Add bidirectional search algorithm implementation

[prajwalc22]

Pull Request Description for Bidirectional Search Algorithm

What I've Added

I've implemented a Bidirectional Search algorithm in Python that efficiently finds the shortest path between two nodes in a graph.

Bidirectional Search Algorithm

The algorithm works by simultaneously searching forward from the source node and backward from the target node, meeting in the middle. This approach significantly reduces the search space compared to traditional unidirectional searches, especially in large graphs.

Key features of this implementation:

1. Uses breadth-first search in both directions to ensure optimal path finding
2. Includes proper handling for edge cases (e.g., disconnected graphs, identical start/goal nodes)
3. Provides a utility function to construct the complete path once an intersection is found
4. Contains comprehensive type hints for better code maintainability
5. Includes detailed documentation and test cases demonstrating the algorithm's usage

Complexity:

• Time Complexity: O(b^(d/2)) where b is the branching factor and d is the depth
• Space Complexity: O(b^(d/2))

This is significantly better than the O(b^d) complexity of a unidirectional approach.

Why This Contribution Is Valuable

This algorithm fills a gap in the current graph algorithm collection in the repository. Bidirectional search is an important technique in pathfinding with applications in:

1. Navigation systems
2. Puzzle solving
3. Network routing
4. Social network analysis

The implementation follows the repository's code style and documentation standards, making it consistent with existing algorithms.

Test Cases

The implementation includes several test cases demonstrating:

• Finding a path in a connected graph
• Handling the case where start and goal are the same node
• Correctly returning None when no path exists

I've manually verified all test cases to ensure correctness.

• Add an algorithm?
• Fix a bug or typo in an existing algorithm?
• Add or change doctests?
• 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 include at least one URL that points to Wikipedia or another similar explanation.
• If this pull request resolves one or more open issues then the description above includes the issue number(s) with a closing keyword: "Fixes #ISSUE-NUMBER".

[algorithms-keeper]

Click here to look at the relevant links ⬇️

🔗 Relevant Links

Repository:

• Contributing guidelines
• Project Euler solution guidelines

Python:

• Formatted string literals (f-strings)
• Type hints
• doctest
• unittest
• pytest

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