Pathfinding Algorithm Visualizer
Visualize how different pathfinding algorithms find routes through a maze.
Grid Visualization
Dijkstra's Algorithm
A weighted algorithm that guarantees the shortest path. It works by visiting nodes in order of increasing distance from the start node.
Time Complexity
O((V + E) log V)
Space Complexity
O(V)
Shortest Path
Guaranteed
Controls
How Dijkstra's Algorithm Works
Dijkstra's algorithm finds the shortest path in a weighted graph by greedily selecting the node with the smallest known distance.
- Assign distance = 0 to start node and infinity to all other nodes
- Visit the unvisited node with the smallest distance
- For each neighbor, calculate distance through current node
- If new distance is smaller, update the neighbor's distance
- Mark current node as visited
- Repeat until end node is reached or all reachable nodes are visited
Algorithm Comparison
| Algorithm | Weighted | Speed | Shortest | Use Case |
|---|---|---|---|---|
| Dijkstra's | Yes | Moderate | Yes | GPS, Network Routing |
| A* Search | Yes | Fast | Yes | Games, Robotics |
| BFS | No | Moderate | Yes* | Web Crawling, Social Networks |
| DFS | No | Fast | No | Maze Generation, Cycle Detection |
| Flood Fill | No | Very Fast | No | Image Filling, Bucket Tool |
| Greedy Best-First | No | Very Fast | No | Real-time games, Approximations |
Real-World Applications of Pathfinding Algorithms
Navigation Systems
GPS and map applications use Dijkstra's and A* algorithms to find the shortest or fastest routes between locations, considering factors like distance, traffic, and road conditions.
Robotics
Autonomous robots use A* and other pathfinding algorithms to navigate physical spaces, avoid obstacles, and reach targets efficiently in warehouses, hospitals, and factories.
Video Games
Game developers implement pathfinding to control how NPCs navigate game worlds. A* is particularly popular for its efficiency and flexibility in dynamic environments.
Network Routing
Internet traffic is routed using algorithms similar to Dijkstra's to find efficient paths through the network, considering bandwidth, latency, and network congestion.
Logistics & Delivery
Shipping companies optimize delivery routes using variations of A* and other algorithms to minimize time, fuel consumption, and costs while delivering packages.
Web Crawlers
Search engines use BFS to discover and index web pages by following links from page to page, efficiently exploring the web graph structure.
Graphics Software
Flood Fill is the algorithm behind the "paint bucket" or "fill" tool in image editing applications like Photoshop to color contiguous regions of similar colors.
Tips for Understanding Pathfinding
Visualize Node Expansion
Pay attention to how each algorithm expands nodes differently. Dijkstra's and BFS expand in all directions, while A* focuses its search toward the goal using its heuristic. DFS follows deep paths first.
Create Different Maze Types
Try both random mazes and recursive division mazes. The recursive division creates more corridor-like structures, while random mazes create more open spaces with scattered obstacles.
Test Edge Cases
Place start and end points on opposite sides with walls between them. See how each algorithm handles when no path exists, or when the shortest path requires a very roundabout route.
Speed vs. Accuracy Tradeoff
Notice how A* typically visits fewer nodes than Dijkstra's yet still finds the optimal path. DFS explores quickly but may find a very sub-optimal path. Each algorithm has its strengths and weaknesses.
Coming Next
Stay tuned for more algorithm visualizations, including graph algorithms, tree traversal, and dynamic programming visualizations!
Back to Algorithm Visualizers