pct_change() for percentage change in Pandas - Time & Space Complexity

Time Complexity: pct_change() for percentage change

O(n)

Understanding Time Complexity

We want to understand how the time needed to calculate percentage changes grows as the data size grows.

How does the work increase when we have more rows in our data?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import pandas as pd

data = pd.Series([10, 20, 30, 40, 50])

pct_changes = data.pct_change()
print(pct_changes)

This code calculates the percentage change between each value and the previous one in a list of numbers.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The function looks at each element and compares it to the one before it.
• How many times: It does this once for every element except the first.

How Execution Grows With Input

As the number of data points grows, the work grows roughly the same amount.

Input Size (n)	Approx. Operations
10	About 9 comparisons
100	About 99 comparisons
1000	About 999 comparisons

Pattern observation: The work grows in a straight line with the number of data points.

Final Time Complexity

Time Complexity: O(n)

This means the time to calculate percentage changes grows directly with the number of values.

Common Mistake

[X] Wrong: "pct_change() compares every value to all previous values, so it takes much longer as data grows."

[OK] Correct: pct_change() only compares each value to the one right before it, so it only does one comparison per value, not many.

Interview Connect

Understanding how simple operations like pct_change() scale helps you explain your code's efficiency clearly and confidently.

Self-Check

"What if pct_change() was asked to compare each value to the value two steps before instead of one? How would the time complexity change?"

Practice

1. What does the pct_change() function in pandas do?

easy

A. Calculates the percentage change between consecutive rows.

B. Calculates the sum of all values in a column.

C. Sorts the DataFrame by index.

D. Removes missing values from the DataFrame.

Solution

1. Step 1: Understand the purpose of pct_change()

   The pct_change() function calculates how much values change in percentage from one row to the next.

2. Step 2: Compare with other options

   Options A, B, and C describe different pandas functions unrelated to percentage change.

3. Final Answer:

   Calculates the percentage change between consecutive rows. -> Option A

4. Quick Check:

   pct_change() = percentage change [OK]

Hint: Think: pct_change means percent change between rows [OK]

Common Mistakes:

• Confusing pct_change() with sum()
• Thinking it sorts data
• Assuming it removes missing values

2. Which of the following is the correct way to use pct_change() on a pandas DataFrame named df?

easy

A. df.pct_change()

B. pct_change(df)

C. df.change_pct()

D. df.percent_change()

Solution

1. Step 1: Recall pandas method syntax

   In pandas, pct_change() is a method called on a DataFrame or Series object, so the correct syntax is df.pct_change().

2. Step 2: Check other options

   Options A, B, and D are not valid pandas syntax or method names.

3. Final Answer:

   df.pct_change() -> Option A

4. Quick Check:

   Method called on DataFrame = df.pct_change() [OK]

Hint: Remember: pandas methods use dot notation like df.method() [OK]

Common Mistakes:

• Using pct_change() as a standalone function
• Mixing method names
• Using incorrect method names

3. Given the DataFrame:

import pandas as pd
df = pd.DataFrame({'Sales': [100, 120, 150, 180]})
print(df.pct_change())

What is the output?

medium

A. 0.2, 0.25, 0.2, NaN

B. 0, 20, 30, 30

C. NaN, 20, 30, 30

D. NaN, 0.2, 0.25, 0.2

Solution

1. Step 1: Calculate percentage changes row by row

   From 100 to 120: (120-100)/100 = 0.2
   From 120 to 150: (150-120)/120 = 0.25
   From 150 to 180: (180-150)/150 = 0.2

2. Step 2: Understand first row result

   The first row has no previous row, so result is NaN.

3. Final Answer:

   NaN, 0.2, 0.25, 0.2 -> Option D

4. Quick Check:

   pct_change() = NaN, 0.2, 0.25, 0.2 [OK]

Hint: First row is always NaN; next rows show percent change [OK]

Common Mistakes:

• Confusing absolute change with percent change
• Forgetting first row is NaN
• Mixing up order of results

4. What is wrong with this code snippet?

import pandas as pd
df = pd.DataFrame({'A': [10, 20, 30]})
result = df.pct_change(axis=1)
print(result)

medium

A. The DataFrame has no numeric columns.

B. The code is correct and will run without errors.

C. pct_change() requires a parameter 'periods' to work.

D. pct_change() cannot be used with axis=1 on this DataFrame.

Solution

1. Step 1: Understand axis parameter in pct_change()

   By default, pct_change() calculates percentage change down rows (axis=0). axis=1 calculates change across columns.

2. Step 2: Check DataFrame shape and axis=1 effect

   The DataFrame has only one column. pct_change(axis=1) produces NaN values everywhere since there are no multiple columns to compare, but the code runs without errors or exceptions.

3. Final Answer:

   The code is correct and will run without errors. -> Option B

4. Quick Check:

   axis=1 on single column = NaN output, no error [OK]

Hint: axis=1 on single column gives NaN but runs fine [OK]

Common Mistakes:

• Thinking axis=1 causes error on single-column DataFrame
• Believing periods parameter is required
• Claiming no numeric columns

5. You have a DataFrame df with daily stock prices:

import pandas as pd
df = pd.DataFrame({'Price': [50, 52, 51, 53, 54]})

You want to calculate the percentage change over 2 days instead of 1. Which code will give the correct result?

hard

A. df.pct_change(axis=1)

B. df.pct_change(periods=1)

C. df.pct_change(periods=2)

D. df.pct_change(periods=0)

Solution

1. Step 1: Understand the periods parameter

   The periods parameter in pct_change() sets how many rows to look back for percentage change calculation. For 2-day change, use periods=2.

2. Step 2: Check other options

   df.pct_change(periods=1) calculates 1-day change, df.pct_change(axis=1) uses axis=1 which is incorrect for this data, and df.pct_change(periods=0) computes zero change.

3. Final Answer:

   df.pct_change(periods=2) -> Option C

4. Quick Check:

   periods=2 for 2-day change [OK]

Hint: Use periods=2 to compare with 2 rows before [OK]

Common Mistakes:

• Using default periods=1 for 2-day change
• Using axis=1 incorrectly
• Setting periods=0 which is invalid