Time Complexity: Multiple legends
O(n)
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Multiple legends in Matplotlib - Time & Space Complexity
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?