bidirectional_bfs

[Prathameshk2024]

1. Purpose:
   Finds the shortest path between a source and target node in an unweighted graph.

2. Approach:
   Runs two simultaneous BFS searches — one from the source and one from the target — until both meet.

3. Initialization:
   Sets up two queues, two visited lists, and two parent arrays for tracking paths.

4. Search Process:
   Expands nodes alternately from both sides and checks for a meeting node (common visited vertex).

5. Path Reconstruction:
   Once the meeting node is found, it traces back to form the complete shortest path from source to target.

Output:
Returns the path, distance (number of edges), and a flag found = TRUE if a path exists.

Complexity:

Time: O(b^(d/2)) → faster than normal BFS

Space: O(V)

[Copilot]

Pull Request Overview

This PR implements a bidirectional breadth-first search algorithm for finding shortest paths in unweighted graphs. The algorithm runs two simultaneous BFS searches from source and target nodes until they meet, offering improved time complexity over standard BFS.

• Implements bidirectional BFS with O(b^(d/2)) time complexity
• Includes path reconstruction from meeting node to both endpoints
• Provides comprehensive documentation and example usage

[siriak]

Looks good, thanks!