Depth-First Search (DFS)

Depth-First Search (DFS) is a graph traversal algorithm that explores as far as possible along each branch before backtracking. It starts at a specified vertex and explores as far as possible along each branch before backtracking.

DFS can be implemented using either recursion or an explicit stack. The recursive implementation is naturally elegant and easier to understand, but it may run into stack overflow errors when dealing with large graphs. The explicit stack implementation eliminates the possibility of stack overflow and is often used in practice.

The DFS algorithm can be used to solve various graph-related problems, such as finding connected components, detecting cycles, and determining reachability.

Here is an example of a basic recursive implementation of the DFS algorithm in Java:

1{{code}}

In this example, we have a Graph class that represents a graph. It has an adjacency list to store the vertices and their corresponding edges. The dfs method is a recursive function that performs the depth-first search traversal. It takes a start vertex as input and explores the graph by visiting each unvisited vertex and recursively calling the dfs method on its neighbors.

DFS is a fundamental algorithm in graph theory and has applications in various domains, such as network routing, maze solving, and solving puzzles. It provides a systematic way to explore and analyze the structure of a graph by visiting all its vertices and edges.

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class Main {

  public static void main(String[] args) {

    // Replace with your Java logic here

    // Example code

    // ... 

  }

}