Figure and axes creation in Data Analysis Python - Time & Space Complexity

Time Complexity: Figure and axes creation

O(n*m)

Understanding Time Complexity

When we create figures and axes in data analysis, we want to know how the time it takes changes as we add more elements.

We ask: How does the work grow when we create more axes or figures?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import matplotlib.pyplot as plt

fig, ax = plt.subplots(nrows=3, ncols=2)

for i in range(3):
    for j in range(2):
        ax[i, j].plot([1, 2, 3], [1, 4, 9])

This code creates a figure with 6 axes arranged in 3 rows and 2 columns, then plots a simple line on each axis.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Nested loops over rows and columns to plot on each axis.
• How many times: The inner plot command runs once for each axis, total 3 x 2 = 6 times.

How Execution Grows With Input

As the number of rows and columns increases, the total axes grow by multiplying these two numbers.

Input Size (rows x cols)	Approx. Operations
3 x 2 = 6	6 plots
10 x 10 = 100	100 plots
30 x 30 = 900	900 plots

Pattern observation: The work grows proportionally to the total number of axes created.

Final Time Complexity

Time Complexity: O(n*m)

This means the time to create and plot on axes grows linearly with the number of axes (rows times columns).

Common Mistake

[X] Wrong: "Creating more axes takes the same time no matter how many there are."

[OK] Correct: Each axis requires separate setup and plotting, so more axes mean more work and more time.

Interview Connect

Understanding how plotting scales helps you manage performance when working with many charts or subplots in real projects.

Self-Check

"What if we added a loop inside each axis to plot multiple lines? How would the time complexity change?"

Practice

1. What does the plt.subplots() function return in matplotlib?

easy

A. A figure and one or more axes objects

B. Only a figure object

C. Only an axes object

D. A list of data points

Solution

1. Step 1: Understand plt.subplots() purpose

   The function is designed to create a figure and axes together for plotting.

2. Step 2: Check the return values

   It returns a tuple: the first is the figure, the second is the axes (single or array).

3. Final Answer:

   A figure and one or more axes objects -> Option A

4. Quick Check:

   plt.subplots() = (figure, axes) [OK]

Hint: Remember plt.subplots() returns figure and axes together [OK]

Common Mistakes:

• Thinking it returns only figure or only axes
• Confusing axes with data points
• Assuming it returns a plot directly

2. Which of the following is the correct syntax to create a figure with 2 rows and 3 columns of axes using matplotlib?

easy

A. fig, axes = plt.subplots(rows=3, cols=2)

B. fig, axes = plt.subplots(2, 3)

C. fig, axes = plt.subplots(3, 2)

D. fig, axes = plt.subplots(2*3)

Solution

1. Step 1: Recall plt.subplots() parameters

   The first argument is number of rows, the second is number of columns.

2. Step 2: Match the correct order

   To create 2 rows and 3 columns, use plt.subplots(2, 3).

3. Final Answer:

   fig, axes = plt.subplots(2, 3) -> Option B

4. Quick Check:

   Rows first, columns second in plt.subplots() [OK]

Hint: Remember rows first, columns second in plt.subplots() [OK]

Common Mistakes:

• Swapping rows and columns order
• Using keyword arguments incorrectly
• Passing a single number instead of two

3. What will be the shape of axes when running fig, axes = plt.subplots(2, 2)?

medium

A. A 2x2 numpy array of AxesSubplot objects

B. A list of 4 AxesSubplot objects

C. A single AxesSubplot object

D. A dictionary of axes objects

Solution

1. Step 1: Understand axes structure for multiple subplots

   When more than one subplot is created, axes is a 2D array matching the grid shape.

2. Step 2: Check the shape for 2 rows and 2 columns

   Axes will be a 2x2 numpy array of AxesSubplot objects.

3. Final Answer:

   A 2x2 numpy array of AxesSubplot objects -> Option A

4. Quick Check:

   Multiple subplots = axes array matching grid [OK]

Hint: Multiple subplots return axes array matching rows and columns [OK]

Common Mistakes:

• Expecting a flat list instead of 2D array
• Thinking axes is a single object always
• Confusing axes with figure

4. Identify the error in this code snippet:

fig, ax = plt.subplots(2, 2)
ax.plot([1, 2, 3], [4, 5, 6])

medium

A. fig and ax are swapped in assignment

B. plt.subplots() cannot create 2x2 axes

C. ax is an array, so ax.plot() causes an error

D. The plot data lists have different lengths

Solution

1. Step 1: Check the shape of ax from plt.subplots(2, 2)

   ax is a 2x2 array of axes, not a single axes object.

2. Step 2: Understand why ax.plot() fails

   Calling plot() on an array causes an AttributeError because arrays don't have plot method.

3. Final Answer:

   ax is an array, so ax.plot() causes an error -> Option C

4. Quick Check:

   Array of axes needs indexing before plot() [OK]

Hint: Index axes array before plotting when multiple subplots exist [OK]

Common Mistakes:

• Trying to plot on axes array directly
• Assuming plt.subplots(2,2) returns single axes
• Ignoring need to index axes for plotting

5. You want to create a figure with 3 subplots stacked vertically and set the figure size to 8 inches wide and 12 inches tall. Which code correctly does this?

hard

A. fig, axes = plt.subplots(1, 3, figsize=(12, 8))

B. fig, axes = plt.subplots(3, figsize=(8, 12))

C. fig, axes = plt.subplots(3, 1, size=(8, 12))

D. fig, axes = plt.subplots(3, 1, figsize=(8, 12))

Solution

1. Step 1: Determine subplot layout for vertical stacking

   3 subplots stacked vertically means 3 rows and 1 column.

2. Step 2: Set figure size correctly

   Use figsize=(width, height) with width=8 and height=12 inches.

3. Final Answer:

   fig, axes = plt.subplots(3, 1, figsize=(8, 12)) -> Option D

4. Quick Check:

   Rows=3, cols=1, figsize=(8,12) [OK]

Hint: Use figsize=(width, height) and rows, columns order [OK]

Common Mistakes:

• Swapping rows and columns
• Using wrong keyword 'size' instead of 'figsize'
• Confusing width and height order