Legend outside the plot in Matplotlib - Time & Space Complexity

Time Complexity: Legend outside the plot

O(n)

Understanding Time Complexity

We want to understand how the time to draw a legend outside the plot changes as the number of legend items grows.

How does adding more items affect the drawing time?

Scenario Under Consideration

Analyze the time complexity of the following matplotlib code snippet.

import matplotlib.pyplot as plt

n = 10  # Define n before using it
fig, ax = plt.subplots()
for i in range(n):
    ax.plot([0, 1], [i, i], label=f'Line {i}')

ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.show()

This code plots n lines and places the legend outside the plot on the right side.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Loop adding n lines and legend entries.
• How many times: The loop runs n times, once per line and legend item.

How Execution Grows With Input

As the number of lines n increases, the number of legend entries also increases, so the drawing work grows.

Input Size (n)	Approx. Operations
10	About 10 legend items drawn
100	About 100 legend items drawn
1000	About 1000 legend items drawn

Pattern observation: The work grows roughly in direct proportion to n.

Final Time Complexity

Time Complexity: O(n)

This means the time to draw the legend grows linearly as you add more items.

Common Mistake

[X] Wrong: "Adding the legend outside the plot does not affect drawing time much."

[OK] Correct: Even outside the plot, each legend item must be drawn, so more items mean more work.

Interview Connect

Understanding how drawing elements scale helps you write efficient plotting code and explain performance in data visualization tasks.

Self-Check

"What if we used fewer legend items by grouping lines? How would the time complexity change?"

Practice

1. What is the main purpose of placing a legend outside the plot in matplotlib?

easy

A. To keep the data area clear and improve readability

B. To make the plot smaller

C. To hide the legend from view

D. To change the plot colors automatically

Solution

1. Step 1: Understand legend placement

   Legends inside the plot can cover data points, making the plot hard to read.

2. Step 2: Effect of placing legend outside

   Placing the legend outside keeps the data visible and the plot clear.

3. Final Answer:

   To keep the data area clear and improve readability -> Option A

4. Quick Check:

   Legend outside = clear data area [OK]

Hint: Legend outside keeps plot data visible and neat [OK]

Common Mistakes:

• Thinking legend outside hides it
• Assuming it changes plot size automatically
• Believing it changes plot colors

2. Which of the following is the correct way to place a legend outside the plot on the right using bbox_to_anchor and loc?

easy

A. plt.legend(loc='upper left', bbox_to_anchor=(-1, 1))

B. plt.legend(loc='center', bbox_to_anchor=(0, 0))

C. plt.legend(loc='lower left', bbox_to_anchor=(0.5, 0.5))

D. plt.legend(loc='upper right', bbox_to_anchor=(1.05, 1))

Solution

1. Step 1: Understand bbox_to_anchor coordinates

   The tuple (1.05, 1) places the legend just outside the right edge at the top.

2. Step 2: Match loc with bbox_to_anchor

   Using loc='upper right' anchors the legend's upper right corner to the point (1.05, 1).

3. Final Answer:

   plt.legend(loc='upper right', bbox_to_anchor=(1.05, 1)) -> Option D

4. Quick Check:

   Right outside = bbox_to_anchor > 1 on x [OK]

Hint: Use bbox_to_anchor >1 on x with loc='upper right' for right outside [OK]

Common Mistakes:

• Using bbox_to_anchor inside plot area (less than 1)
• Mismatching loc and bbox_to_anchor
• Using negative bbox_to_anchor values incorrectly

3. What will be the effect of the following code snippet?

import matplotlib.pyplot as plt
plt.plot([1, 2, 3], label='Line')
plt.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.show()

medium

A. Legend appears outside the plot on the right center

B. Legend appears inside the plot at center left

C. Legend appears below the plot

D. Code will raise an error

Solution

1. Step 1: Analyze bbox_to_anchor coordinates

   The point (1, 0.5) is at the right edge horizontally and center vertically.

2. Step 2: Understand loc='center left'

   The legend's center left side is anchored at (1, 0.5), placing it just outside the plot on the right center.

3. Final Answer:

   Legend appears outside the plot on the right center -> Option A

4. Quick Check:

   loc='center left' + bbox_to_anchor=(1,0.5) = right outside center [OK]

Hint: loc='center left' with bbox_to_anchor=(1,0.5) puts legend right outside center [OK]

Common Mistakes:

• Thinking legend is inside plot
• Confusing loc and bbox_to_anchor roles
• Expecting legend below plot

4. Identify the error in this code that tries to place the legend outside the plot on the right:

import matplotlib.pyplot as plt
plt.plot([1, 2, 3], label='Data')
plt.legend(loc='outer_right', bbox_to_anchor=(1.05, 1))
plt.show()

medium

A. Missing plt.tight_layout() causes overlap

B. bbox_to_anchor coordinates are out of range

C. Invalid loc value 'outer_right' causes an error

D. No label provided for the plot

Solution

1. Step 1: Check loc parameter validity

   Matplotlib does not support 'outer_right' as a valid loc string; valid locs include 'upper right', 'center left', etc.

2. Step 2: Effect of invalid loc

   Using 'outer_right' causes a ValueError and the legend will not display.

3. Final Answer:

   Invalid loc value 'outer_right' causes an error -> Option C

4. Quick Check:

   loc must be valid string like 'upper right' [OK]

Hint: Use only valid loc strings like 'upper right', not 'outer_right' [OK]

Common Mistakes:

• Using invalid loc strings
• Ignoring need for plt.tight_layout()
• Forgetting to add label to plot

5. You want to place a legend outside the plot on the right without overlapping the plot or cutting off the legend text. Which combination of commands is best to achieve this?

hard

A. plt.legend(loc='upper right', bbox_to_anchor=(0.5, 0.5)); plt.show()

B. plt.legend(loc='center left', bbox_to_anchor=(1, 0.5)); plt.tight_layout()

C. plt.legend(loc='lower left', bbox_to_anchor=(-0.5, 0)); plt.tight_layout()

D. plt.legend(loc='center', bbox_to_anchor=(1.5, 1.5)); plt.show()

Solution

1. Step 1: Choose correct legend position

   loc='center left' with bbox_to_anchor=(1, 0.5) places the legend just outside the right center of the plot.

2. Step 2: Use plt.tight_layout() to avoid overlap

   Calling plt.tight_layout() adjusts the plot layout to prevent the legend from overlapping or being cut off.

3. Final Answer:

   plt.legend(loc='center left', bbox_to_anchor=(1, 0.5)); plt.tight_layout() -> Option B

4. Quick Check:

   Right outside + tight_layout = no overlap [OK]

Hint: Use bbox_to_anchor outside + plt.tight_layout() to avoid overlap [OK]

Common Mistakes:

• Not using plt.tight_layout() causing overlap
• Placing legend inside plot by wrong bbox_to_anchor
• Using bbox_to_anchor with negative values incorrectly