apply() on rows (axis=1) in Pandas - Time & Space Complexity

Time Complexity: apply() on rows (axis=1)

O(n)

Understanding Time Complexity

We want to understand how the time to run apply() on rows grows as the data gets bigger.

Specifically, how does the number of rows affect the work done?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import pandas as pd

def sum_row(row):
    return row.sum()

# Create a DataFrame with n rows and 3 columns
n = 1000
df = pd.DataFrame({
    'A': range(n),
    'B': range(n, 2*n),
    'C': range(2*n, 3*n)
})

result = df.apply(sum_row, axis=1)

This code sums each row of the DataFrame using apply() with axis=1.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The function sum_row is called once for each row.
• How many times: It runs exactly n times, once per row.
• Inside each call, it sums 3 values (columns), which is a small fixed amount.

How Execution Grows With Input

As the number of rows grows, the total work grows roughly the same amount.

Input Size (n)	Approx. Operations
10	About 10 sums of 3 numbers each
100	About 100 sums of 3 numbers each
1000	About 1000 sums of 3 numbers each

Pattern observation: The work grows directly with the number of rows.

Final Time Complexity

Time Complexity: O(n)

This means the time to run grows linearly as the number of rows increases.

Common Mistake

[X] Wrong: "Since apply() works on rows and columns, it must be very slow and grow like n squared."

[OK] Correct: Here, apply() runs the function once per row only, so the growth depends mostly on the number of rows, not columns. The columns are fixed and small, so they don't cause squared growth.

Interview Connect

Understanding how apply() scales helps you explain your code choices clearly and shows you know how data size affects performance.

Self-Check

"What if the function inside apply() also loops over all columns instead of just summing? How would the time complexity change?"

Practice

1.

What does apply() with axis=1 do in a pandas DataFrame?

easy

A. It applies a function to each column of the DataFrame.

B. It applies a function to each row of the DataFrame.

C. It applies a function to the entire DataFrame at once.

D. It applies a function only to the first row.

Solution

1. Step 1: Understand the axis parameter

   In pandas, axis=1 means the function is applied across columns for each row.

2. Step 2: Apply function on rows

   Using apply() with axis=1 runs the function on each row individually.

3. Final Answer:

   It applies a function to each row of the DataFrame. -> Option B

4. Quick Check:

   apply(axis=1) = row-wise function [OK]

Hint: Remember axis=1 means row-wise operation [OK]

Common Mistakes:

• Confusing axis=1 with column-wise operation
• Thinking apply(axis=1) applies to the whole DataFrame at once
• Assuming it only applies to the first row

2.

Which of the following is the correct syntax to apply a function f to each row of a DataFrame df?

def f(row):
    return row['A'] + row['B']

easy

A. df.apply(f, axis=1)

B. df.apply(f, axis=0)

C. df.apply(f)

D. df.apply(f, axis='rows')

Solution

1. Step 1: Identify axis for row-wise apply

   Row-wise apply requires axis=1.

2. Step 2: Check syntax correctness

   df.apply(f, axis=1) uses axis=1, which is correct. The other options use incorrect axis parameters.

3. Final Answer:

   df.apply(f, axis=1) -> Option A

4. Quick Check:

   Use axis=1 for rows [OK]

Hint: Use axis=1 to apply function row-wise [OK]

Common Mistakes:

• Using axis=0 applies function column-wise
• Omitting axis defaults to axis=0
• Using incorrect axis string values

3.

What is the output of the following code?

import pandas as pd
df = pd.DataFrame({'A': [1, 2], 'B': [3, 4]})
def sum_row(row):
    return row['A'] + row['B']
df['Sum'] = df.apply(sum_row, axis=1)
print(df)

medium

A. Error: KeyError

B. A B Sum
0 1 3 3
1 2 4 4

C. A B Sum
0 1 3 1
1 2 4 2

D. A B Sum
0 1 3 4
1 2 4 6

Solution

1. Step 1: Understand the function sum_row

   The function adds values from columns 'A' and 'B' for each row.

