Multiple time series comparison in Matplotlib - Time & Space Complexity

Time Complexity: Multiple time series comparison

O(m * n)

Understanding Time Complexity

When we compare multiple time series using matplotlib, we want to know how the time to draw grows as we add more series or points.

How does adding more lines or data points affect the work matplotlib does?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import matplotlib.pyplot as plt
import numpy as np

n = 1000  # number of points
m = 5     # number of time series
x = np.linspace(0, 10, n)

for i in range(m):
    y = np.sin(x + i)
    plt.plot(x, y)
plt.show()

This code plots m time series, each with n points, on the same graph.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Loop over m time series, each plotting n points.
• How many times: The plotting function is called m times, each handling n points.

How Execution Grows With Input

As we add more series or points, the work grows by multiplying these two factors.

Input Size (n points, m series)	Approx. Operations
10 points, 5 series	50
100 points, 5 series	500
1000 points, 10 series	10,000

Pattern observation: Doubling points or series roughly doubles the work, so total work grows with both.

Final Time Complexity

Time Complexity: O(m * n)

This means the time to draw grows proportionally with the number of series and the number of points per series.

Common Mistake

[X] Wrong: "Adding more series doesn't affect time much because each line is simple."

[OK] Correct: Each series adds a full set of points to draw, so time grows with both series count and points.

Interview Connect

Understanding how plotting multiple series scales helps you explain performance in data visualization tasks clearly and confidently.

Self-Check

"What if we used scatter plots instead of line plots for each series? How would the time complexity change?"

Practice

1. What is the main purpose of plotting multiple time series on the same graph using matplotlib?

easy

A. To make the graph load faster

B. To create separate graphs for each time series

C. To hide the data labels for clarity

D. To visually compare trends and differences between series over time

Solution

1. Step 1: Understand the purpose of multiple time series plots

   Plotting multiple lines on one graph helps us see how different series change over time side by side.

2. Step 2: Compare options with this purpose

   Only To visually compare trends and differences between series over time describes this visual comparison goal correctly.

3. Final Answer:

   To visually compare trends and differences between series over time -> Option D

4. Quick Check:

   Multiple time series comparison = Visual comparison [OK]

Hint: Multiple lines on one plot show trends side by side [OK]

Common Mistakes:

• Thinking multiple plots are created instead of one combined plot
• Ignoring the importance of labels and legends
• Believing it speeds up graph loading

2. Which of the following matplotlib code snippets correctly plots two time series series1 and series2 on the same graph with labels?

easy

A. plt.plot(series1, label='Series 1')
plt.legend()
plt.show()

B. plt.plot(series1)
plt.plot(series2)
plt.show()

C. plt.plot(series1, label='Series 1')
plt.plot(series2, label='Series 2')
plt.legend()
plt.show()

D. plt.plot(series1, label='Series 1')
plt.plot(series2, label='Series 2')
plt.show()

Solution

1. Step 1: Check for plotting both series with labels

   plt.plot(series1, label='Series 1') plt.plot(series2, label='Series 2') plt.legend() plt.show() plots both series and adds labels for each.

2. Step 2: Verify legend call to show labels

   plt.plot(series1, label='Series 1') plt.plot(series2, label='Series 2') plt.legend() plt.show() calls plt.legend() to display labels on the graph.

3. Final Answer:

   Code that plots both series with labels and shows legend -> Option C

4. Quick Check:

   Plot both + labels + legend = plt.plot(series1, label='Series 1') plt.plot(series2, label='Series 2') plt.legend() plt.show() [OK]

Hint: Always add labels and call plt.legend() to show them [OK]

Common Mistakes:

• Forgetting to call plt.legend() so labels don't appear
• Plotting only one series instead of both
• Not adding labels to each series

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

import matplotlib.pyplot as plt
series1 = [1, 3, 2, 4]
series2 = [2, 1, 3, 5]
plt.plot(series1, label='A')
plt.plot(series2, label='B')
plt.legend()
plt.show()

medium

A. A graph with two lines labeled 'A' and 'B' showing series1 and series2

B. A graph with one line showing the sum of series1 and series2

C. A graph with two lines but no labels

D. SyntaxError due to missing import

Solution

1. Step 1: Analyze the plotting commands

   Two lines are plotted: series1 with label 'A' and series2 with label 'B'.

2. Step 2: Check legend and show calls

   Calling plt.legend() displays the labels on the graph.

3. Final Answer:

   A graph with two lines labeled 'A' and 'B' showing series1 and series2 -> Option A

4. Quick Check:

   Two labeled lines plotted = A graph with two lines labeled 'A' and 'B' showing series1 and series2 [OK]

Hint: Labels appear only if plt.legend() is called [OK]

Common Mistakes:

• Thinking lines are summed instead of plotted separately
• Forgetting plt.legend() hides labels
• Assuming syntax error without import

4. The following code is intended to plot two time series with labels, but the legend does not appear. What is the error?

import matplotlib.pyplot as plt
series1 = [1, 2, 3]
series2 = [3, 2, 1]
plt.plot(series1, label='First')
plt.plot(series2, label='Second')
plt.show()

medium

A. Missing plt.legend() call to display the legend

B. Labels are incorrectly assigned inside plt.plot()

C. plt.show() should be called before plotting

D. series2 should be plotted before series1

Solution

1. Step 1: Check for legend display code

   The code does not call plt.legend(), so labels won't show.

2. Step 2: Confirm label usage is correct

   Labels are correctly passed in plt.plot(), so no issue there.

3. Final Answer:

   Missing plt.legend() call to display the legend -> Option A

4. Quick Check:

   Legend missing without plt.legend() [OK]

Hint: Always add plt.legend() to show labels on plot [OK]

Common Mistakes:

• Assuming labels show automatically without legend call
• Thinking order of plotting affects legend display
• Calling plt.show() too early

5. You have three time series with different lengths:
series1 = [1, 2, 3, 4], series2 = [2, 3, 4], series3 = [1, 3, 5, 7, 9].
How can you correctly plot all three on the same graph to compare them over time?

hard

A. Plot all series using the length of the longest series only

B. Plot each series with its own x-axis range matching its length, then add labels and legend

C. Pad shorter series with zeros to match the longest series length before plotting

D. Plot only the shortest series to avoid errors

Solution

1. Step 1: Understand different lengths require matching x-axis

   Each series must be plotted with x values matching its length to avoid misalignment.

2. Step 2: Plot each series with its own x range and add labels

   Use range(len(series)) for x-axis, plot all, then add labels and legend.

3. Final Answer:

   Plot each series with its own x-axis range matching its length, then add labels and legend -> Option B

4. Quick Check:

   Match x-axis length per series + labels = Plot each series with its own x-axis range matching its length, then add labels and legend [OK]

Hint: Use range(len(series)) for x-axis of each series [OK]

Common Mistakes:

• Plotting all series without adjusting x-axis causes misaligned lines
• Padding with zeros changes data meaning
• Ignoring series length differences