Update breadth_first_search_2.py

[Cjkjvfnby]

Describe your change:

• Change Queue to deque. https://docs.python.org/3.11/library/queue.html?highlight=queue#module-queue

  collections.deque is an alternative implementation of unbounded queues with fast atomic append() and popleft() operations that do not require locking and also support indexing.

• Change return type from set to list. Order of traversal is important for BFS, set is not good data structure to represent it.
• Changed test to test order of returned values, old test just checks that we iterate over all nodes, even DFS traversal could pass it.

• Add an algorithm?
• Fix a bug or typo in an existing algorithm?
• Documentation change?

Checklist:

• I have read CONTRIBUTING.md.
• This pull request is all my own work -- I have not plagiarized.
• I know that pull requests will not be merged if they fail the automated tests.
• This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
• All new Python files are placed inside an existing directory.
• All filenames are in all lowercase characters with no spaces or dashes.
• All functions and variable names follow Python naming conventions.
• All function parameters and return values are annotated with Python type hints.
• All functions have doctests that pass the automated testing.
• All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
• If this pull request resolves one or more open issues then the commit message contains Fixes: #{$ISSUE_NO}.

[cclauss]

Let's keep both the existing function and the new function in the same file and let's be sure that they are both tested with the same tests and test data so visitors can compare them side-by-side.

Let's also add a timeit benchmark so visitors can understand the performance differences between the two implementations. This repo has lots of timeit benchmarks... https://github.com/TheAlgorithms/Python/search?q=timeit

[Cjkjvfnby]

keep both the existing function and the new function in the same file and let's be sure that they are both tested with the same tests and test data so visitors can compare them side-by-side.

I still need to modify the existing function, because it returns traversed elements in the unordered collection.

Both functions use exactly the same approach, just different data structure that implements a similar API.

The not thread-safe deque beats thread-safe Queue in a single-threaded environment.

breadth_first_search                finished 10000 runs in 0.22710 seconds
breadth_first_search_with_deque     finished 10000 runs in 0.01708 seconds

[cclauss]

I still need to modify the existing function, because it returns traversed elements in the unordered collection.

I do not understand this. Why should the new function force the old function to change? I would think that traversing elements in an unordered collection was the original problem.

The benchmark looks awesome. Please put the benchmark results in the comments so that the reader has a sense of with is faster and by how much.

[Cjkjvfnby]

Why should the new function force the old function to change?

BFS is an algorithm to traverse the tree in a specific order (gif from wiki). So 2 items are important here that all nodes are visited and the order in which they are visited. The problem with the existing implementation is that it returns all nodes in the collection that does not maintain order and remove duplicates (set). And the test was checking only that all nodes have been visited at least once. I consider this to be a very strange return type for the BFS and I am willing to address it.

Another problem is that implementation of the queue data structure that is used in the first function is not really efficient for such tasks. It's like hammering nails with a microscope. I'd prefer o keep only one implementation with a more suitable data structure.

[cclauss]

Maintaining the breadth-first order is vital but the wiki definition says nothing about eliminating duplicate values.

Having only a single implementation is not an option.

[Cjkjvfnby]

Maintaining the breadth-first order is vital but the wiki definition says nothing about eliminating duplicate values.

Yes, because these algorithm does not suppose to have any duplication during traversal. Using set as a return value does not allow testing this.

Having only a single implementation is not an option.

Do not worry about it, there are at least 5 files related to it in the repository.

These two function does not bring any diversity to the implementation, they are pretty much the same. I could keep both implementations, but using Queue here is a bad example.