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?