Earlier I have shown you how to build a simple Graph using Adjacency List. We used a Friendship Graph to demonstrate that. If you haven’t read that I will recommend you to take a look at the following two posts that cover Graphs and Queues, since we will make use of both these structures.

Building on that we are going to see how to traverse that Graph using a very popular approach known as “breadth first traversal”, or **BFS**.

At the end of this Post I have presented code written in C to show you how can BFS be implemented. After all we should be able to write the code and not just talk about the approach.

**Few applications of Breadth First Traversal (BFT)**

- BFT can be used to generate a Tree. This tree can help us find out shortest distances from root node to other nodes. Also it can be used to find Paths between vertices.
- BFT can be used to determine the connected components in a Graph. A connected component means that any vertex in that component can be reached from any other vertex in the same component.
- It can help us solve Vertex Coloring problem, which has applications like assigning resources etc.

**Understanding BFT**

Let’s start by understanding BFT. In BFT we pick a vertex to start with. In our example friendship graph we start with Ankur. We insert this in a Queue (Q) and mark it as visited.

Now we have a starting point. Let’s see a simple algorithm which will give you a basic idea on how this works.

- Check if Queue size is > 0. If yes, perform dequeue operation on Q. If no, exit.
- Let’s say from step 1 we got a vertex S. Say, Ankur.
- Visit all vertices adjacent to S. If we got Ankur as S, then adjacent will be Dikshit and Reena. By visit I mean we need to perform two operations – mark vertex as visited and also enqueue it.
- Repeat.

As you can see we are trying to visit nodes of the Graph level wise.

Let’s now see the code to implement this. It’s available at Github also. The method of interest here is BFS() which does the job of traversing our friendship graph.

#include<stdio.h> #include<stdlib.h> /* Author: @ankur Date: March 24, 2018 Version: 0.1 This Program illustrates Breadth First Traversal. */ #define MAXV 6 /* maximum number of vertices */ #define VISITED 1 /*Structure for Vertex*/ struct node{ int label; /*data*/ char *name; /*data*/ int status; struct node *next; /*Pointer to next node*/ }; struct qnode{ int d; char *info; struct qnode *next; }*f,*r; struct node vertices[MAXV]; char *names[MAXV]; void addToList(struct node *x, int data); void traverseGraph(); void initNames(); void displayNames(); void BFS(); /*Queue Specific*/ void eq(int data); int dq(); void traverseQ(); int qsize(); int main(){ /*Initialize Names*/ initNames(); displayNames(); /*Initialize the Array*/ for(int i=0;i<MAXV;i++){ vertices[i].label = i; vertices[i].name = names[i]; vertices[i].next = NULL; } /* Say we have the following Edges {(0,1), (0,2), (1,2)} Let's build the Adjacency List. */ addToList(&vertices[0], 1); addToList(&vertices[0], 3); addToList(&vertices[1], 2); addToList(&vertices[1], 0); addToList(&vertices[1], 4); addToList(&vertices[2], 1); addToList(&vertices[3], 0); addToList(&vertices[3], 5); addToList(&vertices[4], 1); /*Traverse the Adjacency List*/ traverseGraph(); /*Breadth First Traversal*/ BFS(); return 0; } /*Here we are trying to add an edge x->y*/ void addToList(struct node *x, int data){ printf("Going to Add %d to the Vertex %d \n", data, x->label); struct node *y = (struct node *)(malloc(sizeof(struct node))); if(y!=NULL){ y->label = data; y->name = names[data]; if(x->next != NULL) y->next = x->next; else y->next = NULL; x->next = y; } } void traverseGraph(){ printf("\nLet's see who all are Friends \n\n"); for(int i=0;i<MAXV;i++){ struct node *temp = &vertices[i]; printf("%s is friend to --> ", temp->name); if(temp->next != NULL){ temp = temp->next; while(temp != NULL){ printf("%s", temp->name); if(temp->next != NULL) printf(", "); temp = temp->next; } } printf("\n\n---------------------------------------------\n\n"); } } void initNames(){ names[0] = "Ankur"; names[1] = "Dikshit"; names[2] = "Mohan"; names[3] = "Nidhi"; names[4] = "Reena"; names[5] = "Suresh"; } void displayNames(){ printf("\nWe have the following folks staying in a small town \n\n"); for(int i=0;i<MAXV;i++){ printf("%s ", names[i]); } printf("\n\n---------------------------------------------\n\n"); } void BFS(){ printf("\n\n-------------------BFS Traversal-------------------\n\n"); struct node *qn = &vertices[0]; int tempData; eq(qn->label); while(qsize() != 0){ tempData = dq(); if(tempData != 999) qn = &vertices[tempData]; else qn = NULL; if(qn && qn->status != VISITED){ qn->status = VISITED; printf("Visited %s\n", qn->name); if(qn->next != NULL){ /*for each vetrex adjacent to v do BFS*/ qn = qn->next; while(qn != NULL){ eq(qn->label); qn = qn->next; } } } } printf("\n"); } /*Queue Methods*/ void eq(int data){ struct qnode *new = (struct qnode *)malloc(sizeof(struct qnode)); new->d = data; new->next = NULL; struct qnode *tempf = f; struct qnode *tempr = r; if(f == NULL){ f = new; r = new; }else if(f->next == NULL){ f->next = new; new->next = NULL; r = new; }else{ tempr->next = new; new->next = NULL; r = new; } } int dq(){ int data = 999; if(f && f->d != 999){ data = f->d; f = f->next; }else{ printf("Q is empty \n"); } return data; } void traverseQ(){ printf("Q looks like - "); struct qnode *temp = f; while(temp != NULL){ printf("%s ", temp->info); temp = temp->next; } printf("\n"); } int qsize(){ int count = 0; if(f != NULL){ struct qnode *temp = f; while(temp != NULL){ temp = temp->next; count++; } temp = NULL; } return count; }

When you run this the expected output is

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