markers will have default size because list is invalid

D. Markers will have sizes 20, 50, and 80 respectively

Solution

1. Step 1: Understand s with list input

   The s parameter accepts a list to assign different sizes to each marker.

2. Step 2: Match sizes to points

   Since sizes = [20, 50, 80], the first point gets size 20, second 50, third 80.

3. Final Answer:

   Markers will have sizes 20, 50, and 80 respectively -> Option D

4. Quick Check:

   List in s sets sizes per point [OK]

Hint: List in s sets sizes point-wise [OK]

Common Mistakes:

• Assuming all markers get the first size
• Thinking list input causes error
• Confusing s with color list

4. Identify the error in this code snippet that tries to vary marker sizes:

import matplotlib.pyplot as plt
x = [1, 2, 3]
y = [4, 5, 6]
sizes = [30, 60]
plt.scatter(x, y, s=sizes)
plt.show()

medium

A. The plt.scatter function is misspelled

B. The s parameter cannot accept lists

C. The sizes list length does not match x and y length

D. The variable sizes is not defined

Solution

1. Step 1: Check lengths of data and sizes

   The x and y lists have 3 points, but sizes list has only 2 values.

2. Step 2: Understand size list requirement

   The s list must match the number of points; otherwise, matplotlib raises a ValueError.

3. Final Answer:

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

4. Quick Check:

   Sizes list length must equal data points [OK]

Hint: Match sizes list length to data points [OK]

Common Mistakes:

• Ignoring size list length mismatch
• Thinking s can't be a list
• Assuming matplotlib auto-fills missing sizes

5. You want to create a scatter plot where marker sizes represent the population of cities. Given:

cities = ['A', 'B', 'C']
population = [1000, 5000, 3000]
x = [1, 2, 3]
y = [4, 5, 6]

Which code correctly scales the population to marker sizes and plots them?

hard

A. plt.scatter(x, y, s=[p*10 for p in population])

B. plt.scatter(x, y, s=[p/10 for p in population])

C. plt.scatter(x, y, s=population)

D. plt.scatter(x, y, s=[p**2 for p in population])

Solution

1. Step 1: Understand marker size scaling

   Population values are large; directly using them as sizes will create huge markers.

2. Step 2: Choose appropriate scaling

   Multiplying population by 10 scales sizes visibly but keeps them reasonable. Dividing by 10 makes markers too small; squaring makes them too large.

3. Final Answer:

   plt.scatter(x, y, s=[p*10 for p in population]) -> Option A

4. Quick Check:

   Scale sizes for visibility using multiplication [OK]

Hint: Scale data to reasonable marker sizes by multiplying [OK]

Common Mistakes:

• Using raw large values causing huge markers
• Dividing sizes too much making markers tiny
• Using squared sizes causing disproportionate markers