Before-after comparison plots in Matplotlib - Time & Space Complexity

Time Complexity: Before-after comparison plots

O(n)

Understanding Time Complexity

We want to understand how the time to create before-after comparison plots changes as the amount of data grows.

How does the plotting time increase when we add more points to compare?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import matplotlib.pyplot as plt

before = [1, 2, 3, 4, 5]
after = [2, 3, 5, 7, 11]

plt.figure(figsize=(6,4))
plt.plot(before, label='Before')
plt.plot(after, label='After')
plt.legend()
plt.show()

This code plots two lines showing values before and after some change for 5 points.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Plotting each data point for both before and after lists.
• How many times: Once for each point in the data arrays (n times per line).

How Execution Grows With Input

As the number of points increases, the plotting work grows roughly in direct proportion.

Input Size (n)	Approx. Operations
10	Plot about 20 points (10 before + 10 after)
100	Plot about 200 points
1000	Plot about 2000 points

Pattern observation: Doubling the number of points doubles the plotting work.

Final Time Complexity

Time Complexity: O(n)

This means the time to create the plot grows linearly with the number of data points.

Common Mistake

[X] Wrong: "Plotting two lines takes twice as long as plotting one line, so time complexity is O(2n)."

[OK] Correct: Constants like 2 are ignored in time complexity, so O(2n) is simplified to O(n).

Interview Connect

Understanding how plotting time grows helps you explain performance when working with bigger datasets in real projects.

Self-Check

"What if we added a loop to create multiple before-after plots for different groups? How would the time complexity change?"

Practice

1. What is the main purpose of a before-after comparison plot in matplotlib?

easy

A. To visually compare data from two different time points

B. To show the distribution of a single dataset

C. To display the correlation between two variables

D. To create a 3D surface plot

Solution

1. Step 1: Understand the concept of before-after plots

   Before-after plots are used to compare data points from two different times or conditions to see changes.

2. Step 2: Identify the correct purpose

   Among the options, only To visually compare data from two different time points describes comparing data from two time points, which matches the before-after plot purpose.

3. Final Answer:

   To visually compare data from two different time points -> Option A

4. Quick Check:

   Before-after plots = compare two time points [OK]

Hint: Before-after plots compare two sets of data visually [OK]

Common Mistakes:

• Confusing before-after plots with distribution plots
• Thinking they show correlation instead of change
• Assuming they create 3D plots

2. Which of the following is the correct way to plot two sets of data side-by-side for before-after comparison using matplotlib?

easy

A. plt.plot(before_data); plt.plot(after_data)

B. plt.bar([0,1], before_data); plt.bar([0,1], after_data)

C. plt.bar([0,1], before_data); plt.bar([1,2], after_data)

D. plt.bar([1,2], [before_data, after_data])

Solution

1. Step 1: Understand bar plot positioning

   To show before and after side-by-side, bars must not overlap. Using different x positions for before and after data avoids overlap.

2. Step 2: Analyze options for correct bar positions

   plt.bar([0,1], before_data); plt.bar([1,2], after_data) places before_data at positions 0 and 1, and after_data at 1 and 2, so bars for the same category are side-by-side without overlap.

3. Final Answer:

   plt.bar([0,1], before_data); plt.bar([1,2], after_data) -> Option C

4. Quick Check:

   Side-by-side bars need different x positions [OK]

Hint: Use different x positions to avoid bar overlap [OK]

Common Mistakes:

• Plotting bars at same x positions causing overlap
• Using plt.plot instead of plt.bar for categorical data
• Passing data incorrectly as list of lists

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

import matplotlib.pyplot as plt
before = [5, 7]
after = [8, 6]
plt.plot([1, 2], before, label='Before')
plt.plot([1, 2], after, label='After')
plt.legend()
plt.show()

medium

A. An error because plt.plot cannot take two lists

B. A bar chart comparing before and after data

C. A scatter plot with points at (1,5), (2,7), (1,8), (2,6)

D. Two overlapping line plots showing before and after data

Solution

1. Step 1: Understand plt.plot with x and y lists

   plt.plot([1, 2], before) plots points (1,5) and (2,7) connected by a line. Similarly for after data.

2. Step 2: Identify plot type and legend

   Two line plots will appear overlapping on the same axes with labels 'Before' and 'After'. No error occurs.

3. Final Answer:

   Two overlapping line plots showing before and after data -> Option D

4. Quick Check:

   plt.plot with x,y lists = line plot [OK]

Hint: plt.plot(x, y) draws lines connecting points [OK]

Common Mistakes:

• Thinking plt.plot creates bar charts
• Expecting scatter plot without plt.scatter
• Assuming plt.plot with two lists causes error

4. Identify the error in this code for before-after bar plot:

import matplotlib.pyplot as plt
before = [3, 4]
after = [5, 6]
plt.bar([0, 1], before)
plt.bar([0, 1], after)
plt.show()

medium

A. plt.show() is missing

B. Bars for before and after overlap at same positions

C. before and after lists must be same length

D. plt.bar requires three arguments

Solution

1. Step 1: Check bar positions

   Both before and after bars are plotted at positions 0 and 1, causing them to overlap and hide one another.

2. Step 2: Identify correct fix

   To avoid overlap, after bars should be shifted to different x positions, e.g., [0.3, 1.3].

3. Final Answer:

   Bars for before and after overlap at same positions -> Option B

4. Quick Check:

   Same x positions cause bar overlap [OK]

Hint: Shift bars on x-axis to avoid overlap [OK]

Common Mistakes:

• Thinking plt.bar needs 3 arguments
• Ignoring bar overlap issue
• Assuming plt.show() is missing

5. You have sales data before and after a marketing campaign for 3 products: before = [100, 150, 200], after = [120, 180, 210]. How would you create a clear before-after bar plot with labels and legend in matplotlib?

hard

A. Use plt.bar with shifted x positions for before and after, add labels and legend

B. Plot before and after using plt.plot without labels

C. Use plt.scatter for both datasets on same x positions

D. Plot only after data as a bar chart

Solution

1. Step 1: Plan bar positions and labels

   To compare before and after clearly, plot bars side-by-side with shifted x positions, e.g., before at [0,1,2], after at [0.3,1.3,2.3]. Add x-axis labels for products.

2. Step 2: Add legend and labels for clarity

   Use plt.legend() to distinguish before and after bars, and plt.xlabel/plt.ylabel for axis labels.

3. Final Answer:

   Use plt.bar with shifted x positions for before and after, add labels and legend -> Option A

4. Quick Check:

   Shift bars + labels + legend = clear before-after plot [OK]

Hint: Shift bars and add legend for clear comparison [OK]

Common Mistakes:

• Plotting bars at same positions causing confusion
• Skipping labels and legend
• Using scatter plot instead of bar plot