How does depth-first search work in graph traversal?

Can you explain how depth-first search works in graph traversal?

Depth-first search (DFS) is an algorithm for traversing or searching tree or graph data structures. It starts at the root (or an arbitrary node) and explores as far as possible along each branch before backtracking.

How can I visualize the depth-first search process?

You can visualize DFS using a stack. Imagine starting at a node, pushing it onto the stack, and then exploring its neighbors. When you reach a node with no unvisited neighbors, you backtrack by popping from the stack.

What are some practical applications of depth-first search?

DFS is used in various applications like solving puzzles, pathfinding algorithms, and analyzing networks. It's also useful in topological sorting and finding connected components.

Can you show me a simple example of DFS in action?

Sure! Let's say we have a graph with nodes A, B, C, and D. Starting from A, DFS would visit A, then B, then backtrack to A, then visit C, and finally D.