In this tutorial, you will learn about the breadth-first search algorithm. Additionally, you will discover working instances of bfs algorithm in C, C++, Java, and Python.

The Breadth-First Search (BFS) is an algorithm for traversing or searching through tree or graph data structures. It explores all the nodes at the current depth before proceeding onward to the nodes at the next depth level.

Note: It can be implemented using a queue.

Traversal implies visiting all the nodes of a graph. Breadth First Traversal or Breadth First Search is a recursive algorithm for searching through all the vertices of a graph or tree data structure.

## BFS algorithm

A standard BFS execution places every vertex of the graph into one of two classifications:

1. Visited
2. Not Visited

The purpose of the algorithm is to mark every vertex as visited while keeping away from cycles.

The algorithm functions as follows:

1. Start by putting any of the graph’s vertices at the back of a queue.
2. Take the front item of the queue 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 back of the queue.
4. Continue to repeating stages 2 and 3 until the queue is vacant.

The graph may have two diverse disconnected parts so to ensure that we cover each vertex, we can likewise run the BFS algorithm on each node

## BFS example

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

We start from vertex 0, the BFS 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 front of queue 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 back of the queue and visit 3, which is at the front of the queue.

Just 4 remaining parts in the queue since the only adjacent node of 3 for example 0 is as of now visited. We visit it.

Since the queue is vacant, we have finished the Breadth First Traversal of the graph.

## BFS pseudocode

```create a queue Q
mark v as visited and put v into Q
while Q is non-empty
remove the head u of Q
mark and enqueue all (unvisited) neighbours of u
```

## Python, Java, and C/C++ Examples

The code for the Breadth-First Search Algorithm with an example appears beneath. The code has been simplified so we can focus on the algorithm instead of different details.

Python

```# BFS algorithm in Python

import collections

# BFS algorithm
def bfs(graph, root):

visited, queue = set(), collections.deque([root])

while queue:

# Dequeue a vertex from queue
vertex = queue.popleft()
print(str(vertex) + " ", end="")

# If not visited, mark it as visited, and
# enqueue it
for neighbour in graph[vertex]:
if neighbour not in visited:
queue.append(neighbour)

if __name__ == '__main__':
graph = {0: [1, 2], 1: [2], 2: [3], 3: [1, 2]}
print("Following is Breadth First Traversal: ")
bfs(graph, 0)```

Java

```// BFS algorithm in Java

import java.util.*;

public class Graph {
private int V;

// Create a graph
Graph(int v) {
V = v;
for (int i = 0; i < v; ++i)
}

// Add edges to the graph
void addEdge(int v, int w) {
}

// BFS algorithm
void BFS(int s) {

boolean visited[] = new boolean[V];

visited[s] = true;

while (queue.size() != 0) {
s = queue.poll();
System.out.print(s + " ");

while (i.hasNext()) {
int n = i.next();
if (!visited[n]) {
visited[n] = true;
}
}
}
}

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

System.out.println("Following is Breadth First Traversal " + "(starting from vertex 2)");

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

C

```// BFS algorithm in C

#include <stdio.h>
#include <stdlib.h>
#define SIZE 40

struct queue {
int items[SIZE];
int front;
int rear;
};

struct queue* createQueue();
void enqueue(struct queue* q, int);
int dequeue(struct queue* q);
void display(struct queue* q);
int isEmpty(struct queue* q);
void printQueue(struct queue* q);

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

struct node* createNode(int);

struct Graph {
int numVertices;
int* visited;
};

// BFS algorithm
void bfs(struct Graph* graph, int startVertex) {
struct queue* q = createQueue();

graph->visited[startVertex] = 1;
enqueue(q, startVertex);

while (!isEmpty(q)) {
printQueue(q);
int currentVertex = dequeue(q);
printf("Visited %d\n", currentVertex);

while (temp) {

}
temp = temp->next;
}
}
}

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

// Creating a 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);
}

// Create a queue
struct queue* createQueue() {
struct queue* q = malloc(sizeof(struct queue));
q->front = -1;
q->rear = -1;
return q;
}

// Check if the queue is empty
int isEmpty(struct queue* q) {
if (q->rear == -1)
return 1;
else
return 0;
}

void enqueue(struct queue* q, int value) {
if (q->rear == SIZE - 1)
printf("\nQueue is Full!!");
else {
if (q->front == -1)
q->front = 0;
q->rear++;
q->items[q->rear] = value;
}
}

// Removing elements from queue
int dequeue(struct queue* q) {
int item;
if (isEmpty(q)) {
printf("Queue is empty");
item = -1;
} else {
item = q->items[q->front];
q->front++;
if (q->front > q->rear) {
printf("Resetting queue ");
q->front = q->rear = -1;
}
}
return item;
}

// Print the queue
void printQueue(struct queue* q) {
int i = q->front;

if (isEmpty(q)) {
printf("Queue is empty");
} else {
printf("\nQueue contains \n");
for (i = q->front; i < q->rear + 1; i++) {
printf("%d ", q->items[i]);
}
}
}

int main() {
struct Graph* graph = createGraph(6);

bfs(graph, 0);

return 0;
}```

C++

```// BFS algorithm in C++

#include <iostream>
#include <list>

using namespace std;

class Graph {
int numVertices;
bool* visited;

public:
Graph(int vertices);
void BFS(int startVertex);
};

// Create a graph with given vertices,
// and maintain an adjacency list
Graph::Graph(int vertices) {
numVertices = vertices;
}

// Add edges to the graph
void Graph::addEdge(int src, int dest) {
}

// BFS algorithm
void Graph::BFS(int startVertex) {
visited = new bool[numVertices];
for (int i = 0; i < numVertices; i++)
visited[i] = false;

list<int> queue;

visited[startVertex] = true;
queue.push_back(startVertex);

list<int>::iterator i;

while (!queue.empty()) {
int currVertex = queue.front();
cout << "Visited " << currVertex << " ";
queue.pop_front();

}
}
}
}

int main() {
Graph g(4);

g.BFS(2);

return 0;
}```

## BFS Algorithm Complexity

The time intricacy of the BFS algorithm is addressed as O(V + E), where V is the number of nodes and E is the number of edges.

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

## BFS Algorithm Applications

1. To build index by search index