Matrix BFS Visualizer - Breadth-First Search Exploration

Grid Pathfinding Algorithms: how it works

Visualize how various algorithms search for a path from a start node (green) to a target node (red) on a 2D grid filled with obstacles.

1. Breadth-First Search (BFS)

   Explores the grid level-by-level, radiating outwards from the source. Guarantees the shortest path on an unweighted grid.

2. Depth-First Search (DFS)

   Explores as far as possible along each branch before backtracking. Does not guarantee the shortest path.

3. Editing the Grid

   Click or drag over cells to toggle walls (obstacles). The algorithm will avoid these walls when searching for the target.

Complexity

Best-case time

O(1)

Average time

O(V + E)

Worst-case time

O(V + E)

Space

O(V)

V is the number of cells (rows × cols), and E is the number of connections between cells (at most 4 for each). BFS is ideal for unweighted grids, while DFS is rarely used for shortest paths but great for exploring entire mazes.