1. Depth First Search Neil Tang 4/10/2008
CS223 Advanced Data Structures and Algorithms

2. CS223 Advanced Data Structures and Algorithms
Class Overview
Breadth First Search (BFS)
Depth First Search (DFS)
DFS on an undirected graph
DFS on a digraph
Strong connected components
CS223 Advanced Data Structures and Algorithms

3. CS223 Advanced Data Structures and Algorithms
BFS
Visit the nodes that are one-hop away from the starting node one by one, then the nodes that are two-hop away, then …
A queue should be used to implement the BFS.
Make sure each node is visited exactly once.
CS223 Advanced Data Structures and Algorithms

4. CS223 Advanced Data Structures and Algorithms
DFS
A generalized pre-order traversal
Time Complexity: O(|V|+|E|)
CS223 Advanced Data Structures and Algorithms

5. DFS on An Undirected Graph
DFS(A): A,B,C,D,E
CS223 Advanced Data Structures and Algorithms

6. DFS on An Undirected Graph
DFS can be used to find if an undirected graph is connected or not.
DFS can also be used to find all the connected components.
CS223 Advanced Data Structures and Algorithms

7. CS223 Advanced Data Structures and Algorithms
DFS on A Digraph
DFS(B): B,C,A,D,E,F;
DFS(H): H,J,I;
DFS(G): G.
CS223 Advanced Data Structures and Algorithms

8. Strong Connected Components
Perform DFS until all nodes are visited.
Construct an auxiliary graph Gr.
Perform DFS on Gr in the reverse order of the numbers.
CS223 Advanced Data Structures and Algorithms

9. Strong Connected ComponentsGr
DFS(G): G;
DFS(H): H,I,J;
DFS(B): B,A,C,F;
DFS(D): D; DFS(E): E.
Strong Connected Components: (G), (H,I,J), (B,A,C,F),(D),(E)
The spanning tree after the first DFS
CS223 Advanced Data Structures and Algorithms