feat(pathfinding): Add Bidirectional BFS Algorithm

[Sanan507]

Overview

Implement Bidirectional BFS in the pathfinding engine. It simultaneously expands two frontiers — one from the source node and one from the target node — meeting in the middle to halve search depth and explore significantly fewer nodes.

Implementation Details & File Reference

• Algorithm Model: Create backend/src/main/java/com/algorithmrace/visualizer/algorithms/pathfinding/BidirectionalBFSModel.java extending PathfindingModel.
  • Maintain forward queue (start) and backward queue (end), alternating step expansions.
  • Record visited cells with distinct CellState values (VISITED_FORWARD, VISITED_BACKWARD) for visual distinction.
  • Join parent chains when frontiers intersect to reconstruct the complete path.
• Factory Registration: Register "Bidirectional BFS" in PathfindingFactory.java.
• Complexity Catalog: Add entry with O(b^(d/2)) time note in ComplexityCatalog.java.
• Frontend Metadata: Add entry in frontend/src/data/algorithmMetadata.ts.

Definition of Done

• Bidirectional BFS appears in the Pathfinding Arena.
• Grid visualization displays two expanding frontiers converging in the middle.
• Metrics accurately display total cells visited and optimal path length.

Skill Level

Medium — requires dual-frontier state management and path stitching at intersection.