34-DFSForestsProps

34-DFSForestsProps - Discussion#34 Properties and Applications of Depth-First Search Trees and Forests Discussion#34 Chapter 7 Pages 436-8 1/13

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Discussion #34 Chapter 7, Pages 436-8 1/13 Discussion #34 Properties and Applications of Depth-First Search Trees and Forests

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Discussion #34 Chapter 7, Pages 436-8 2/13 Topics Depth-first search trees and forests Tree edges; forward, backward, and cross edges Post order numbers Applications Cycles Topological sorting Reachability Connected components Reading assignment, pages 436 to 438, Exercises 1-3.
Discussion #34 Chapter 7, Pages 436-8 3/13 DFS Trees and Forests 3 2 5 4 1 6 1 3 5 2 4 6 1 Convention: increasing order 5 2 4 3 DFS Tree DFS Trees Forest Note: O( m ) to create (check each edge once) 6 Convention: Roots in decreasing order; other nodes in increasing order

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Discussion #34 Chapter 7, Pages 436-8 4/13 Edge Classification 3 2 5 4 1 6 1 3 5 2 4 6 forward backward backward cross 1 5 2 4 3 backward cross cross cross Add all edges but make them dashed if a marked node is encountered. 6 backward cross cross Tree edge if y is a child of x in DFS forest. Forward edge if y is a descendent of x , but not a child. Backward edge if y is an ancestor of x or if x = y . Cross edge if y is not x and is neither a descendent nor an ancestor of x . cross
Discussion #34 Chapter 7, Pages 436-8 5/13 Observations about Edge Classification Requires O( m ) to create each edge considered only once Only go between trees in a forest with cross edges If we go left to right in building the DFS tree, then

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This note was uploaded on 03/02/2012 for the course C S 236 taught by Professor Michaelgoodrich during the Winter '12 term at BYU.

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34-DFSForestsProps - Discussion#34 Properties and Applications of Depth-First Search Trees and Forests Discussion#34 Chapter 7 Pages 436-8 1/13

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