# Depth First Search (DFS) In this tutorial, you will learn about depth-first search algorithms with examples and pseudocode. Additionally, you will learn how to implement DFS in C, Java, Python, and C++.

## What is Depth First Search?

The Depth First Search (DFS) is an algorithm for traversing or searching through tree or graph data structures that uses backtracking. It investigates all the nodes by going ahead if conceivable or uses backtracking.

Note: It can be implemented using a stack.

Depth-first Search or Depth-first traversal is a recursive algorithm for looking through all the vertices of a graph or tree data structure. Traversal implies visiting all the nodes of a graph.

## Depth First Search Algorithm

A standard DFS execution places every vertex of the graph into one of two classes:

1. Visited
2. Not Visited

The reason for the algorithm is to mark every vertex as visited while evading cycles.

The DFS algorithm functions as follows:

1. Start by putting any of the graph’s vertices on top of a stack.
2. Take the top item of the stack and add it to the visited list.
3. Create a list of that vertex’s adjacent nodes. Add the ones which aren’t in the visited list to the top of the stack.
4. Continue to repeating stages 2 and 3 until the stack is vacant.

## Depth First Search Example

Let’s see how the Depth First Search algorithm functions with an example. We use an undirected graph with 5 vertices.

We start from vertex 0, the DFS algorithm begins by placing it in the Visited list and placing all its adjacent vertices in the stack.

Then, we visit the element at the top of the stack for example 1, and go to its adjacent nodes. Since 0 has just been visited, we visit 2 instead.

Vertex 2 has an unvisited adjacent vertex in 4, so we add that to the top of the stack and visit it. Vertex 2 has an unvisited adjacent vertex in 4, so we add that to the top of the stack and visit it. Vertex 2 has an unvisited adjacent vertex in 4, so we add that to the top of the stack and visit it.

After we visit the last element 3, it doesn’t have any unvisited adjacent nodes, so we have finished the Depth First Traversal of the graph. After we visit the last element 3, it doesn’t have any unvisited adjacent nodes, so we have finished the Depth First Traversal of the graph.

## DFS Pseudocode (recursive Implementation)

The pseudocode for DFS appears beneath. In the init() work, notice that we run the DFS work on each node. This is on the grounds that the graph may have two diverse separated parts so to ensure that we cover each vertex, we can likewise run the DFS algorithm on each node.

```DFS(G, u)
u.visited = true
if v.visited == false
DFS(G,v)

init() {
For each u ∈ G
u.visited = false
For each u ∈ G
DFS(G, u)
}```

## DFS Implementation in Python, Java, and C/C++

The code for the Depth First Search Algorithm with an example appears underneath. The code has been rearranged so that we can focus on the algorithm instead of different details.

Python

```# DFS algorithm in Python

# DFS algorithm
def dfs(graph, start, visited=None):
if visited is None:
visited = set()

print(start)

for next in graph[start] - visited:
dfs(graph, next, visited)
return visited

graph = {'0': set(['1', '2']),
'1': set(['0', '3', '4']),
'2': set(['0']),
'3': set(['1']),
'4': set(['2', '3'])}

dfs(graph, '0')```

Java

```// DFS algorithm in Java

import java.util.*;

class Graph {
private boolean visited[];

// Graph creation
Graph(int vertices) {
visited = new boolean[vertices];

for (int i = 0; i < vertices; i++)
}

void addEdge(int src, int dest) {
}

// DFS algorithm
void DFS(int vertex) {
visited[vertex] = true;
System.out.print(vertex + " ");

while (ite.hasNext()) {
}
}

public static void main(String args[]) {
Graph g = new Graph(4);

System.out.println("Following is Depth First Traversal");

g.DFS(2);
}
}```

C

```// DFS algorithm in C

#include <stdio.h>
#include <stdlib.h>

struct node {
int vertex;
struct node* next;
};

struct node* createNode(int v);

struct Graph {
int numVertices;
int* visited;

// We need int** to store a two dimensional array.
// Similary, we need struct node** to store an array of Linked lists
};

// DFS algo
void DFS(struct Graph* graph, int vertex) {

graph->visited[vertex] = 1;
printf("Visited %d \n", vertex);

while (temp != NULL) {
int connectedVertex = temp->vertex;

if (graph->visited[connectedVertex] == 0) {
DFS(graph, connectedVertex);
}
temp = temp->next;
}
}

// Create a node
struct node* createNode(int v) {
struct node* newNode = malloc(sizeof(struct node));
newNode->vertex = v;
newNode->next = NULL;
return newNode;
}

// Create graph
struct Graph* createGraph(int vertices) {
struct Graph* graph = malloc(sizeof(struct Graph));
graph->numVertices = vertices;

graph->adjLists = malloc(vertices * sizeof(struct node*));

graph->visited = malloc(vertices * sizeof(int));

int i;
for (i = 0; i < vertices; i++) {
graph->visited[i] = 0;
}
return graph;
}

void addEdge(struct Graph* graph, int src, int dest) {
// Add edge from src to dest
struct node* newNode = createNode(dest);

// Add edge from dest to src
newNode = createNode(src);
}

// Print the graph
void printGraph(struct Graph* graph) {
int v;
for (v = 0; v < graph->numVertices; v++) {
printf("\n Adjacency list of vertex %d\n ", v);
while (temp) {
printf("%d -> ", temp->vertex);
temp = temp->next;
}
printf("\n");
}
}

int main() {
struct Graph* graph = createGraph(4);

printGraph(graph);

DFS(graph, 2);

return 0;
}
```

C++

```// DFS algorithm in C++

#include <iostream>
#include <list>
using namespace std;

class Graph {
int numVertices;
bool *visited;

public:
Graph(int V);
void DFS(int vertex);
};

// Initialize graph
Graph::Graph(int vertices) {
numVertices = vertices;
visited = new bool[vertices];
}

void Graph::addEdge(int src, int dest) {
}

// DFS algorithm
void Graph::DFS(int vertex) {
visited[vertex] = true;

cout << vertex << " ";

list<int>::iterator i;
if (!visited[*i])
DFS(*i);
}

int main() {
Graph g(4);

g.DFS(2);

return 0;
}```

## The complexity of Depth First Search

The time complexity of the DFS algorithm is addressed as O(V + E), where V is the number of hubs and E is the number of edges.

The space complexity of the algorithm is O(V).

## Application of DFS Algorithm

1. For finding the path
2. To test if the graph is bipartite
3. For finding the strongly connected components of a graph
4. For detecting cycles in a graph

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