Depth First Search Neil Tang 4/1/2010

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Presentation transcript:

Depth First Search Neil Tang 4/1/2010 CS223 Advanced Data Structures and Algorithms

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

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 …, i.e., layer by layer. A queue should be used to implement the BFS. Make sure each node is visited exactly once. CS223 Advanced Data Structures and Algorithms

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

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

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

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

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

Strongly Connected Components Gr DFS(G): G; DFS(H): H,I,J; DFS(B): B,A,C,F; DFS(D): D; DFS(E): E. Strongly Connected Components: (G), (H,I,J), (B,A,C,F),(D),(E) The forest after the first DFS CS223 Advanced Data Structures and Algorithms