CS223 Advanced Data Structures and Algorithms 1

Depth First Search Depth First Search

Neil TangNeil Tang4/1/20104/1/2010

CS223 Advanced Data Structures and Algorithms 2

Class OverviewClass 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

BFSBFS

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.

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DFSDFS

A generalized pre-order traversal

Time Complexity: O(|V|+|E|)

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DFS on An Undirected GraphDFS on An Undirected Graph

DFS(A): A,B,C,D,E

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DFS on An Undirected GraphDFS 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.

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DFS on A DigraphDFS on A Digraph

DFS(B): B,C,A,D,E,F;

DFS(H): H,J,I;

DFS(G): G.

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Strongly Connected ComponentsStrongly 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.

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Strongly Connected ComponentsStrongly Connected Components

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)

Gr

The forest after the first DFS