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)