Depth-First Search (DFS) Visualizer

Setup Graph

DFS Controls

Graph Visualization

Colors: Green = Start, Yellow = Current, Blue = Visited, Purple = On Stack

Algorithm Steps

Stack

Conclusion

How to Use

Setup: Click "Sample Graph" or "Random Graph" to create a graph
Start Node: Enter the starting node (e.g., A, B, C) and click "Start DFS"
Step Through: Click "Next Step" to see each step of the DFS execution
Run Through: Click "Run Through" to automatically execute all steps
Observe: Watch nodes change colors and the stack update as DFS progresses
Reset: Click "Reset" to start over with a new search

DFS Concept

Depth-First Search (DFS) is a graph traversal algorithm that explores as far as possible along each branch before backtracking.

How it works:

Start with a node and push it onto the stack
Mark the current node as visited
Push unvisited neighbors onto the stack
Pop from stack and repeat with the new current node
Backtrack when no unvisited neighbors exist
Continue until stack is empty

Time Complexity: O(V + E) where V = vertices, E = edges

Use Cases

Maze Solving: Finding paths through mazes by exploring all possible routes before backtracking
Topological Sorting: Ordering tasks with dependencies, crucial for project scheduling and compilation
Cycle Detection: Identifying cycles in graphs for deadlock detection in operating systems
Strongly Connected Components: Partitioning directed graphs into components for network analysis
Backtracking Algorithms: Solving constraint satisfaction problems like Sudoku and N-Queens
Parenthesis Matching: Checking balanced brackets and expressions in compilers and parsers
Tree Traversal: Pre-order, in-order, and post-order traversal of hierarchical data structures
Game Tree Search: AI decision-making in chess engines and game-playing algorithms

Real-World Example

Scenario: A maze solver uses DFS to find all possible paths from the entrance to the exit, backtracking when reaching dead ends.

Input: Maze graph with start node 'A' and goal node 'F'
Process: Explore deeply along each path before trying alternatives
Output: Path found: A → B → D → ... → F or all possible solutions

DFS is ideal for maze solving because it uses minimal memory (only stores current path) compared to BFS. When the maze is represented as a graph, DFS explores deeply into each corridor before backtracking, systematically checking all routes. This approach is memory-efficient and naturally implements backtracking, making it perfect for scenarios where finding any solution quickly is more important than finding the shortest path.

Benefits: Memory efficient, natural backtracking, suitable for deep exploration, fast for solution-finding