2. Step 2: Apply function row-wise and add new column

   Applying with axis=1 sums each row's 'A' and 'B'. For row 0: 1+3=4, row 1: 2+4=6.

3. Final Answer:

   A B Sum 0 1 3 4 1 2 4 6 -> Option D

4. Quick Check:

   Row sums = 4, 6 [OK]

Hint: Sum columns per row with apply(axis=1) [OK]

Common Mistakes:

• Using axis=0 sums columns, not rows
• Forgetting to assign result back to DataFrame
• Mixing up row and column indices

4.

Identify the error in the following code snippet:

import pandas as pd
df = pd.DataFrame({'X': [10, 20], 'Y': [30, 40]})
def multiply(row):
    return row['x'] * row['Y']
df['Product'] = df.apply(multiply, axis=1)
print(df)

medium

A. KeyError because 'x' column does not exist (case sensitive).

B. TypeError due to wrong axis parameter.

C. No error, output is correct.

D. SyntaxError in function definition.

Solution

1. Step 1: Check column names in DataFrame

   Columns are 'X' and 'Y' with uppercase letters.

2. Step 2: Check function usage of column names

   Function uses 'x' (lowercase), which does not match 'X' (uppercase), causing KeyError.

3. Final Answer:

   KeyError because 'x' column does not exist (case sensitive). -> Option A

4. Quick Check:

   Column names are case sensitive [OK]

Hint: Check exact column names and case sensitivity [OK]

Common Mistakes:

• Ignoring case sensitivity in column names
• Using wrong axis parameter
• Assuming no error without testing

5.

You have a DataFrame df with columns 'Name', 'Math', and 'English'. You want to create a new column 'Result' that shows 'Pass' if the average of 'Math' and 'English' is 50 or more, otherwise 'Fail'. Which code correctly uses apply() with axis=1 to do this?

hard

A. df['Result'] = df.apply(lambda row: 'Pass' if row['Math'] + row['English'] >= 50 else 'Fail', axis=1)

B. df['Result'] = df.apply(lambda col: 'Pass' if (col['Math'] + col['English']) / 2 >= 50 else 'Fail', axis=0)

C. df['Result'] = df.apply(lambda row: 'Pass' if (row['Math'] + row['English']) / 2 >= 50 else 'Fail', axis=1)

D. df['Result'] = df.apply(lambda row: 'Pass' if row['Math'] >= 50 and row['English'] >= 50 else 'Fail')

Solution

1. Step 1: Understand the condition for passing

   Pass if average of 'Math' and 'English' >= 50, else Fail.

2. Step 2: Check each option's logic and axis

   df['Result'] = df.apply(lambda row: 'Pass' if (row['Math'] + row['English']) / 2 >= 50 else 'Fail', axis=1) correctly uses axis=1 for row-wise apply and calculates average properly. df['Result'] = df.apply(lambda col: 'Pass' if (col['Math'] + col['English']) / 2 >= 50 else 'Fail', axis=0) uses axis=0 (column-wise), which is wrong. df['Result'] = df.apply(lambda row: 'Pass' if row['Math'] >= 50 and row['English'] >= 50 else 'Fail') misses axis=1 and uses wrong condition. df['Result'] = df.apply(lambda row: 'Pass' if row['Math'] + row['English'] >= 50 else 'Fail', axis=1) checks sum >= 50, which is incorrect for average >= 50.

3. Final Answer:

   df['Result'] = df.apply(lambda row: 'Pass' if (row['Math'] + row['English']) / 2 >= 50 else 'Fail', axis=1) -> Option C

4. Quick Check:

   Use axis=1 and correct average condition [OK]

Hint: Use axis=1 and check average inside lambda [OK]

Common Mistakes:

• Using axis=0 applies function column-wise
• Forgetting to divide sum by 2 for average
• Using wrong logical conditions