Stacked area chart in Matplotlib - Time & Space Complexity

Time Complexity: Stacked area chart

O(n)

Understanding Time Complexity

We want to understand how the time to draw a stacked area chart changes as the data size grows.

How does the number of data points affect the work matplotlib does to create the chart?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import matplotlib.pyplot as plt
import numpy as np

x = np.arange(0, 1000)
y = np.random.rand(3, 1000)

plt.stackplot(x, y[0], y[1], y[2])
plt.show()

This code creates a stacked area chart with 3 layers and 1000 data points each.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Drawing each point for each layer in the stacked area chart.
• How many times: For each of the 3 layers, matplotlib processes all 1000 points.

How Execution Grows With Input

As the number of points increases, the work grows proportionally because each point must be drawn for each layer.

Input Size (n)	Approx. Operations
10	About 30 (3 layers x 10 points)
100	About 300 (3 layers x 100 points)
1000	About 3000 (3 layers x 1000 points)

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

Final Time Complexity

Time Complexity: O(n)

This means the time to draw the chart grows directly in proportion to the number of data points.

Common Mistake

[X] Wrong: "Adding more layers does not affect the time much because they overlap."

[OK] Correct: Each layer requires processing all points separately, so more layers multiply the work.

Interview Connect

Understanding how data size affects plotting time helps you explain performance in data visualization tasks clearly and confidently.

Self-Check

"What if we increased the number of layers instead of points? How would the time complexity change?"

Practice

1. What does a stacked area chart in matplotlib primarily show?

easy

A. How different parts add up to a whole over categories or time

B. Only the total sum of all data points

C. The relationship between two unrelated variables

D. The frequency distribution of a single variable

Solution

1. Step 1: Understand the purpose of stacked area charts

   Stacked area charts display multiple data series stacked on top of each other to show how each part contributes to the total over time or categories.

2. Step 2: Compare options with this purpose

   How different parts add up to a whole over categories or time correctly describes this purpose. Options A, B, and C describe other chart types or incorrect uses.

3. Final Answer:

   How different parts add up to a whole over categories or time -> Option A

4. Quick Check:

   Stacked area chart = parts adding to whole [OK]

Hint: Stacked area charts show parts stacked to form a whole [OK]

Common Mistakes:

• Confusing stacked area chart with line chart
• Thinking it shows only totals, not parts
• Mixing it up with scatter plots

2. Which of the following is the correct way to create a stacked area chart using matplotlib.pyplot?

easy

A. plt.stackplot(x, y1, y2, labels=['A', 'B'])

B. plt.area(x, y1, y2)

C. plt.plot_area(x, y1, y2)

D. plt.stack(x, y1, y2)

Solution

1. Step 1: Recall the correct function name

   The correct function to create stacked area charts in matplotlib is stackplot from matplotlib.pyplot.

2. Step 2: Check the syntax

   plt.stackplot(x, y1, y2, labels=['A', 'B']) uses plt.stackplot(x, y1, y2, labels=['A', 'B']), which is correct. Other options use non-existent functions.

3. Final Answer:

   plt.stackplot(x, y1, y2, labels=['A', 'B']) -> Option A

4. Quick Check:

   Function name is stackplot [OK]

Hint: Use plt.stackplot for stacked area charts [OK]

Common Mistakes:

• Using plt.area which does not exist
• Trying plt.plot_area instead of stackplot
• Forgetting to pass x and multiple y arrays

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

import matplotlib.pyplot as plt
x = [1, 2, 3]
y1 = [1, 2, 3]
y2 = [2, 1, 2]
plt.stackplot(x, y1, y2, labels=['A', 'B'])
plt.legend()
plt.show()

medium

A. An error because y arrays have different lengths

B. A line chart with two lines labeled 'A' and 'B'

C. A bar chart with two bars for each x value

D. A stacked area chart with two layers labeled 'A' and 'B' over x=1 to 3

Solution

1. Step 1: Analyze the data lengths and function

   Both y1 and y2 have length 3 matching x. The function plt.stackplot creates a stacked area chart.

2. Step 2: Understand the output

   The code plots two stacked areas labeled 'A' and 'B' over x values 1 to 3, then shows a legend.

3. Final Answer:

   A stacked area chart with two layers labeled 'A' and 'B' over x=1 to 3 -> Option D

4. Quick Check:

   Stackplot with matching lengths = stacked area chart [OK]

Hint: Check lengths of x and y arrays match for stackplot [OK]

Common Mistakes:

• Thinking stackplot creates line or bar charts
• Assuming error due to lengths when they match
• Ignoring legend labels

4. Identify the error in this code that tries to plot a stacked area chart:

import matplotlib.pyplot as plt
x = [1, 2, 3]
y1 = [1, 2]
y2 = [2, 1, 2]
plt.stackplot(x, y1, y2)
plt.show()

medium

A. Missing labels argument causes the plot to fail

B. plt.stackplot does not accept multiple y arrays

C. x and y1 have different lengths causing a ValueError

D. plt.show() is missing parentheses

Solution

1. Step 1: Check lengths of x and y arrays

   x has length 3, y1 has length 2, y2 has length 3. Length mismatch causes error.

2. Step 2: Understand stackplot requirements

   All y arrays must have the same length as x. This mismatch causes a ValueError.

3. Final Answer:

   x and y1 have different lengths causing a ValueError -> Option C

4. Quick Check:

   Length mismatch in stackplot = error [OK]

Hint: Ensure all y arrays match x length in stackplot [OK]

Common Mistakes:

• Assuming labels are required to avoid errors
• Thinking stackplot accepts different length arrays
• Forgetting to call plt.show() with parentheses

5. You have monthly sales data for three products over 6 months:

months = [1, 2, 3, 4, 5, 6]
product_a = [5, 7, 8, 6, 7, 9]
product_b = [3, 4, 2, 5, 6, 4]
product_c = [2, 3, 4, 3, 2, 3]

How would you create a stacked area chart showing each product's contribution over time with a legend?

hard

A. plt.plot(months, product_a + product_b + product_c)
plt.legend(['Total'])
plt.show()

B. plt.stackplot(months, product_a, product_b, product_c, labels=['A', 'B', 'C'])
plt.legend()
plt.show()

C. plt.bar(months, product_a, bottom=product_b)
plt.show()

D. plt.stackplot(product_a, product_b, product_c, labels=['A', 'B', 'C'])
plt.legend()
plt.show()

Solution

1. Step 1: Use plt.stackplot with x and multiple y arrays

   Pass months as x and product sales as y arrays with labels for legend.

2. Step 2: Add legend and show plot

   Call plt.legend() to show labels and plt.show() to display the chart.

3. Final Answer:

   plt.stackplot(months, product_a, product_b, product_c, labels=['A', 'B', 'C']) plt.legend() plt.show() -> Option B

4. Quick Check:

   Stackplot with labels + legend = stacked area chart [OK]

Hint: Pass x, multiple y arrays, labels, then call plt.legend() [OK]

Common Mistakes:

• Adding y arrays instead of stacking
• Using bar chart with wrong bottom parameter
• Forgetting to pass x as first argument