In this instructional exercise, we will talk about Breadth-First Search or BFS program in C with calculation and a model. Before hopping to genuine coding lets talk about something about Graph and BFS.

**A Graph G = (V, E) is an accumulation of sets V and E where V is a gathering of vertices and E is a gathering of edges. **

A Graph can be of two kinds:

Coordinated Graph

Undirected Graph

In information structures, there is a prevalent term known as ‘Traversal’. It is the procedure of methodicallly visiting or looking at (might be to refresh the Graph hubs) every hub in a tree information structure, precisely once.

There are two most basic techniques to navigate a Graph:

Expansiveness First Search

Profundity First Search

In this instructional exercise, we are going to concentrate on the Breadth-First Search procedure.

In this procedure, we first visit the vertex and afterward visit all the vertices adjoining the beginning vertex i.e., 0. Next, we pick the neighboring vertices in a steady progression and visit their contiguous vertices and this procedure continues forever until we arrive at the last vertex.

**Broadness First Search (BFS) Example **

Consider underneath Graph for instance.

The vertex 0 is the beginning vertex for our situation. We start our traversal from the vertex 0. At that point we will visit all vertices neighboring vertex 0 i.e., 1, 4, 3. Here, we can visit these three vertices in any request. Assume we visit the vertices all together 1,3,4.

The traversal would be: 0 1 3 4

Presently, we will visit all the vertices nearby 1, at that point all the vertices neighbouring 3 and afterwards all the vertices adjoining 4. So first we will visit 2 (since it is contiguous 1), at that point 6 (since it is adjoining 3) and 5, 7 (since these are neighbouring 4).

Note: Vertex 4 is adjoining vertices 1 and 3, however, it has just been visited so we’ve overlooked it.

The traversal would be: 0 1 3 4 2 6 5 7

Presently, we will visit all the vertices contiguous 2, 6, 5, and 7 individually. We can see that vertex 5 is adjoining vertex 2. Since it has just been navigated upon previously, we have don’t have to cross through it again and proceed onward to the following vertex.

Presently, the vertices 4 and 7 are adjoining the vertex 6. Since they have been navigated upon previously, we won’t cross on them once more. Vertex 5 doesn’t have any contiguous vertices.

Vertices 5 and 8 are neighbouring vertex 7. Since vertex 5 has been navigated upon previously, we won’t cross it once more. Be that as it may, vertex 8 has not yet been visited. So we will navigate on vertex 8.

The traversal would be: 0 1 3 4 2 6 5 7 8

Presently, we have to visit vertices neighbouring vertex 8. Notwithstanding, there is no vertex adjoining vertex 8 and consequently, we should stop the traversal here.

Note: There’s no special traversal and it very well may be diverse depending on the request for the successors.

We will take a gander at a BFS program in C for coordinated Graph utilizing a Queue. This program arrives at just those vertices that are reachable from the beginning vertex.

**Broadness First Search (BFS) Program in C **

```
#include<stdio.h>
#include<stdlib.h>
#define MAX 100
#define initial 1
#define waiting 2
#define visited 3
int n;
int adj[MAX][MAX];
int state[MAX];
void create_graph();
void BF_Traversal();
void BFS(int v);
int queue[MAX], front = -1,rear = -1;
void insert_queue(int vertex);
int delete_queue();
int isEmpty_queue();
int main()
{
create_graph();
BF_Traversal();
return 0;
}
void BF_Traversal()
{
int v;
for(v=0; v<n; v++)
state[v] = initial;
printf("Enter Start Vertex for BFS: \n");
scanf("%d", &v);
BFS(v);
}
void BFS(int v)
{
int i;
insert_queue(v);
state[v] = waiting;
while(!isEmpty_queue())
{
v = delete_queue( );
printf("%d ",v);
state[v] = visited;
for(i=0; i<n; i++)
{
if(adj[v][i] == 1 && state[i] == initial)
{
insert_queue(i);
state[i] = waiting;
}
}
}
printf("\n");
}
void insert_queue(int vertex)
{
if(rear == MAX-1)
printf("Queue Overflow\n");
else
{
if(front == -1)
front = 0;
rear = rear+1;
queue[rear] = vertex ;
}
}
int isEmpty_queue()
{
if(front == -1 || front > rear)
return 1;
else
return 0;
}
int delete_queue()
{
int delete_item;
if(front == -1 || front > rear)
{
printf("Queue Underflow\n");
exit(1);
}
delete_item = queue[front];
front = front+1;
return delete_item;
}
void create_graph()
{
int count,max_edge,origin,destin;
printf("Enter number of vertices : ");
scanf("%d",&n);
max_edge = n*(n-1);
for(count=1; count<=max_edge; count++)
{
printf("Enter edge %d( -1 -1 to quit ) : ",count);
scanf("%d %d",&origin,&destin);
if((origin == -1) && (destin == -1))
break;
if(origin>=n || destin>=n || origin<0 || destin<0)
{
printf("Invalid edge!\n");
count--;
}
else
{
adj[origin][destin] = 1;
}
}
}
```

**Output**

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