Dual y-axis for different scales in Matplotlib - Time & Space Complexity

Time Complexity: Dual y-axis for different scales

O(n)

Understanding Time Complexity

When we create a plot with two y-axes in matplotlib, we want to understand how the time to draw the plot changes as we add more data points.

We ask: How does the plotting time grow when the data size grows?

Scenario Under Consideration

Analyze the time complexity of the following matplotlib code snippet.

import matplotlib.pyplot as plt

n = 10  # Example value for n
x = range(n)
y1 = [i for i in x]
y2 = [i**2 for i in x]

fig, ax1 = plt.subplots()
ax2 = ax1.twinx()

ax1.plot(x, y1, 'g-')
ax2.plot(x, y2, 'b-')

plt.show()

This code plots two lines sharing the same x-axis but with different y-axes scales.

Identify Repeating Operations

• Primary operation: Plotting each data point for both y1 and y2 lines.
• How many times: Each line plots n points, so 2 * n plotting operations.

How Execution Grows With Input

As the number of data points n increases, the number of plotting operations grows roughly in direct proportion.

Input Size (n)	Approx. Operations
10	20 (2 lines * 10 points)
100	200 (2 lines * 100 points)
1000	2000 (2 lines * 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 plot grows directly in proportion to the number of data points.

Common Mistake

[X] Wrong: "Adding a second y-axis doubles the time complexity to O(n^2)."

[OK] Correct: The second y-axis adds another line to plot, but plotting each point is still done once per point, so the growth stays linear, not squared.

Interview Connect

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

Self-Check

What if we added a third y-axis with another line? How would the time complexity change?

Practice

1. What is the main purpose of using a dual y-axis in a matplotlib plot?

easy

A. To compare two datasets with different scales on the same plot

B. To create two separate plots side by side

C. To add a legend to the plot

D. To change the color of the plot lines

Solution

1. Step 1: Understand the purpose of dual y-axis

   A dual y-axis allows plotting two datasets with different value ranges on the same graph for easy comparison.

2. Step 2: Identify the correct use case

   Comparing datasets with different scales requires two y-axes; other options do not describe this purpose.

3. Final Answer:

   To compare two datasets with different scales on the same plot -> Option A

4. Quick Check:

   Dual y-axis = compare different scales [OK]

Hint: Dual y-axis means two y-scales on one graph [OK]

Common Mistakes:

• Thinking dual y-axis creates two separate plots
• Confusing dual y-axis with adding legends
• Assuming it changes line colors only

2. Which matplotlib function is used to create a second y-axis sharing the same x-axis?

easy

A. plt.subplots()

B. ax.twiny()

C. ax.twinx()

D. plt.plot()

Solution

1. Step 1: Recall matplotlib methods for axes

   The method twinx() creates a second y-axis sharing the x-axis.

2. Step 2: Differentiate from similar methods

   twiny() creates a second x-axis, not y-axis; subplots() creates figure and axes; plot() draws lines.

3. Final Answer:

   ax.twinx() -> Option C

4. Quick Check:

   Second y-axis = twinx() [OK]

Hint: Use ax.twinx() for second y-axis, twiny() is for x-axis [OK]

Common Mistakes:

• Using plt.subplots() to create second y-axis
• Confusing twinx() with twiny()
• Trying to use plt.plot() to add axes

3. What will the following code output?

import matplotlib.pyplot as plt
fig, ax1 = plt.subplots()
ax2 = ax1.twinx()
ax1.plot([1, 2, 3], [10, 20, 30], 'g-')
ax2.plot([1, 2, 3], [100, 200, 300], 'b-')
print(len(fig.axes))

medium

A. 2

B. 1

C. 3

D. 4

Solution

1. Step 1: Understand axes creation

   plt.subplots() creates one axes (ax1), then ax1.twinx() adds a second y-axis (ax2), so total axes are 2.

2. Step 2: Check figure axes count

   fig.axes is a list of all axes in the figure; after adding ax2, length is 2.

3. Final Answer:

   2 -> Option A

4. Quick Check:

   Two axes after twinx() = 2 [OK]

Hint: twinx() adds one more axes, so total axes count increases by 1 [OK]

Common Mistakes:

• Assuming twinx() replaces the original axes
• Thinking twinx() adds multiple axes
• Confusing axes count with number of plots

4. Identify the error in this code snippet for creating dual y-axis:

import matplotlib.pyplot as plt
fig, ax = plt.subplots()
ax2 = plt.twinx()
ax.plot([1,2,3], [10,20,30])
ax2.plot([1,2,3], [100,200,300])
plt.show()

medium

A. plt.show() is missing

B. plt.subplots() should be plt.figure()

C. ax2.plot() should be ax.plot()

D. plt.twinx() should be ax.twinx()

Solution

1. Step 1: Check method usage for second y-axis

   twinx() is a method of an axes object, not plt module. So plt.twinx() is invalid.

2. Step 2: Correct method call

   Use ax.twinx() to create the second y-axis sharing the x-axis.

3. Final Answer:

   plt.twinx() should be ax.twinx() -> Option D

4. Quick Check:

   twinx() is an axes method, not plt function [OK]

Hint: twinx() must be called on axes object, not plt [OK]

Common Mistakes:

• Calling twinx() on plt instead of axes
• Confusing figure and axes creation methods
• Missing plt.show() (though present here)

5. You want to plot temperature (°C) and rainfall (mm) over months on the same plot with dual y-axes. Which of these code snippets correctly sets different y-axis labels and colors for clarity?

hard

A. ax1.set_xlabel('Temperature (°C)', color='red')\nax2.set_xlabel('Rainfall (mm)', color='blue')

B. ax1.set_ylabel('Temperature (°C)', color='red')\nax2.set_ylabel('Rainfall (mm)', color='blue')

C. ax1.set_ylabel('Rainfall (mm)', color='blue')\nax2.set_ylabel('Temperature (°C)', color='red')

D. ax1.set_title('Temperature and Rainfall')\nax2.set_title('Temperature and Rainfall')

Solution

1. Step 1: Assign correct y-axis labels

   Temperature and rainfall are y-axis data, so use set_ylabel() on each axis with matching labels.

2. Step 2: Use colors to distinguish axes

   Setting label colors helps visually separate the two y-axes for clarity.

3. Final Answer:

   ax1.set_ylabel('Temperature (°C)', color='red')\nax2.set_ylabel('Rainfall (mm)', color='blue') -> Option B

4. Quick Check:

   Correct y-labels and colors = ax1.set_ylabel('Temperature (°C)', color='red')\nax2.set_ylabel('Rainfall (mm)', color='blue') [OK]

Hint: Label y-axes with units and colors for clear dual-axis plots [OK]

Common Mistakes:

• Setting x-axis labels instead of y-axis
• Swapping labels between axes
• Using titles instead of axis labels