nunique() for cardinality in Data Analysis Python - Time & Space Complexity

Time Complexity: nunique() for cardinality

O(n)

Understanding Time Complexity

We want to understand how the time to count unique values grows as the data size increases.

How does the work change when we have more rows to check for unique items?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import pandas as pd

data = pd.Series([1, 2, 2, 3, 4, 4, 4, 5])
unique_count = data.nunique()
print(unique_count)

This code counts how many different values are in the data series.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Checking each element to see if it is unique.
• How many times: Once for each item in the data series.

How Execution Grows With Input

As the number of items grows, the work grows roughly in the same way.

Input Size (n)	Approx. Operations
10	About 10 checks
100	About 100 checks
1000	About 1000 checks

Pattern observation: The number of operations grows directly with the number of items.

Final Time Complexity

Time Complexity: O(n)

This means the time to count unique values grows linearly with the number of items.

Common Mistake

[X] Wrong: "Counting unique values is instant no matter how big the data is."

[OK] Correct: The function must look at each item at least once, so bigger data means more work.

Interview Connect

Understanding how counting unique items scales helps you explain data processing speed clearly and confidently.

Self-Check

"What if we used a sorted list before counting unique values? How would the time complexity change?"

Practice

1. What does the nunique() function do when applied to a pandas DataFrame column?

easy

A. Finds the maximum value in that column

B. Calculates the sum of all values in that column

C. Returns the total number of rows in the DataFrame

D. Counts the number of unique values in that column

Solution

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

   The nunique() function counts how many distinct or unique values exist in a column.

2. Step 2: Compare with other functions

   Unlike sum or max, nunique() focuses on counting unique entries, not numerical calculations.

3. Final Answer:

   Counts the number of unique values in that column -> Option D

4. Quick Check:

   nunique() = unique count [OK]

Hint: Remember: nunique() counts unique items only [OK]

Common Mistakes:

• Confusing nunique() with count()
• Thinking it sums values instead of counting unique ones
• Assuming it returns total rows instead of unique values

2. Which of the following is the correct syntax to count unique values in the 'Age' column of a pandas DataFrame named df?

easy

A. df.nunique('Age')

B. df['Age'].nunique()

C. df.nunique['Age']

D. df.nunique.Age()

Solution

1. Step 1: Access the column correctly

   To apply nunique() on a column, first select the column using df['Age'].

2. Step 2: Apply the nunique() method

   Then call nunique() as a method: df['Age'].nunique().

3. Final Answer:

   df['Age'].nunique() -> Option B

4. Quick Check:

   Correct syntax = df['column'].nunique() [OK]

Hint: Use bracket notation for columns before nunique() [OK]

Common Mistakes:

• Passing column name as argument to nunique()
• Using dot notation with parentheses on column name
• Trying to index nunique like a dictionary

3. Given the DataFrame below, what is the output of df['City'].nunique()?

import pandas as pd
data = {'City': ['Paris', 'London', 'Paris', 'Berlin', 'London', 'Rome']}
df = pd.DataFrame(data)

medium

A. 4

B. 3

C. 5

D. 6

Solution

1. Step 1: Identify unique cities in the list

   The cities are: 'Paris', 'London', 'Paris', 'Berlin', 'London', 'Rome'. Unique cities are 'Paris', 'London', 'Berlin', and 'Rome'.

2. Step 2: Count unique cities

   There are 4 unique cities in total.

3. Final Answer:

   4 -> Option A

4. Quick Check:

   Unique cities count = 4 [OK]

Hint: Count distinct values ignoring duplicates [OK]

Common Mistakes:

• Counting all entries instead of unique ones
• Miscounting duplicates as unique
• Confusing number of rows with unique count

4. What is wrong with this code snippet if we want to count unique values in the 'Product' column?

import pandas as pd
data = {'Product': ['A', 'B', 'A', 'C']}
df = pd.DataFrame(data)
unique_count = df.nunique('Product')

medium

A. The nunique() method does not take column names as arguments

B. The DataFrame is missing the 'Product' column

C. The nunique() method should be called without parentheses

D. The DataFrame constructor syntax is incorrect

Solution

1. Step 1: Check how nunique() works on DataFrames

   When called on a DataFrame, nunique() counts unique values for each column and does not accept column names as arguments.

2. Step 2: Correct way to count unique values in one column

   To count unique values in 'Product', select the column first: df['Product'].nunique().

3. Final Answer:

   The nunique() method does not take column names as arguments -> Option A

4. Quick Check:

   nunique() on DataFrame has no column argument [OK]

Hint: Call nunique() on column, not DataFrame with argument [OK]

Common Mistakes:

• Passing column name as argument to nunique() on DataFrame
• Calling nunique without parentheses
• Misunderstanding DataFrame constructor syntax

5. You have a DataFrame df with a column 'Score' containing some missing values (NaN). How do you count unique scores including the missing values as a unique category?

hard

A. df['Score'].count()

B. df['Score'].nunique(dropna=True)

C. df['Score'].nunique(dropna=False)

D. df['Score'].unique()

Solution

1. Step 1: Understand dropna parameter in nunique()

   By default, nunique() ignores missing values (NaN). Setting dropna=False counts NaN as a unique value.

2. Step 2: Apply nunique() with dropna=False

   Use df['Score'].nunique(dropna=False) to include NaN in the unique count.

3. Final Answer:

   df['Score'].nunique(dropna=False) -> Option C

4. Quick Check:

   Include NaN by setting dropna=False [OK]

Hint: Use dropna=False to count NaN as unique [OK]

Common Mistakes:

• Ignoring dropna and missing NaN count
• Using count() which excludes NaN
• Using unique() without counting length