What Is DFS in Data Structure Example?

In the field of computer science, data structures are used to store and organize data efficiently. One such data structure is Depth First Search (DFS). DFS is a graph traversal algorithm that explores as far as possible along each branch before backtracking.

## Understanding DFS

DFS is based on the principle of exploring all the vertices of a graph by going deep into each branch before backtracking. It starts at an arbitrary vertex and visits all its adjacent vertices recursively until there are no more unvisited vertices. It then backtracks to the previous vertex and repeats the process until all vertices have been visited.

Let’s consider an example to understand DFS better:

### The Graph

We have a directed graph with five vertices (A, B, C, D, and E) and six edges connecting them. The edges are represented by arrows indicating the direction of traversal.

A --> B / \ | | v v | C --> D | ^ \______| E

### The Algorithm

- Choose an arbitrary starting vertex (let’s say A) and mark it as visited.
- Visit any unvisited adjacent vertex (B) from the current vertex (A).
- Mark the visited vertex (B) as visited.
- If there are any unvisited adjacent vertices from the current vertex (B), choose one and repeat steps 2-4.
- If all adjacent vertices of the current vertex (B) have been visited or there are no adjacent vertices, backtrack to the previous vertex (A).
- Repeat steps 2-5 until all vertices have been visited.

### The DFS Traversal

Using the above algorithm, we can perform a Depth First Search traversal on the given graph:

- Start at vertex A.
- Visit vertex B (unvisited and adjacent to A).
- Visit vertex C (unvisited and adjacent to B).
- Visit vertex D (unvisited and adjacent to C).
- No unvisited adjacent vertices from D, backtrack to C.
- No unvisited adjacent vertices from C, backtrack to B.
- Visit vertex E (unvisited and adjacent to B).
- No unvisited adjacent vertices from E, backtrack to B.
- No unvisited adjacent vertices from B, backtrack to A.

The DFS traversal order of the given graph is: A → B → C → D → E.

## Applications of DFS

DFS has various applications in computer science. Some of them include:

**Maze Solving:**DFS can be used to solve mazes by exploring all possible paths until a solution is found.**Cycle Detection:**DFS can be used to detect cycles in a graph by checking for back edges during traversal.**Topological Sorting:**DFS can be used to perform topological sorting of directed acyclic graphs.

In conclusion, Depth First Search (DFS) is a graph traversal algorithm that explores as far as possible along each branch before backtracking. It is widely used in various applications such as maze solving, cycle detection, and topological sorting. Understanding DFS and its applications can be beneficial in solving complex problems efficiently.