Sample() for random rows in Data Analysis Python - Time & Space Complexity

Time Complexity: Sample() for random rows

O(k)

Understanding Time Complexity

We want to understand how the time to pick random rows from data grows as the data gets bigger.

How does the sampling time change when the dataset size increases?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import pandas as pd

n = 1000  # example size
k = 3     # example sample size
data = pd.DataFrame({'A': range(n)})
sample_rows = data.sample(k)

This code creates a table with n rows and picks k random rows from it.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Selecting k random rows from n rows.
• How many times: The operation depends on k, the number of rows sampled.

How Execution Grows With Input

Picking k rows from n rows takes time mostly based on k, not n.

Input Size (n)	Approx. Operations
10	About k operations (e.g., 3)
100	About k operations (e.g., 3)
1000	About k operations (e.g., 3)

Pattern observation: The time grows with k, the sample size, not with n, the total data size.

Final Time Complexity

Time Complexity: O(k)

This means the time to pick random rows grows with how many rows you want, not how big the whole data is.

Common Mistake

[X] Wrong: "Sampling random rows takes longer as the whole dataset gets bigger."

[OK] Correct: The sampling method usually picks only the needed rows, so time depends on sample size, not total data size.

Interview Connect

Knowing how sampling scales helps you explain efficient data handling in real projects, showing you understand practical data work.

Self-Check

"What if we change k to be a fraction of n (like 10% of n)? How would the time complexity change then?"

Practice

1. What does the sample() function do when used on a DataFrame in pandas?

easy

A. It groups the DataFrame by a column.

B. It sorts the DataFrame by index.

C. It selects random rows from the DataFrame.

D. It removes duplicate rows from the DataFrame.

Solution

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

   The sample() function is designed to pick random rows from a DataFrame.

2. Step 2: Compare with other options

   Sorting, removing duplicates, and grouping are different operations and not related to sample().

3. Final Answer:

   It selects random rows from the DataFrame. -> Option C

4. Quick Check:

   sample() = random rows [OK]

Hint: Remember: sample() picks random rows only [OK]

Common Mistakes:

• Confusing sample() with sort()
• Thinking sample() removes duplicates
• Assuming sample() groups data

2. Which of the following is the correct syntax to get 5 random rows from a DataFrame named df?

easy

A. df.sample(n=5)

B. df.sample(frac=5)

C. df.sample(rows=5)

D. df.sample(size=5)

Solution

1. Step 1: Recall sample() parameters

   The correct parameter to specify number of rows is n, so df.sample(n=5) is correct.

2. Step 2: Check other options

   df.sample(frac=5) is invalid because frac must be between 0 and 1; rows and size are invalid parameters.

3. Final Answer:

   df.sample(n=5) -> Option A

4. Quick Check:

   Use n= to specify row count [OK]

Hint: Use n=5 to specify number of rows in sample() [OK]

Common Mistakes:

• Using invalid parameters like rows or size
• Forgetting to use n= when specifying count
• Using frac with count value instead of fraction

3. Given the DataFrame df below:

import pandas as pd
df = pd.DataFrame({'A': [10, 20, 30, 40, 50]})
sample_df = df.sample(n=2, random_state=1)

What will sample_df contain?

medium

A. Rows with index 1 and 4

B. Rows with index 2 and 4

C. Rows with index 0 and 3

D. Rows with index 0 and 1

Solution

1. Step 1: Understand random_state effect

   Setting random_state=1 makes sampling reproducible, so the same rows are picked every time.

2. Step 2: Check which rows are picked

   Running the code picks rows with index 1 and 4 (values 20 and 50).

3. Final Answer:

   Rows with index 1 and 4 -> Option A

4. Quick Check:

   random_state=1 fixes sample rows [OK]

Hint: Use random_state to get same sample every time [OK]

Common Mistakes:

• Ignoring random_state and expecting different rows
• Assuming sample picks first rows always
• Confusing index with row position

4. What is wrong with this code snippet to get 3 random rows from df?

sampled = df.sample(3, random_state=42, frac=0.5)

medium

A. The sample size must be greater than the DataFrame length.

B. You cannot use both n and frac together.

C. random_state must be an integer greater than 100.

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

Solution

1. Step 1: Understand sample() parameters

   You can specify either n (number of rows) or frac (fraction of rows), but not both at the same time.

2. Step 2: Identify the error

   Using both 3 (positional for n) and frac=0.5 causes an error.

3. Final Answer:

   You cannot use both n and frac together. -> Option B

4. Quick Check:

   Use either n or frac, not both [OK]

Hint: Use only n or frac in sample(), never both [OK]

Common Mistakes:

• Trying to use n and frac together
• Thinking random_state must be >100
• Assuming sample size can exceed DataFrame length

5. You have a DataFrame df with 1000 rows. You want to randomly select 10% of the rows but ensure the sample is the same every time you run the code. Which code snippet correctly does this?

hard

A. df.sample(n=0.1, random_state=42)

B. df.sample(n=100)

C. df.sample(frac=10, random_state=42)

D. df.sample(frac=0.1, random_state=42)

Solution

1. Step 1: Understand fraction sampling

   To select 10% of rows, use frac=0.1. Using n=100 selects fixed rows (not percentage-based) and df.sample(n=100) lacks random_state so not reproducible every time.

2. Step 2: Check random_state for reproducibility

   Setting random_state=42 ensures the sample is the same every run.

3. Step 3: Identify incorrect options

   frac=10 is invalid (fraction >1), and n=0.1 is invalid because n must be integer.

4. Final Answer:

   df.sample(frac=0.1, random_state=42) -> Option D

5. Quick Check:

   Use frac=0.1 and random_state for fixed 10% sample [OK]

Hint: Use frac=0.1 and random_state for fixed 10% sample [OK]

Common Mistakes:

• Using frac > 1 instead of fraction
• Passing float to n instead of int
• Not setting random_state for reproducibility