Plotting multiple lines in Matplotlib - Time & Space Complexity

Time Complexity: Plotting multiple lines

O(n)

Understanding Time Complexity

When plotting multiple lines with matplotlib, it's important to understand how the time to draw grows as we add more lines.

We want to know how the plotting time changes when we increase the number of lines.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import matplotlib.pyplot as plt
import numpy as np

x = np.linspace(0, 10, 100)
for i in range(50):
    y = np.sin(x + i)
    plt.plot(x, y)
plt.show()

This code plots 50 sine waves, each shifted by a different amount, on the same graph.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The loop that calls plt.plot() 50 times to draw each line.
• How many times: Once for each line, so 50 times in this example.

How Execution Grows With Input

Each additional line adds roughly the same amount of work to draw.

Input Size (n)	Approx. Operations
10	10 plot calls
100	100 plot calls
1000	1000 plot calls

Pattern observation: The work grows linearly as the number of lines increases.

Final Time Complexity

Time Complexity: O(n)

This means the time to plot grows directly in proportion to the number of lines you draw.

Common Mistake

[X] Wrong: "Plotting multiple lines is almost as fast as plotting one line because the data points are the same."

[OK] Correct: Each line requires a separate draw call and rendering, so the time adds up with each new line.

Interview Connect

Understanding how plotting time grows helps you write efficient visualization code and explain performance in real projects.

Self-Check

"What if we plotted all lines using a single call with multiple y arrays? How would the time complexity change?"

Practice

1. What is the main way to plot multiple lines on the same graph using matplotlib?

easy

A. Use plt.hist() multiple times

B. Use plt.scatter() for each line

C. Call plt.plot() multiple times with different data sets before plt.show()

D. Call plt.bar() for each line

Solution

1. Step 1: Understand plotting multiple lines

   In matplotlib, to plot multiple lines on the same graph, you call plt.plot() for each line's data before showing the plot.

2. Step 2: Identify correct plotting function

   plt.scatter(), plt.bar(), and plt.hist() are for scatter plots, bar charts, and histograms, not line plots.

3. Final Answer:

   Call plt.plot() multiple times with different data sets before plt.show() -> Option C

4. Quick Check:

   Multiple plt.plot() calls = multiple lines [OK]

Hint: Use multiple plt.plot() calls to add lines [OK]

Common Mistakes:

• Using plt.scatter() instead of plt.plot() for lines
• Calling plt.show() after each line instead of once
• Using bar or histogram functions for line plots

2. Which of the following code snippets correctly plots two lines on the same graph?

easy

A. plt.plot([1, 2, 3], [4, 5, 6])
plt.plot([1, 2, 3], [6, 5, 4])
plt.show()

B. plt.plot([1, 2, 3], [4, 5, 6])
plt.show()
plt.plot([1, 2, 3], [6, 5, 4])

C. plt.show()
plt.plot([1, 2, 3], [4, 5, 6])
plt.plot([1, 2, 3], [6, 5, 4])

D. plt.plot([1, 2, 3], [4, 5, 6])
plt.plot([1, 2, 3], [6, 5, 4])

Solution

1. Step 1: Check order of plotting and showing

   To plot multiple lines, call plt.plot() for each line, then call plt.show() once at the end.

2. Step 2: Identify correct snippet

   plt.plot([1, 2, 3], [4, 5, 6]) plt.plot([1, 2, 3], [6, 5, 4]) plt.show() calls plt.plot() twice then plt.show(), which is correct. plt.plot([1, 2, 3], [4, 5, 6]) plt.show() plt.plot([1, 2, 3], [6, 5, 4]) calls plt.show() too early, splitting the plots. plt.show() plt.plot([1, 2, 3], [4, 5, 6]) plt.plot([1, 2, 3], [6, 5, 4]) calls plt.show() before plotting, so nothing shows. plt.plot([1, 2, 3], [4, 5, 6]) plt.plot([1, 2, 3], [6, 5, 4]) misses plt.show() entirely.

3. Final Answer:

   Two plt.plot() calls followed by plt.show() -> Option A

4. Quick Check:

   Plot lines first, show once after [OK]

Hint: Call plt.show() only after all plt.plot() calls [OK]

Common Mistakes:

• Calling plt.show() before all plots
• Forgetting plt.show() to display plot
• Plotting after plt.show() call

3. What will be the output of this code?

import matplotlib.pyplot as plt
x = [1, 2, 3]
y1 = [2, 4, 6]
y2 = [1, 3, 5]
plt.plot(x, y1, label='Line 1')
plt.plot(x, y2, label='Line 2')
plt.legend()
plt.show()

medium

A. A graph with two lines but no legend

B. A graph with two lines labeled 'Line 1' and 'Line 2'

C. A graph with one line labeled 'Line 2' only

D. No graph displayed due to error

Solution

1. Step 1: Analyze plotting commands

   The code plots two lines with plt.plot() and assigns labels 'Line 1' and 'Line 2'.

