[Shubham-Padkonde]

Describe your change

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

Initialize the visited set with the start node itself. set(start) splits string node names into characters and raises TypeError for integer node names.

For example, bfs_shortest_path_distance({'AB': ['A'], 'A': ['C'], 'C': []}, 'AB', 'C') returns -1 before this fix and 2 afterward. The edge from integer node 0 to 1 now returns 1 instead of raising.

Validation on free-threaded Python 3.15: all 11 existing BFS doctest items pass. An external exhaustive check compares all source/target pairs in every directed four-node graph against Floyd-Warshall, with string, integer and tuple labels: 196,608 comparisons pass. Existing doctests remain unchanged, per the contribution guidance.

AI-assisted contribution.

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.
• 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.

[rahul05ranjan]

Nice catch — set(start) iterates the string, so it only worked while every node name was a single character. Confirmed the failure with a two-node graph: bfs_shortest_path_distance({"AB": ["B"], "B": []}, "AB", "B") returns -1 on the old code (the neighbour "B" is already in set("AB"), so it's never enqueued) and 1 with your change.

There's a second effect worth mentioning since it's the same root cause: start itself is not in visited ("G1" in set("G1") is False), so with the old code any edge pointing back to the start re-enqueues it and lets dist[start] be overwritten from 0. Your {start} fixes that too, because the if adjacent not in visited guard now covers the start node.

Nit: since the function is only correct when node names are hashable singletons (which {start} now guarantees), the docstring's -1 if no path exists contract is what the repro above exercises — might be worth adding one doctest with a multi-character node name, e.g. the {"AB": ["B"]} case, so this regression can't come back silently.