Time series with fill_between in Matplotlib - Time & Space Complexity

Time Complexity: Time series with fill_between

O(n)

Understanding Time Complexity

When plotting time series with shaded areas using fill_between, it is important to understand how the plotting time grows as the data size increases.

We want to know how the number of points affects the time matplotlib takes to draw the plot.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import matplotlib.pyplot as plt
import numpy as np

time = np.arange(0, 1000)
values = np.sin(time * 0.01)

plt.plot(time, values)
plt.fill_between(time, values - 0.1, values + 0.1, alpha=0.3)
plt.show()

This code plots a time series and shades the area around the line using fill_between.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Iterating over each point in the time array to draw the line and fill the area.
• How many times: Once for each of the n points in the time series.

How Execution Grows With Input

As the number of points increases, matplotlib processes each point to draw lines and fill areas, so the work grows with the number of points.

Input Size (n)	Approx. Operations
10	About 10 operations to draw and fill
100	About 100 operations to draw and fill
1000	About 1000 operations to draw and fill

Pattern observation: The operations increase roughly in direct proportion to the number of points.

Final Time Complexity

Time Complexity: O(n)

This means the time to plot grows linearly with the number of data points.

Common Mistake

[X] Wrong: "Adding fill_between does not affect the plotting time much because it just colors the area."

[OK] Correct: fill_between processes every point to create the shaded area, so it adds work proportional to the data size.

Interview Connect

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

Self-Check

"What if we used fewer points but more fill_between calls? How would the time complexity change?"

Practice

1. What does the fill_between function do in a time series plot using matplotlib?

easy

A. Creates a bar chart from time series data

B. Plots scatter points on the time series

C. Colors the area between two lines to highlight differences or ranges

D. Removes grid lines from the plot

Solution

1. Step 1: Understand the purpose of fill_between

   The fill_between function is used to color the area between two lines or curves in a plot.

2. Step 2: Connect to time series visualization

   In time series plots, it highlights differences or ranges between two data series by filling the area between them.

3. Final Answer:

   Colors the area between two lines to highlight differences or ranges -> Option C

4. Quick Check:

   fill_between colors area between lines = A [OK]

Hint: Remember fill_between fills area between lines visually [OK]

Common Mistakes:

• Confusing fill_between with scatter plot
• Thinking it creates bar charts
• Assuming it removes grid lines

2. Which of the following is the correct syntax to fill the area between two time series arrays y1 and y2 over time points x using matplotlib?

easy

A. plt.fill_between(x, y1, y2, color='blue', alpha=0.3)

B. plt.fill_between(x, y1, color='blue', alpha=0.3)

C. plt.fill_between(y1, y2, x, color='blue')

D. plt.fill_between(x, y1, y2, linestyle='--')

Solution

1. Step 1: Check function parameters order

   The correct order for fill_between is x (time points), then y1 and y2 (values to fill between).

2. Step 2: Validate optional arguments

   Color and transparency (alpha) are valid optional arguments; linestyle is not used for fill_between.

3. Final Answer:

   plt.fill_between(x, y1, y2, color='blue', alpha=0.3) -> Option A

4. Quick Check:

   fill_between(x, y1, y2) with color and alpha = C [OK]

Hint: Remember order: x, y1, y2 in fill_between [OK]

Common Mistakes:

• Swapping y1 and y2 with x
• Using linestyle instead of color or alpha
• Omitting one of the y arrays

3. What will be the output of this code snippet?

import matplotlib.pyplot as plt
import numpy as np
x = np.arange(5)
y1 = np.array([1, 3, 2, 5, 4])
y2 = np.array([2, 4, 3, 6, 5])
plt.plot(x, y1, label='y1')
plt.plot(x, y2, label='y2')
plt.fill_between(x, y1, y2, color='green', alpha=0.4)
plt.legend()
plt.show()

medium

A. An error because fill_between requires y1 > y2

B. A plot with two lines but no shaded area

C. A plot with only one line and a green shaded area below it

D. A plot with two lines and a green shaded area between them

Solution

1. Step 1: Understand plot and fill_between behavior

   The code plots two lines y1 and y2 over x, then fills the area between them with green color and transparency.

2. Step 2: Confirm fill_between works with any order

   fill_between fills area between y1 and y2 regardless of which is greater, so no error occurs.

3. Final Answer:

   A plot with two lines and a green shaded area between them -> Option D

4. Quick Check:

   Two lines + green fill_between area = A [OK]

Hint: fill_between shades area between lines regardless of order [OK]

Common Mistakes:

• Thinking fill_between needs y1 > y2 always
• Expecting no shaded area without fill_between call
• Confusing plot lines with fill_between shading

4. Identify the error in this code snippet that tries to fill between two time series:

import matplotlib.pyplot as plt
x = [0, 1, 2, 3]
y1 = [1, 2, 3]
y2 = [2, 3, 4, 5]
plt.fill_between(x, y1, y2, color='red')
plt.show()

medium

A. x and y1 have different lengths causing a ValueError

B. fill_between does not accept list inputs

C. Missing plt.plot calls before fill_between

D. Color argument must be uppercase

Solution

1. Step 1: Check lengths of x, y1, and y2

   x has 4 points, y1 has 3 points, y2 has 4 points; mismatch causes error.

2. Step 2: Understand fill_between input requirements

   fill_between requires x, y1, y2 arrays to have the same length to plot correctly.

3. Final Answer:

   x and y1 have different lengths causing a ValueError -> Option A

4. Quick Check:

   Length mismatch in inputs = B [OK]

Hint: Check all input arrays have same length before fill_between [OK]

Common Mistakes:

• Ignoring length mismatch errors
• Thinking fill_between needs plot calls first
• Assuming color argument case matters

5. You have two time series arrays y1 and y2 representing daily temperatures for two cities over 7 days. You want to highlight only the days when y1 is higher than y2 using fill_between. Which code snippet correctly achieves this?

hard

A. plt.fill_between(x, y1, y2, condition=(y1 > y2), color='orange')

B. plt.fill_between(x, y1, y2, where=(y1 > y2), color='orange', alpha=0.5)

C. plt.fill_between(x, y1, y2, where=(y1 < y2), color='orange', alpha=0.5)

D. plt.fill_between(x, y1, y2, color='orange', alpha=0.5)

Solution

1. Step 1: Use the 'where' parameter to specify condition

   The where argument in fill_between allows filling only where the condition is True.

2. Step 2: Set condition to y1 > y2 and specify color and transparency

   Using where=(y1 > y2) fills only days when y1 is higher than y2 with orange color and alpha 0.5.

3. Final Answer:

   plt.fill_between(x, y1, y2, where=(y1 > y2), color='orange', alpha=0.5) -> Option B

4. Quick Check:

   Use where=(y1 > y2) to fill selectively = D [OK]

Hint: Use 'where' to fill conditionally between lines [OK]

Common Mistakes:

• Using 'condition' instead of 'where'
• Filling without condition fills entire area
• Reversing the condition (y1 < y2) by mistake