Interactive BFS Visualization
Graph Traversal
Watch how BFS traverses a graph, visiting all vertices at the current level before moving to the next level.
Interactive Visualization:
Step 0 of 37: Initial state
Shortest Path Finding
See how BFS finds the shortest path between two vertices in an unweighted graph.
Interactive Visualization:
Step 0 of 29: Initial state
Level Order Tree Traversal
Explore how BFS traverses a tree level by level, visiting all nodes at each level before moving to the next level.
Interactive Visualization:
Step 0 of 23: Initial state
Learning Objective
Visualize how breadth-first search works through interactive examples of graph traversal, shortest path finding, and level order tree traversal.
Visualizing Breadth-First Search
Breadth-First Search can be easier to understand when you see it in action. These visualizations will help you grasp how BFS explores graphs and trees layer by layer.
Graph Traversal
Watch how BFS traverses a graph, visiting all vertices at the current level before moving to the next level.
Shortest Path
See how BFS finds the shortest path between two vertices in an unweighted graph.
Level Order Traversal
Explore how BFS traverses a tree level by level, visiting all nodes at each level before moving to the next level.
Graph Traversal
Watch how BFS traverses a graph, visiting all vertices at the current level before moving to the next level.
Interactive Visualization:
Step 0 of 37: Initial state
How it works: Starting from a source vertex, BFS explores all its neighbors before moving to their neighbors. It uses a queue to keep track of vertices to visit next, ensuring that vertices are processed in the order they were discovered.
BFS Graph Traversal Properties
BFS graph traversal has several important properties:
- Level-by-Level Exploration: BFS explores all vertices at the current distance before moving to vertices at the next distance.
- Queue-Based: BFS uses a queue data structure to maintain the order of vertices to be explored.
- Visited Set: BFS keeps track of visited vertices to avoid cycles and redundant processing.
- Time Complexity: O(V + E) where V is the number of vertices and E is the number of edges.
- Space Complexity: O(V) for the queue and visited set.
The visualization shows how BFS explores the graph level by level, starting from the source vertex and gradually expanding outward.
Notice how the queue ensures that vertices are processed in the order they were discovered, which is essential for the level-by-level exploration property of BFS.