In graph theory, breadth-first search (BFS) is a strategy for searching in a graph when search is limited to essentially two operations: (a) visit and inspect a node of a graph; (b) gain access to visit the nodes that neighbor the currently visited node. The BFS begins at a root node and inspects all the neighboring nodes. Then for each of those neighbor nodes in turn, it inspects their neighbor nodes which were unvisited, and so on. Compare BFS with the equivalent, but more memory-efficient Iterative deepening depth-first search and contrast with depth-first search.

## Algorithm

The algorithm uses a queue data structure to store intermediate results as it traverses the graph, as follows:

1) Enqueue the root node

2) Dequeue a node and examine it

- If the element sought is found in this node, quit the search and return a result.
- Otherwise enqueue any successors (the direct child nodes) that have not yet been discovered.

3)If the queue is empty, every node on the graph has been examined – quit the search and return “not found”. 4)If the queue is not empty, repeat from Step 2.

## C program

#include<stdio.h> #include<conio.h> int a[20][20],q[20],visited[20],n,i,j,f=0,r=-1; void bfs(int v) { for(i=1;i<=n;i++) if(a[v][i] && !visited[i]) q[++r]=i; if(f<=r) { visited[q[f]]=1; bfs(q[f++]); } } void main() { int v; clrscr(); printf("n Enter the number of vertices:"); scanf("%d",&n); for(i=1;i<=n;i++) { q[i]=0; visited[i]=0; } printf("n Enter graph data in matrix form:n"); for(i=1;i<=n;i++) for(j=1;j<=n;j++) scanf("%d",&a[i][j]); printf("n Enter the starting vertex:"); scanf("%d",&v); bfs(v); printf("n The node which are reachable are:n"); for(i=1;i<=n;i++) if(visited[i]) printf("%dt",i); else printf("n Bfs is not possible"); getch(); }