2. Step 2: Understand legend usage

   Calling plt.legend() displays the legend with the labels for both lines.

3. Final Answer:

   A graph with two lines labeled 'Line 1' and 'Line 2' -> Option B

4. Quick Check:

   Labels + plt.legend() = labeled lines [OK]

Hint: Use plt.legend() to show labels for all lines [OK]

Common Mistakes:

• Forgetting plt.legend() so labels don't show
• Assigning labels incorrectly
• Plotting only one line

4. Identify the error in this code that tries to plot two lines:

import matplotlib.pyplot as plt
x = [1, 2, 3]
y1 = [2, 4, 6]
y2 = [1, 3, 5]
plt.plot(x, y1, label='Line 1')
plt.plot(x, y2, label='Line 2')
plt.legend
plt.show()

medium

A. Missing parentheses after plt.legend() call

B. x and y lists have different lengths

C. plt.show() is called before plotting

D. Labels are not assigned to lines

Solution

1. Step 1: Check function calls

   The code calls plt.legend without parentheses, so the legend function is not executed.

2. Step 2: Understand effect of missing parentheses

   Without calling plt.legend(), the legend does not appear, so labels won't show.

3. Final Answer:

   Missing parentheses after plt.legend() call -> Option A

4. Quick Check:

   Call plt.legend() with () to show legend [OK]

Hint: Always add () after plt.legend to display legend [OK]

Common Mistakes:

• Forgetting () after plt.legend
• Assuming legend shows without calling function
• Mixing up order of plt.show()

5. You want to plot three lines with different colors and styles on the same graph and add a legend. Which code snippet correctly achieves this?

hard

A. plt.plot(x, y1, 'r-', label='Red solid')
plt.plot(x, y2, 'g--')
plt.plot(x, y3, 'b:')
plt.legend()
plt.show()

B. plt.plot(x, y1, color='red', linestyle='-', label='Red solid')
plt.plot(x, y2, color='green', linestyle='--', label='Green dashed')
plt.plot(x, y3, color='blue', linestyle=':', label='Blue dotted')
plt.legend()
plt.show()

C. plt.plot(x, y1, 'red', 'solid', label='Red solid')
plt.plot(x, y2, 'green', 'dashed', label='Green dashed')
plt.plot(x, y3, 'blue', 'dotted', label='Blue dotted')
plt.legend()
plt.show()

D. plt.plot(x, y1, 'r-', label='Red solid')
plt.plot(x, y2, 'g--', label='Green dashed')
plt.plot(x, y3, 'b:', label='Blue dotted')
plt.legend()
plt.show()

Solution

1. Step 1: Understand color and style shorthand

   In matplotlib, shorthand like 'r-' means red solid line, 'g--' green dashed, 'b:' blue dotted.

2. Step 2: Check label usage and legend

   plt.plot(x, y1, 'r-', label='Red solid') plt.plot(x, y2, 'g--', label='Green dashed') plt.plot(x, y3, 'b:', label='Blue dotted') plt.legend() plt.show() assigns labels to all lines and calls plt.legend() to show them. plt.plot(x, y1, color='red', linestyle='solid', label='Red solid') plt.plot(x, y2, color='green', linestyle='dashed', label='Green dashed') plt.plot(x, y3, color='blue', linestyle='dotted', label='Blue dotted') plt.legend() plt.show() uses invalid linestyle names ('solid', 'dashed', 'dotted' are not valid; correct are '-', '--', ':'). plt.plot(x, y1, 'red', 'solid', label='Red solid') plt.plot(x, y2, 'green', 'dashed', label='Green dashed') plt.plot(x, y3, 'blue', 'dotted', label='Blue dotted') plt.legend() plt.show() uses positional strings incorrectly. plt.plot(x, y1, 'r-', label='Red solid') plt.plot(x, y2, 'g--') plt.plot(x, y3, 'b:') plt.legend() plt.show() misses labels for second and third lines.

3. Final Answer:

   Shorthand format strings like 'r-', 'g--', 'b:' for each plt.plot() -> Option D

4. Quick Check:

   Use shorthand 'color-style' and label each line [OK]

Hint: Use shorthand like 'r-', 'g--', 'b:' with labels [OK]

Common Mistakes:

• Using invalid linestyle names like 'solid'
• Forgetting labels on all lines
• Not calling plt.legend() to show labels