Multiple legends in Matplotlib - Time & Space Complexity

Time Complexity: Multiple legends

O(n)

Understanding Time Complexity

When creating multiple legends in matplotlib, the program does extra work to draw each legend separately.

We want to know how the time to draw grows as we add more legends.

Scenario Under Consideration

Analyze the time complexity of this matplotlib code snippet.

import matplotlib.pyplot as plt

fig, ax = plt.subplots()
line1, = ax.plot([1, 2, 3], label='Line 1')
line2, = ax.plot([3, 2, 1], label='Line 2')

legend1 = ax.legend(handles=[line1], loc='upper left')
ax.add_artist(legend1)
legend2 = ax.legend(handles=[line2], loc='upper right')
ax.add_artist(legend2)
plt.show()

This code creates a plot with two lines and adds two separate legends for each line.

Identify Repeating Operations

Look for repeated actions that take time.

• Primary operation: Drawing each legend box and its items.
• How many times: Once per legend added (here, twice).

How Execution Grows With Input

Adding more legends means more boxes and labels to draw.

Number of Legends (n)	Approx. Drawing Steps
1	1 unit (one legend drawn)
5	5 units (five legends drawn)
10	10 units (ten legends drawn)

Pattern observation: The drawing work grows directly with the number of legends added.

Final Time Complexity

Time Complexity: O(n)

This means the time to draw legends grows in a straight line as you add more legends.

Common Mistake

[X] Wrong: "Adding multiple legends is just as fast as one legend because they are small."

[OK] Correct: Each legend requires separate drawing steps, so more legends mean more work and more time.

Interview Connect

Understanding how adding multiple legends affects drawing time helps you think about performance when making complex plots.

Self-Check

What if we combined all labels into a single legend instead of multiple legends? How would the time complexity change?

Practice

1. What is the main reason to use multiple legends in a matplotlib plot?

easy

A. To increase the plot size automatically

B. To change the color of the plot lines

C. To label different groups or data sets separately on the same plot

D. To save the plot as an image file

Solution

1. Step 1: Understand the purpose of legends

   Legends help identify what each line or marker in a plot represents.

2. Step 2: Recognize why multiple legends are needed

   When a plot has multiple groups or categories, separate legends make it easier to understand each group distinctly.

3. Final Answer:

   To label different groups or data sets separately on the same plot -> Option C

4. Quick Check:

   Multiple legends = separate group labels [OK]

Hint: Multiple legends label different groups clearly [OK]

Common Mistakes:

• Thinking legends change plot colors
• Confusing legends with saving files
• Assuming legends resize plots

2. Which matplotlib method is used to keep the first legend visible when adding a second legend?

easy

A. ax.add_artist()

B. plt.show()

C. plt.legend()

D. ax.set_title()

Solution

1. Step 1: Identify how legends are added

   Legends are usually added with plt.legend() or ax.legend().

2. Step 2: Understand how to keep multiple legends

   To keep the first legend visible after adding a second, you must add the first legend as an artist using ax.add_artist().

3. Final Answer:

   ax.add_artist() -> Option A

4. Quick Check:

   Keep first legend visible = add_artist() [OK]

Hint: Use add_artist() to keep first legend visible [OK]

Common Mistakes:

• Using plt.legend() twice without add_artist()
• Calling plt.show() to fix legends
• Trying to set title to fix legends

3. What will the following code display?

import matplotlib.pyplot as plt
fig, ax = plt.subplots()
line1, = ax.plot([1, 2, 3], label='Line 1')
line2, = ax.plot([3, 2, 1], label='Line 2')
leg1 = ax.legend(handles=[line1], loc='upper left')
ax.add_artist(leg1)
ax.legend(handles=[line2], loc='upper right')
plt.show()

medium

A. Two legends: 'Line 1' at upper left and 'Line 2' at upper right

B. Only one legend showing 'Line 2' at upper right

C. Only one legend showing 'Line 1' at upper left

D. No legends displayed

Solution

1. Step 1: Analyze legend creation

   The first legend is created for 'Line 1' and added as an artist to keep it visible.

2. Step 2: Analyze second legend addition

   The second legend is created for 'Line 2' and placed at upper right. Both legends appear separately.

3. Final Answer:

   Two legends: 'Line 1' at upper left and 'Line 2' at upper right -> Option A

4. Quick Check:

   add_artist() + second legend = two legends [OK]

Hint: add_artist() keeps first legend when adding second [OK]

Common Mistakes:

• Expecting only one legend to show
• Forgetting to add_artist() for first legend
• Placing both legends at same location

4. Identify the error in this code that tries to add two legends:

import matplotlib.pyplot as plt
fig, ax = plt.subplots()
line1, = ax.plot([1, 2, 3], label='A')
line2, = ax.plot([3, 2, 1], label='B')
ax.legend(handles=[line1], loc='upper left')
ax.legend(handles=[line2], loc='upper right')
plt.show()

medium

A. Syntax error due to missing parentheses

B. Second legend call overwrites the first, so only one legend shows

C. Plot lines are not labeled correctly

D. The plot will not display because plt.show() is missing

Solution

1. Step 1: Understand legend behavior

   Calling ax.legend() twice replaces the previous legend each time.

2. Step 2: Identify why only one legend appears

   Without using ax.add_artist(), the first legend is removed when the second is added.

3. Final Answer:

   Second legend call overwrites the first, so only one legend shows -> Option B

4. Quick Check:

   Multiple legend calls overwrite without add_artist() [OK]

Hint: Use add_artist() to keep multiple legends visible [OK]

Common Mistakes:

• Assuming multiple legend() calls stack automatically
• Thinking missing plt.show() causes no plot
• Believing labels cause syntax errors

5. You want to plot three data groups with separate legends placed at 'upper left', 'upper right', and 'lower left' without overlap. Which approach correctly achieves this?

hard

A. Plot all lines without legends and add a single legend manually

B. Call ax.legend() three times without add_artist(), changing loc each time

C. Use plt.legend() once with all labels combined

D. Create first legend, add it with ax.add_artist(), then create second and third legends with different loc values

Solution

1. Step 1: Understand legend placement

   Legends placed at different loc positions avoid overlap visually.

2. Step 2: Use add_artist() to keep multiple legends

   Adding the first legend as an artist keeps it visible when adding others.

3. Step 3: Create all three legends with distinct locations

   Creating legends separately with loc set to 'upper left', 'upper right', and 'lower left' places them without overlap.

4. Final Answer:

   Create first legend, add it with ax.add_artist(), then create second and third legends with different loc values -> Option D

5. Quick Check:

   add_artist() + distinct loc = multiple legends no overlap [OK]

Hint: Add first legend as artist, set loc differently for others [OK]

Common Mistakes:

• Calling legend() multiple times without add_artist()
• Placing all legends at same location causing overlap
• Using single legend for all groups losing clarity