![Basic Traversal And Search
Techniques
Presented by
S.Vijayalakshmi I-MSC[IT]](https://image.slidesharecdn.com/dsappt-220202134932/85/Basic-Traversal-and-Search-Techniques-1-320.jpg)
![Determining Connected
Components
void Graph::Components()
{
visited = new Boolean[n];
for(int i=0 ; i<n ; i++)
visited[i]= False;
for(i=0 ; i<n ; i++)
if(!visited[i])
{
DFS(i);
OutputNewComponent();
}
delete[]vivited;
}](https://image.slidesharecdn.com/dsappt-220202134932/85/Basic-Traversal-and-Search-Techniques-6-320.jpg)
Basic Traversal and Search Techniques
- 1. Basic Traversal And Search Techniques Presented by S.Vijayalakshmi I-MSC[IT]
- 4. Connected Components • A connected components is a subgraph in which any two vertices are connected to each other by paths and which is connected to no additional vertices of the super graph
- 5. Algorithm For Connected Components • Connected components(G) For each vertex V G Make –set (V) For each edge (U,V) G E If find –set(4) find-set(V) Union(U,V) • Same Component(U,V) If find-set(U)= =find-set(V) Return true Else return false
- 6. Determining Connected Components void Graph::Components() { visited = new Boolean[n]; for(int i=0 ; i<n ; i++) visited[i]= False; for(i=0 ; i<n ; i++) if(!visited[i]) { DFS(i); OutputNewComponent(); } delete[]vivited; }
- 8. GRAPHS • Graphs are one of the most interesting data structures in computer science • Graphs and tree are somewhat similar by their structure and in fact tree is derived from the graph and data structure • Commonly used graph traversal algorithms are: DFS BFS
- 9. BFS • In this we visit the node level by level so it will start with 0, which is the root node then next ,then the last level • Queue is used to implement BFS DFS • In this we visit the root node first then its children until it reaches the end node • Stack is used to implement DFS
- 10. Spanning Tree • Spanning tree have a connected undirected graph connected : every node reachable from every other node Undirected: edges do not have automatic direction • Spanning tree of the graph is a connected sub - graph in which there are no cycles • A spanning of a graph has no cycles but still connects to every house • If G is a connected graph with n vertices and m edges, spanning tree of G must have n-1 edges , and no.of edges deleted from G to get a spanning tree must be m -(n-1)=m-n+1
- 11. • A graph may have many spanning tree;for instance the complete graph of four vertices. A connected, undirected graph four of the spanning tree of the graph
- 13. Biconnected Components Basically it is a graph theory. A graph is biconnected if it contains no ‘articulation’ points . A components of a graph G is maximal “biconnected subgraph”. That means it is not contained any larger biconnected subgraph of G
- 14. Articulation Points Let G = (V,E) be a connected undirected graph. • Articulation point : is any vertex f G whose removal result in a disconnected graph
- 15. Articulation Point • Articulation point : is any vertex of G whose removal results in a disconnected graph
- 16. Biconnected Components • A graph is biconnected if it contains no articulation points.
- 18. Definition • The aim of the DFS algorithm is travers the graph in such a way that is try to go for from the root node. Stack is use in the implementation of the DFS. lets see hoe DFS work with respect to the following graph. • DFS – Depth First Search • It implements stack, the concept of LIFO – Last In First Out.
- 19. Un Directed Graph • Let G = (N,A)be an undirected graph all of whose nodes we wish to visit • To carry out a depth first traversal of the graph choose any node V N as the starting point
- 20. Directed Graph • The algorithm is essentially the same as for undirected graph , the different residing in the interpretation of the word “adjacent”. • In a directed graph, node W is an adjacent to node V but is not adjacent to W