Multiple conditions with & and | in Pandas - Time & Space Complexity

Time Complexity: Multiple conditions with & and |

O(n)

Understanding Time Complexity

We want to understand how the time needed to filter data with multiple conditions changes as the data grows.

How does combining conditions with & and | affect the work done?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import pandas as pd

n = 100  # example size

df = pd.DataFrame({
    'A': range(n),
    'B': range(n, 0, -1),
    'C': ['x', 'y'] * (n // 2)
})

filtered = df[(df['A'] > 10) & ((df['B'] < 50) | (df['C'] == 'x'))]

This code filters rows in a DataFrame using multiple conditions combined with & (and) and | (or).

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Checking each row against the conditions.
• How many times: Once per row, so n times where n is the number of rows.

How Execution Grows With Input

Each row is checked once for all conditions combined. As the number of rows grows, the total checks grow proportionally.

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

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

Final Time Complexity

Time Complexity: O(n)

This means the time to filter grows in a straight line with the number of rows.

Common Mistake

[X] Wrong: "Using multiple conditions with & and | makes the filtering much slower, like multiplying the time by the number of conditions."

[OK] Correct: The conditions are checked together for each row in one pass, so time grows with rows, not conditions count.

Interview Connect

Understanding how filtering with multiple conditions scales helps you explain data processing efficiency clearly and confidently.

Self-Check

What if we added a new condition that requires scanning another column? How would the time complexity change?

Practice

1. Which operator should you use in pandas to select rows where age is greater than 30 and salary is above 50000?

easy

A. Use and to combine the two conditions without parentheses.

B. Use | to combine the two conditions without parentheses.

C. Use & to combine the two conditions with parentheses around each.

D. Use or to combine the two conditions with parentheses.

Solution

1. Step 1: Understand the condition type

   We want rows where both conditions are true, so this is an AND condition.

2. Step 2: Choose the correct pandas operator

   In pandas, & is used for AND between conditions, and each condition must be in parentheses.

3. Final Answer:

   Use & to combine the two conditions with parentheses around each. -> Option C

4. Quick Check:

   AND condition = & with parentheses [OK]

Hint: Use & with parentheses for AND conditions in pandas [OK]

Common Mistakes:

• Using 'and' instead of & causes errors.
• Not wrapping each condition in parentheses.
• Using | instead of & for AND conditions.

2. Which of the following is the correct syntax to filter a DataFrame df for rows where df['A'] > 10 or df['B'] < 5?

easy

A. df[(df['A'] > 10) | (df['B'] < 5)]

B. df[(df['A'] > 10) & (df['B'] < 5)]

C. df[df['A'] > 10 | df['B'] < 5]

D. df[df['A'] > 10 or df['B'] < 5]

Solution

1. Step 1: Identify the condition type

   The question asks for rows where either condition is true, so this is an OR condition.

2. Step 2: Use correct pandas syntax for OR

   In pandas, | is used for OR, and each condition must be wrapped in parentheses inside the DataFrame filter.

3. Final Answer:

   df[(df['A'] > 10) | (df['B'] < 5)] -> Option A

4. Quick Check:

   OR condition = | with parentheses [OK]

Hint: Use | with parentheses for OR conditions in pandas [OK]

Common Mistakes:

• Using & instead of | for OR conditions.
• Not wrapping conditions in parentheses.
• Using Python 'or' instead of | causes errors.

3. Given the DataFrame df below:

import pandas as pd
df = pd.DataFrame({'age': [25, 40, 35, 28], 'salary': [40000, 60000, 50000, 45000]})
filtered = df[(df['age'] > 30) & (df['salary'] >= 50000)]
print(filtered)

What will be the output?

medium

A. Rows with age > 30 or salary >= 50000: rows 1, 2, and 3

B. Rows with age > 30 and salary >= 50000: rows 1 and 2

C. Rows with age > 30 and salary >= 50000: row 1 only

D. Empty DataFrame

Solution

1. Step 1: Check each row against conditions

   Row 0: age=25 (no), salary=40000 (no)
   Row 1: age=40 (yes), salary=60000 (yes)
   Row 2: age=35 (yes), salary=50000 (yes)
   Row 3: age=28 (no), salary=45000 (no)

2. Step 2: Select rows where both conditions are true

   Rows 1 and 2 satisfy both conditions.

3. Final Answer:

   Rows with age > 30 and salary >= 50000: rows 1 and 2 -> Option B

4. Quick Check:

   Both conditions true for rows 1 and 2 [OK]

Hint: Check each condition row-wise, then combine with & [OK]

Common Mistakes:

• Confusing & with | and selecting wrong rows.
• Ignoring parentheses causing syntax errors.
• Misreading >= as > or vice versa.

4. What is wrong with this pandas filter code?

df[(df['score'] > 80) & df['age'] < 30]

Choose the best fix.

medium

A. Use 'and' instead of &.

B. Replace & with | to fix the syntax.

C. Remove parentheses around the first condition.

D. Add parentheses around the second condition: df[(df['score'] > 80) & (df['age'] < 30)]

Solution

1. Step 1: Identify the syntax error

   The second condition df['age'] < 30 is not wrapped in parentheses, which is required when using &.

2. Step 2: Correct the syntax by adding parentheses

   Wrap the second condition in parentheses to fix the error: df[(df['score'] > 80) & (df['age'] < 30)]

3. Final Answer:

   Add parentheses around the second condition: df[(df['score'] > 80) & (df['age'] < 30)] -> Option D

4. Quick Check:

   Each condition must be in parentheses with & [OK]

Hint: Wrap each condition in parentheses when using & or | [OK]

Common Mistakes:

• Not using parentheses around all conditions.
• Using 'and' instead of &.
• Changing & to | without reason.

5. You have a DataFrame df with columns temperature and humidity. You want to select rows where temperature is between 20 and 30 inclusive, or humidity is below 40. Which of the following code snippets correctly applies these conditions?

hard

A. df[((df['temperature'] >= 20) & (df['temperature'] <= 30)) | (df['humidity'] < 40)]

B. df[(df['temperature'] >= 20) & df['temperature'] <= 30 | (df['humidity'] < 40)]

C. df[(df['temperature'] >= 20) | (df['temperature'] <= 30) & (df['humidity'] < 40)]

D. df[(df['temperature'] >= 20) & (df['humidity'] < 40) | (df['temperature'] <= 30)]

Solution

1. Step 1: Understand the condition logic

   We want rows where temperature is between 20 and 30 (both conditions combined with AND), OR humidity is below 40.

2. Step 2: Apply correct operator precedence with parentheses

   Use parentheses to group the temperature range conditions with & and then combine with | for humidity condition.

3. Final Answer:

   df[((df['temperature'] >= 20) & (df['temperature'] <= 30)) | (df['humidity'] < 40)] -> Option A

4. Quick Check:

   Group AND conditions, then OR with other condition [OK]

Hint: Group AND conditions in parentheses before OR [OK]

Common Mistakes:

• Missing parentheses causing wrong logic.
• Mixing & and | without grouping.
• Using | inside AND group incorrectly.