Stack and unstack in Data Analysis Python - Time & Space Complexity

Time Complexity: Stack and unstack

O(n)

Understanding Time Complexity

We want to understand how the time needed to stack and unstack data changes as the data size grows.

How does the number of operations grow when we combine or separate data tables?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import pandas as pd

df1 = pd.DataFrame({'A': range(1000), 'B': range(1000, 2000)})
df2 = pd.DataFrame({'A': range(1000, 2000), 'B': range(2000, 3000)})

stacked = pd.concat([df1, df2], keys=['df1', 'df2'])  # stacking rows
unstacked = stacked.unstack(level=0)   # unstacking the DataFrame

This code stacks two data tables by rows and then unstacks the combined table.

Identify Repeating Operations

• Primary operation: Combining rows with concat and reshaping with unstack.
• How many times: Each row from both tables is processed once during stacking, and each element is processed once during unstacking.

How Execution Grows With Input

When the number of rows doubles, the stacking operation processes twice as many rows, and unstacking processes twice as many elements.

Input Size (n rows per DataFrame)	Approx. Operations
10	About 20 rows stacked, 20 elements unstacked
100	About 200 rows stacked, 200 elements unstacked
1000	About 2000 rows stacked, 2000 elements unstacked

Pattern observation: Operations grow roughly in direct proportion to the total number of rows combined.

Final Time Complexity

Time Complexity: O(n)

This means the time to stack and unstack grows linearly with the number of rows involved.

Common Mistake

[X] Wrong: "Stacking two tables takes constant time no matter how big they are."

[OK] Correct: Each row must be copied or referenced, so more rows mean more work, making time grow with data size.

Interview Connect

Understanding how stacking and unstacking scale helps you handle data efficiently and shows you can reason about data operations in real projects.

Self-Check

"What if we stacked three or more DataFrames instead of two? How would the time complexity change?"

Practice

1. What does the stack() method do to a DataFrame in pandas?

easy

A. It moves columns into rows, making the data longer.

B. It moves rows into columns, making the data wider.

C. It sorts the DataFrame by index.

D. It removes duplicate rows from the DataFrame.

Solution

1. Step 1: Understand the stack operation

   The stack() method compresses columns into a single column, turning columns into rows.

2. Step 2: Compare with unstack

   Unlike unstack(), which moves rows to columns, stack() makes data longer by stacking columns.

3. Final Answer:

   It moves columns into rows, making the data longer. -> Option A

4. Quick Check:

   Stack = columns to rows [OK]

Hint: Stack compresses columns into rows, making data longer [OK]

Common Mistakes:

• Confusing stack with unstack direction
• Thinking stack sorts data
• Assuming stack removes duplicates

2. Which of the following is the correct syntax to unstack the last level of a MultiIndex DataFrame df?

easy

A. df.stack(axis=0)

B. df.stack(level=-1)

C. df.unstack(level=-1)

D. df.unstack(axis=1)

Solution

1. Step 1: Recall unstack syntax

   The unstack() method by default unstacks the last level of the index, and level=-1 explicitly specifies this.

2. Step 2: Differentiate from stack

   stack() is the opposite operation, so options A and B are incorrect. unstack() does not take an axis parameter, so df.unstack(axis=1) is invalid.

3. Final Answer:

   df.unstack(level=-1) -> Option C

4. Quick Check:

   Unstack last level = df.unstack(level=-1) [OK]

Hint: Use unstack(level=-1) to unstack last index level [OK]

Common Mistakes:

• Using stack instead of unstack
• Passing axis parameter to unstack
• Not specifying level when needed

3. Given the DataFrame df below:

import pandas as pd
d = {('A', 'x'): 1, ('A', 'y'): 2, ('B', 'x'): 3, ('B', 'y'): 4}
df = pd.Series(d).unstack()

What is the output of df.stack()?

medium

A. A DataFrame with columns 'A' and 'B' stacked

B. A Series with MultiIndex where second level is stacked into rows

C. A DataFrame with columns 'x' and 'y' unchanged

D. An error because stack cannot be applied here

Solution

1. Step 1: Understand the initial DataFrame

   The unstack() converts the Series with MultiIndex into a DataFrame with columns 'x' and 'y' and index 'A' and 'B'.

2. Step 2: Apply stack() on the DataFrame

   Calling stack() moves the columns 'x' and 'y' back into the inner level of the row index, producing a Series with MultiIndex.

3. Final Answer:

   A Series with MultiIndex where second level is stacked into rows -> Option B

4. Quick Check:

   Stack reverses unstack, making columns into row index [OK]

Hint: Stack reverses unstack, turning columns back into row index [OK]

Common Mistakes:

• Expecting a DataFrame output instead of Series
• Confusing which index level is stacked
• Thinking stack causes error here

4. You run the code below and get an error:

df = pd.DataFrame({
  'A': [1, 2],
  'B': [3, 4]
})
stacked = df.stack(level=1)

What is the cause of the error?

medium

A. The DataFrame index is missing.

B. Stack requires numeric data only.

C. Stack cannot be used on DataFrames, only Series.

D. DataFrame columns have no MultiIndex, so level=1 is invalid.

Solution

1. Step 1: Check DataFrame columns

   The DataFrame has simple columns 'A' and 'B', which are not a MultiIndex, so specifying level=1 is invalid.

2. Step 2: Understand stack level parameter

   The level parameter in stack() refers to the level of the columns MultiIndex to stack. Without MultiIndex columns, level=1 causes an error.

3. Final Answer:

   DataFrame columns have no MultiIndex, so level=1 is invalid. -> Option D

4. Quick Check:

   Stack level requires MultiIndex columns [OK]

Hint: Stack level needs MultiIndex columns; simple columns cause error [OK]

Common Mistakes:

• Assuming stack only works on Series
• Thinking stack requires numeric data
• Ignoring the column index type

5. You have a DataFrame df with a MultiIndex on rows (levels: 'City', 'Year') and columns as years (e.g., 2020, 2021). You want to reshape it so that the 'Year' level from rows becomes columns, and the columns years become a new row level. Which sequence of operations correctly achieves this?

hard

A. First unstack the 'Year' level from rows, then stack the columns.

B. First stack the columns, then unstack the 'City' level from rows.

C. Use only stack on the columns without unstacking rows.

D. Use only unstack on the 'City' level.

Solution

1. Step 1: Unstack the 'Year' level from rows

   Unstacking the 'Year' level moves it from the row index to columns, widening the DataFrame.

2. Step 2: Stack the columns

   Stacking the columns moves the columns years into a new row index level, making the data longer again but reshaped as desired.

3. Final Answer:

   First unstack the 'Year' level from rows, then stack the columns. -> Option A

4. Quick Check:

   Unstack rows then stack columns reshapes MultiIndex correctly [OK]

Hint: Unstack row level first, then stack columns to reshape MultiIndex [OK]

Common Mistakes:

• Stacking before unstacking causes wrong shape
• Unstacking wrong index level
• Ignoring the need to reshape both rows and columns