sort_values() by multiple columns in Pandas - Time & Space Complexity

Time Complexity: sort_values() by multiple columns

O(n log n)

Understanding Time Complexity

We want to understand how the time needed to sort data changes as the data grows.

Specifically, how sorting by multiple columns affects the work done.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import pandas as pd

df = pd.DataFrame({
    'A': [3, 1, 2, 1],
    'B': [4, 3, 2, 1],
    'C': [10, 20, 30, 40]
})

sorted_df = df.sort_values(by=['A', 'B'])

This code sorts the DataFrame first by column 'A', then by column 'B' to break ties.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Comparing and rearranging rows based on column values.
• How many times: The sorting algorithm compares elements multiple times, roughly proportional to the number of rows times the logarithm of the number of rows.

How Execution Grows With Input

As the number of rows grows, the sorting work grows faster than just the number of rows.

Input Size (n)	Approx. Operations
10	About 30 to 40 comparisons
100	About 600 to 700 comparisons
1000	About 10,000 to 12,000 comparisons

Pattern observation: The number of operations grows a bit faster than the number of rows, roughly like n times log n.

Final Time Complexity

Time Complexity: O(n log n)

This means sorting takes more time as data grows, but not as fast as checking every pair; it grows in a balanced way.

Common Mistake

[X] Wrong: "Sorting by multiple columns multiplies the time by the number of columns."

[OK] Correct: Sorting still mainly depends on the number of rows; adding columns to sort by only changes how comparisons are done, not the overall growth rate.

Interview Connect

Understanding how sorting scales helps you explain data processing steps clearly and shows you know how data size affects performance.

Self-Check

"What if we sorted by only one column instead of multiple? How would the time complexity change?"

Practice

1.

What does the sort_values() function do when used on a pandas DataFrame?

easy

A. It sorts the DataFrame rows based on the values in one or more columns.

B. It filters rows that match a condition.

C. It changes the data types of columns.

D. It adds new columns to the DataFrame.

Solution

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

   This function organizes the rows of a DataFrame by sorting them according to the values in specified columns.

2. Step 2: Compare with other DataFrame operations

   Filtering selects rows, changing data types modifies columns, and adding columns is unrelated to sorting.

3. Final Answer:

   It sorts the DataFrame rows based on the values in one or more columns. -> Option A

4. Quick Check:

   Sorting = Organizing rows by column values [OK]

Hint: Remember: sort_values() arranges rows by column values [OK]

Common Mistakes:

• Confusing sorting with filtering rows
• Thinking it changes data types
• Assuming it adds or removes columns

2.

Which of the following is the correct syntax to sort a DataFrame df by columns 'A' ascending and 'B' descending?

df.sort_values(??? )

easy

A. columns=['A', 'B'], ascending=[False, True]

B. by=['A', 'B'], ascending=[True, False]

C. by=['A', 'B'], ascending=True

D. sort=['A', 'B'], order=[True, False]

Solution

1. Step 1: Identify correct parameter names

   The method uses by to specify columns and ascending to specify order per column.

2. Step 2: Match order for each column

   To sort 'A' ascending and 'B' descending, use ascending=[True, False].

3. Final Answer:

   by=['A', 'B'], ascending=[True, False] -> Option B

4. Quick Check:

   Correct parameters = by=['A', 'B'], ascending=[True, False] [OK]

Hint: Use by=columns and ascending=list of booleans [OK]

Common Mistakes:

• Using wrong parameter names like columns or sort
• Passing a single boolean for multiple columns
• Mixing ascending order values

3.

Given the DataFrame:

import pandas as pd
df = pd.DataFrame({
  'Name': ['Anna', 'Bob', 'Anna', 'Bob'],
  'Score': [90, 92, 85, 80]
})

What is the result of df.sort_values(by=['Name', 'Score'], ascending=[True, False])?

medium

A. Rows sorted by Name ascending, then Score descending: Anna(90), Anna(85), Bob(92), Bob(80)

B. Rows sorted by Name descending, then Score ascending: Bob(80), Bob(92), Anna(85), Anna(90)

C. Rows sorted by Score ascending only: Bob(80), Anna(85), Anna(90), Bob(92)

D. Rows sorted by Score descending only: Bob(92), Anna(90), Anna(85), Bob(80)

Solution

1. Step 1: Sort by 'Name' ascending

   Names order: Anna, Anna, Bob, Bob.

2. Step 2: Within each Name, sort 'Score' descending

   For Anna: 90 then 85; for Bob: 92 then 80.

3. Final Answer:

   Rows sorted by Name ascending, then Score descending: Anna(90), Anna(85), Bob(92), Bob(80) -> Option A

4. Quick Check:

   Sort by Name ↑, Score ↓ = Rows sorted by Name ascending, then Score descending: Anna(90), Anna(85), Bob(92), Bob(80) [OK]

Hint: Sort first column ascending, second descending as list [OK]

Common Mistakes:

• Mixing ascending and descending order
• Sorting only by one column
• Confusing order of sorting columns

4.

What is wrong with this code snippet?

df.sort_values(by=['A', 'B'], ascending=True)

Assuming df has columns 'A' and 'B'.

medium

A. The method sort_values does not accept the ascending parameter.

B. The by parameter should be a string, not a list.

C. The ascending parameter should be a list when sorting by multiple columns.

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

Solution

1. Step 1: Recall sort_values() parameters

   by accepts list of columns, ascending accepts bool (applies to all) or list of bools.

2. Step 2: Validate the code

   The code uses ascending=True, which correctly sorts both columns ascending. No errors.

3. Final Answer:

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

4. Quick Check:

   ascending=True valid for multi-column sort [OK]

Hint: ascending=True sorts all columns ascending; use list for mixed orders [OK]

Common Mistakes:

• Believing ascending must be a list for multiple columns
• Using string instead of list for 'by' parameter
• Assuming sort_values lacks ascending parameter

5.

You have a DataFrame df with columns 'City', 'Temperature', and 'Humidity'. You want to sort the data so that cities are in alphabetical order, but within each city, rows with higher temperature come first, and if temperatures are equal, rows with lower humidity come first.

Which sort_values() call achieves this?

hard

A. df.sort_values(by=['City', 'Temperature', 'Humidity'], ascending=[False, True, False])

B. df.sort_values(by=['City', 'Humidity', 'Temperature'], ascending=[True, True, False])

C. df.sort_values(by=['City', 'Temperature', 'Humidity'], ascending=[True, False, True])

D. df.sort_values(by=['Temperature', 'City', 'Humidity'], ascending=[False, True, True])

Solution

1. Step 1: Sort 'City' alphabetically ascending

   Set ascending=True for 'City' to get alphabetical order.

2. Step 2: Sort 'Temperature' descending within each city

   Use ascending=False for 'Temperature' to have higher temperatures first.

3. Step 3: Sort 'Humidity' ascending when temperatures tie

   Use ascending=True for 'Humidity' to get lower humidity first.

4. Final Answer:

   df.sort_values(by=['City', 'Temperature', 'Humidity'], ascending=[True, False, True]) -> Option C

5. Quick Check:

   City ↑, Temp ↓, Humidity ↑ = df.sort_values(by=['City', 'Temperature', 'Humidity'], ascending=[True, False, True]) [OK]

Hint: Match ascending list to desired order per column [OK]

Common Mistakes:

• Mixing order of columns in 'by' list
• Using wrong ascending booleans
• Sorting humidity before temperature