Depth-First Search


















Review Preorder and Postorder traversals of trees.


Visiting Nodes Only Once

How do you visit each node in a graph exactly once?

How do you avoid visiting a node multiple times?

	1. mark nodes when they are visited

	2. check the mark before visiting a node


















Depth-First Order

In what order are nodes visited when doing a Depth-First Search?

	1. first visit nodes along a single path until the path ends

	2. then backup and visit nodes along alternate paths

	a. start at a node and recursively visit connected nodes

	b. similar to preorder and postorder traversals of trees


List the order in which the nodes are visited when traversing
the directed graph Depth-First starting with node c.

(When there is a choice of nodes to visit,
choose the one that is first in alphabetic order.)
(graph3.pdf)

	V = { a, b, c, d, e, f }

	E = { (a,b), (a,d), (b,d), (b,e), (c,b),
	      (c,f), (e,a), (e,d), (f,b), (f,e) }

	a---b---c
	| X | \ |
	d---e---f


















Classwork

You may work with a partner.

List the order in which the nodes are visited when traversing
the directed graph Depth-First starting with node d.

(When there is a choice of nodes to visit,
choose the one that is first in alphabetic order.)
(graph2.pdf)

	V = { a, b, c, d, e }

	E = { (b,a), (b,c), (b,d), (b,e), (c,b), (d,c), (d,e), (e,a) }

	a---b---c
	 \ / \ /
	  e---d


















Depth-First Search Code

What's the code for Depth-First Search?

	dfs(Node x)

	   mark x visited

	   for each node y that is adjacent to node x

	      if node y is not marked
	         dfs(y)
	      end if

	   end for

	end dfs

What data structure is used to store the nodes that
have not yet been visited in a Depth-First Search?

What's the Big-Oh for the running time of Depth-First Search?

	O(1) work for each node and each edge