Package structure and usage in Python - Time & Space Complexity

Time Complexity: Package structure and usage

O(n)

Understanding Time Complexity

When working with packages in Python, it's important to know how the structure affects the time it takes to import and use code.

We want to understand how the time to load and access parts of a package changes as the package grows.

Scenario Under Consideration

Analyze the time complexity of importing modules from a package with multiple submodules.

# package/__init__.py
from .module1 import func1
from .module2 import func2

# module1.py
def func1():
    return "Hello from module1"

# module2.py
def func2():
    return "Hello from module2"

# main.py
from package import func1, func2
print(func1())
print(func2())
    

This code shows importing functions from different modules inside a package and using them.

Identify Repeating Operations

Look at what happens when importing the package:

• Primary operation: Importing each module listed in the package's __init__.py
• How many times: Once per module during the import process

How Execution Grows With Input

As the number of modules in the package increases, the import time grows roughly in proportion.

Number of Modules (n)	Approx. Import Operations
10	10 module imports
100	100 module imports
1000	1000 module imports

Pattern observation: Import time grows linearly as more modules are imported.

Final Time Complexity

Time Complexity: O(n)

This means the time to import grows directly with the number of modules you import from the package.

Common Mistake

[X] Wrong: "Importing a package always takes the same time, no matter how many modules it has."

[OK] Correct: Each module imported runs its code once, so more modules mean more work and longer import time.

Interview Connect

Understanding how package structure affects import time helps you write cleaner, faster-loading code and shows you think about efficiency in real projects.

Self-Check

"What if the package uses lazy imports inside functions instead of importing all modules at once? How would the time complexity change?"