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Performance is a crucial consideration when designing a database system. While the flexibility of our document-oriented database provides rich querying capabilities, it can also lead to performance issues if not properly managed.

Interactions with the database (like retrieval or storage of a document) can be quite costly in terms of time and resources. The time complexity of the operations can range from O(1) to O(n), depending on how efficiently we design our database.

Fetching documents based on some condition involves scanning through all documents - an operation of O(n) complexity. Iterating through every document is only feasible when we have a small amount of data. As data grows, this method becomes less and less efficient, and alternatives should be considered.

One performance improvement could be the use of indexes or hashing structures to speed up the search operations. This could potentially reduce the time complexity to O(1).

Performance in Python can be measured using the timeit module, which provides a simple way to measure the execution times of small Python codes. It has both command-line interface and callable one. The timeit function runs the setup statement once, then returns the time it takes to execute the main statement.

In our code section we use it to time the square operation over a range. By using this module you can continuously monitor the performance of your document-oriented database as you make changes and optimizations, ensuring your database stays as efficient as possible.

PYTHON
OUTPUT
:001 > Cmd/Ctrl-Enter to run, Cmd/Ctrl-/ to comment