![ALGORITHM
Algorithm for Breadth First Search
Algorithm BFS(v)
//A breadth first search of G is carried out beginning
//at vertex v. For any node i, visited[i] = 1 if i has
//already been visited. The graph G and array visited[]
//are global; visited[] is initialized to zero.
{
u:=v; //q is a queue of unexplored vertices.
visited[v]:=1;
repeat
{
for all vertices w adjacent from u do
{
if(visited[w]=0) then
{
Add w to q; //w is unexplored.
visited[w]:=1;
}
}
if q is empty then return;// No unexplored vertex.](https://image.slidesharecdn.com/datastructure-180908012725/85/Data-structure-7-320.jpg)
![ALGORITHM
Algorithm for Depth First Search
Algorithm DFS(v)
//Given an undirected(directed)graph G=(V,E) with
//n vertices and an array visited[] initially set
//to zero, this algorithm visits all vertices
//reachable from v. G and visited[] are global.
{
visited[v]:=1;
for each vertex w adjacent from v do
{
if(visited[w]=0) then
DFS(w);](https://image.slidesharecdn.com/datastructure-180908012725/85/Data-structure-11-320.jpg)
Data structure
- 1. BREADTH FIRST SEARCH & DEPTH FIRST SEARCH PRESENTED BY, K.LALITHAMBIGA, II- Msc (CS & IT), Nadar Saraswathi College of Arts and Science, Theni.
- 2. SYNOPSIS Introduction BFS Diagram Algorithm DFS Diagram Algorithm
- 3. TECHNIQUES FOR GRAPHS Definition 1: Traversal of a binary tree involves examining every node in the tree. Definition 2: Search involves visiting nodes in a graph in a systematic manner, and may or may not result into a visit to all nodes. Different nodes of a graph may be visited, possibly more than once, during traversal or search If search results into a visit to all the vertices, it is called traversal
- 4. BFS (BREADTH FIRST SEARCH) Breadth First Search (BFS) algorithm traverses a graph in a breadth ward motion and uses a queue to remember to get the next vertex to start a search, when a dead end occurs in any iteration. As in the example given, BFS algorithm traverses from A to B to E to F first then to C and G lastly to D. It employs the following rules. Rule 1 − Visit the adjacent unvisited vertex. Mark it as visited. Display it. Insert it in a queue. Rule 2 − If no adjacent vertex is found, remove the first vertex from the queue. Rule 3 − Repeat Rule 1 and Rule 2 until the queue is empty.
- 5. Step Traversal Description 1 Initialize the queue. 2 We start from visiting S(starting node), and mark it as visited. 3 We then see an unvisited adjacent node from S. In this example, we have three nodes but alphabetically we choose A, mark it as visited and enqueue it.
- 6. 4 Next, the unvisited adjacent node from S& B. We mark it as visited and enqueue it. 5 Next, the unvisited adjacent node from S is C. We mark it as visited and enqueue it. 6 Now, S is left with no unvisited adjacent nodes. So, we dequeue and find A. 7 From A we have D as unvisited adjacent node. We mark it as visited and enqueue it. Atthisstage,weareleftwithnounmarked(unvisited)nodes.Butasperthealgorithm wekeepondequeuinginordertogetallunvisitednodes. Whenthequeuegetsemptied,theprogramisover.
- 7. ALGORITHM Algorithm for Breadth First Search Algorithm BFS(v) //A breadth first search of G is carried out beginning //at vertex v. For any node i, visited[i] = 1 if i has //already been visited. The graph G and array visited[] //are global; visited[] is initialized to zero. { u:=v; //q is a queue of unexplored vertices. visited[v]:=1; repeat { for all vertices w adjacent from u do { if(visited[w]=0) then { Add w to q; //w is unexplored. visited[w]:=1; } } if q is empty then return;// No unexplored vertex.
- 8. DFS (DEPTH FIRST SEARCH) Depth First Search (DFS) algorithm traverses a graph in a depth ward motion and uses a stack to remember to get the next vertex to start a search, when a dead end occurs in any iteration. As in the example given, DFS algorithm traverses from S to A to D to G to E to B first, then to F and lastly to C. It employs the following rules. Rule 1 − Visit the adjacent unvisited vertex. Mark it as visited. Display it. Push it in a stack. Rule 2 − If no adjacent vertex is found, pop up a vertex from the stack. (It will pop up all the vertices from the stack, which do not have adjacent vertices.) Rule 3 − Repeat Rule 1 and Rule 2 until the stack is empty.
- 9. Step Traversal Description 1 Initialize the stack. 2 Mark S as visited and put it onto the stack. Explore any unvisited adjacent node from S. We have three nodes and we can pick any of them. Example, we shall take the node in an alphabetical order. 3 Mark A as visited and put it onto the stack. Explore any unvisited adjacent node from A. Both Sand D are adjacent to A but we are concerned for unvisited nodes only.
- 10. 4 Visit D and mark it as visited and put onto the stack. Here, we have B and C nodes, which are adjacent to D and both are unvisited. However, we shall again choose in an alphabetical order. 5 We choose B, mark it as visited and put onto the stack. Here B does not have any unvisited adjacent node. So, we pop B from the stack. 6 we check the stack top for return to the previous node and check if it has any unvisited nodes. Here, we find D to be on the top of the stack. 7 Only unvisited adjacent node is from D is C now. So we visit C, mark it as visited and put it onto the stack. AsCdoesnothaveanyunvisitedadjacentnodesowekeeppoppingthestackuntil wefindanodethathasanunvisitedadjacentnode. Inthiscase,there'snoneandwekeeppoppinguntilthestackisempty.
- 11. ALGORITHM Algorithm for Depth First Search Algorithm DFS(v) //Given an undirected(directed)graph G=(V,E) with //n vertices and an array visited[] initially set //to zero, this algorithm visits all vertices //reachable from v. G and visited[] are global. { visited[v]:=1; for each vertex w adjacent from v do { if(visited[w]=0) then DFS(w);