Stacked bar charts in Matplotlib - Time & Space Complexity

Time Complexity: Stacked bar charts

O(n * g)

Understanding Time Complexity

When creating stacked bar charts, we want to know how the time to draw the chart changes as we add more data.

How does the drawing time grow when we increase the number of bars or stacks?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import matplotlib.pyplot as plt

labels = ['A', 'B', 'C', 'D']
values1 = [3, 5, 1, 7]
values2 = [2, 3, 4, 1]

plt.bar(labels, values1, label='Group 1')
plt.bar(labels, values2, bottom=values1, label='Group 2')
plt.legend()
plt.show()

This code draws a stacked bar chart with two groups stacked on four bars.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Drawing bars for each group and label.
• How many times: For each group, it loops over all labels once.

How Execution Grows With Input

As we add more bars or more groups, the number of drawing steps grows.

Input Size (n)	Approx. Operations
10 bars, 2 groups	20 drawing steps
100 bars, 2 groups	200 drawing steps
1000 bars, 5 groups	5000 drawing steps

Pattern observation: The total drawing steps grow by multiplying the number of bars by the number of groups.

Final Time Complexity

Time Complexity: O(n * g)

This means the time to draw grows linearly with the number of bars (n) and the number of stacked groups (g).

Common Mistake

[X] Wrong: "Adding more groups does not affect drawing time much because bars are stacked."

[OK] Correct: Each group adds a full set of bars to draw, so more groups multiply the work.

Interview Connect

Understanding how drawing time grows helps you explain performance when visualizing large datasets, a useful skill in data science roles.

Self-Check

What if we used a grouped bar chart instead of stacked bars? How would the time complexity change?

Practice

1. What is the main purpose of using a stacked bar chart in data visualization?

easy

A. To create a pie chart with multiple slices

B. To display data points as individual dots on a graph

C. To plot a line connecting data points over time

D. To show how different parts contribute to the total within each group

Solution

1. Step 1: Understand the concept of stacked bar charts

   Stacked bar charts combine multiple data parts into one bar to show totals and parts.

2. Step 2: Identify the purpose of stacking

   Stacking helps visualize how each part contributes to the total for each group.

3. Final Answer:

   To show how different parts contribute to the total within each group -> Option D

4. Quick Check:

   Stacked bars = parts + total [OK]

Hint: Stacked bars add parts vertically to show totals [OK]

Common Mistakes:

• Confusing stacked bars with line charts
• Thinking stacked bars show individual points only
• Mixing stacked bars with pie charts

2. Which matplotlib parameter is used to stack bars on top of each other in a bar chart?

easy

A. height

B. bottom

C. width

D. align

Solution

1. Step 1: Recall bar chart parameters

   In matplotlib, height sets bar size, width sets bar thickness, align controls bar alignment.

2. Step 2: Identify stacking parameter

   The bottom parameter sets where the bar starts vertically, allowing stacking on previous bars.

3. Final Answer:

   bottom -> Option B

4. Quick Check:

   Stack bars use bottom parameter [OK]

Hint: Use bottom to place bars on top of others [OK]

Common Mistakes:

• Using height to stack bars (it sets bar size)
• Confusing width with stacking
• Using align which only shifts bars horizontally

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

import matplotlib.pyplot as plt

labels = ['A', 'B']
values1 = [3, 5]
values2 = [2, 4]

plt.bar(labels, values1)
plt.bar(labels, values2, bottom=values1)
plt.show()

medium

A. Two bars per label, stacked vertically

B. Error because bottom parameter is incorrect

C. Only one bar per label showing values2

D. Two bars per label, side by side

Solution

1. Step 1: Analyze the first bar call

   The first plt.bar draws bars of height 3 and 5 for labels 'A' and 'B'.

2. Step 2: Analyze the second bar call with bottom

   The second plt.bar draws bars of height 2 and 4 stacked on top of the first bars using bottom=values1.

3. Final Answer:

   Two bars per label, stacked vertically -> Option A

4. Quick Check:

   bottom stacks bars vertically [OK]

Hint: bottom stacks bars vertically on previous bars [OK]

Common Mistakes:

• Thinking bars appear side by side without bottom
• Assuming only one bar per label is drawn
• Believing bottom parameter causes error

4. Identify the error in this code for creating a stacked bar chart:

import matplotlib.pyplot as plt

labels = ['X', 'Y']
values1 = [4, 6]
values2 = [3, 5]

plt.bar(labels, values1)
plt.bar(labels, values2, bottom=values2)
plt.show()

medium

A. Labels list is missing an element

B. plt.bar cannot be called twice

C. Using bottom=values2 instead of bottom=values1 causes incorrect stacking

D. values1 and values2 must be the same length

Solution

1. Step 1: Check the bottom parameter usage

   The second bar uses bottom=values2, which stacks bars on themselves, not on the first bars.

2. Step 2: Correct stacking requires bottom=values1

   To stack bars correctly, the second bars should start at the height of the first bars, so bottom=values1 is needed.

3. Final Answer:

   Using bottom=values2 instead of bottom=values1 causes incorrect stacking -> Option C

4. Quick Check:

   bottom must be previous bar heights [OK]

Hint: Stack bars using bottom=previous bar heights [OK]

Common Mistakes:

• Setting bottom to current bar heights instead of previous
• Thinking plt.bar can only be called once
• Ignoring length matching of values

5. You have three categories of sales data for two stores:

store_labels = ['Store1', 'Store2']
sales_A = [10, 15]
sales_B = [5, 7]
sales_C = [3, 4]

How do you create a stacked bar chart showing all three sales categories stacked for each store?

hard

A. Plot sales_A, then sales_B with bottom=sales_A, then sales_C with bottom=sales_A + sales_B

B. Plot sales_A, sales_B, sales_C all with bottom=0

C. Plot sales_A, then sales_B with bottom=sales_A, then sales_C with bottom=sales_B

D. Plot sales_A with bottom=sales_B, sales_B with bottom=sales_C, sales_C with bottom=sales_A

Solution

1. Step 1: Plot the first category normally

   Plot sales_A bars starting at zero (default).

2. Step 2: Stack second category on first

   Plot sales_B bars with bottom=sales_A to stack on top of sales_A.

3. Step 3: Stack third category on sum of first two

   Plot sales_C bars with bottom=[a+b for a,b in zip(sales_A, sales_B)] to stack on top of both.

4. Final Answer:

   Plot sales_A, then sales_B with bottom=sales_A, then sales_C with bottom=sales_A + sales_B -> Option A

5. Quick Check:

   Stack each bar on sum of all below [OK]

Hint: Stack bars using cumulative sums for bottom [OK]

Common Mistakes:

• Stacking third category only on second, ignoring first
• Plotting all bars at bottom=0 causing overlap
• Using wrong bottom values causing incorrect stacking