Presentation is loading. Please wait.

Presentation is loading. Please wait.

Depth-first search COMP171 Fall 2005. Graph / Slide 2 Depth-First Search (DFS) * DFS is another popular graph search strategy n Idea is similar to pre-order.

Published by Modified over 8 years ago

Similar presentations

Presentation on theme: "Depth-first search COMP171 Fall 2005. Graph / Slide 2 Depth-First Search (DFS) * DFS is another popular graph search strategy n Idea is similar to pre-order."— Presentation transcript:

1 Depth-first search COMP171 Fall 2005

2 Graph / Slide 2 Depth-First Search (DFS) * DFS is another popular graph search strategy n Idea is similar to pre-order traversal (visit children first) * DFS can provide certain information about the graph that BFS cannot n It can tell whether we have encountered a cycle or not n More in COMP271

3 Graph / Slide 3 DFS Algorithm * DFS will continue to visit neighbors in a recursive pattern n Whenever we visit v from u, we recursively visit all unvisited neighbors of v. Then we backtrack (return) to u. n Note: it is possible that w2 was unvisited when we recursively visit w1, but became visited by the time we return from the recursive call. u v w1 w2 w3

4 Graph / Slide 4 DFS Algorithm Flag all vertices as not visited Flag yourself as visited For unvisited neighbors, call RDFS(w) recursively We can also record the paths using pred[ ].

5 Graph / Slide 5 Example 2 4 3 5 1 7 6 9 8 0 Adjacency List source 0 1 2 3 4 5 6 7 8 9 Visited Table (T/F) F F F F F F F F F F Initialize visited table (all False) Initialize Pred to -1 - - - - - - - - - - Pred

6 Graph / Slide 6 Example 2 4 3 5 1 7 6 9 8 0 Adjacency List source 0 1 2 3 4 5 6 7 8 9 Visited Table (T/F) F F T F F F F F F F Mark 2 as visited - - - - - - - - - - Pred RDFS( 2 ) Now visit RDFS(8)

7 Graph / Slide 7 Example 2 4 3 5 1 7 6 9 8 0 Adjacency List source 0 1 2 3 4 5 6 7 8 9 Visited Table (T/F) F F T F F F F F T F Mark 8 as visited mark Pred[8] - - - - - - - - 2 - Pred RDFS( 2 ) RDFS(8) 2 is already visited, so visit RDFS(0) Recursive calls

8 Graph / Slide 8 Example 2 4 3 5 1 7 6 9 8 0 Adjacency List source 0 1 2 3 4 5 6 7 8 9 Visited Table (T/F) T F T F F F F F T F Mark 0 as visited Mark Pred[0] 8 - - - - - - - 2 - Pred RDFS( 2 ) RDFS(8) RDFS(0) -> no unvisited neighbors, return to call RDFS(8) Recursive calls

9 Graph / Slide 9 Example 2 4 3 5 1 7 6 9 8 0 Adjacency List source 0 1 2 3 4 5 6 7 8 9 Visited Table (T/F) T F T F F F F F T F 8 - - - - - - - 2 - Pred RDFS( 2 ) RDFS(8) Now visit 9 -> RDFS(9) Recursive calls Back to 8

10 Graph / Slide 10 Example 2 4 3 5 1 7 6 9 8 0 Adjacency List source 0 1 2 3 4 5 6 7 8 9 Visited Table (T/F) T F T F F F F F T T Mark 9 as visited Mark Pred[9] 8 - - - - - - - 2 8 Pred RDFS( 2 ) RDFS(8) RDFS(9) -> visit 1, RDFS(1) Recursive calls

11 Graph / Slide 11 Example 2 4 3 5 1 7 6 9 8 0 Adjacency List source 0 1 2 3 4 5 6 7 8 9 Visited Table (T/F) T T T F F F F F T T Mark 1 as visited Mark Pred[1] 8 9 - - - - - - 2 8 Pred RDFS( 2 ) RDFS(8) RDFS(9) RDFS(1) visit RDFS(3) Recursive calls

12 Graph / Slide 12 Example 2 4 3 5 1 7 6 9 8 0 Adjacency List source 0 1 2 3 4 5 6 7 8 9 Visited Table (T/F) T T T T F F F F T T Mark 3 as visited Mark Pred[3] 8 9 - 1 - - - - 2 8 Pred RDFS( 2 ) RDFS(8) RDFS(9) RDFS(1) RDFS(3) visit RDFS(4) Recursive calls

13 Graph / Slide 13 RDFS( 2 ) RDFS(8) RDFS(9) RDFS(1) RDFS(3) RDFS(4)  STOP all of 4’s neighbors have been visited return back to call RDFS(3) Example 2 4 3 5 1 7 6 9 8 0 Adjacency List source 0 1 2 3 4 5 6 7 8 9 Visited Table (T/F) T T T T T F F F T T Mark 4 as visited Mark Pred[4] 8 9 - 1 3 - - - 2 8 Pred Recursive calls

14 Graph / Slide 14 Example 2 4 3 5 1 7 6 9 8 0 Adjacency List source 0 1 2 3 4 5 6 7 8 9 Visited Table (T/F) T T T T T F F F T T 8 9 - 1 3 - - - 2 8 Pred RDFS( 2 ) RDFS(8) RDFS(9) RDFS(1) RDFS(3) visit 5 -> RDFS(5) Recursive calls Back to 3

15 Graph / Slide 15 Example 2 4 3 5 1 7 6 9 8 0 Adjacency List source 0 1 2 3 4 5 6 7 8 9 Visited Table (T/F) T T T T T T F F T T 8 9 - 1 3 3 - - 2 8 Pred RDFS( 2 ) RDFS(8) RDFS(9) RDFS(1) RDFS(3) RDFS(5) 3 is already visited, so visit 6 -> RDFS(6) Recursive calls Mark 5 as visited Mark Pred[5]

16 Graph / Slide 16 Example 2 4 3 5 1 7 6 9 8 0 Adjacency List source 0 1 2 3 4 5 6 7 8 9 Visited Table (T/F) T T T T T T T F T T 8 9 - 1 3 3 5 - 2 8 Pred RDFS( 2 ) RDFS(8) RDFS(9) RDFS(1) RDFS(3) RDFS(5) RDFS(6) visit 7 -> RDFS(7) Recursive calls Mark 6 as visited Mark Pred[6]

17 Graph / Slide 17 Example 2 4 3 5 1 7 6 9 8 0 Adjacency List source 0 1 2 3 4 5 6 7 8 9 Visited Table (T/F) T T T T T T T T T T 8 9 - 1 3 3 5 6 2 8 Pred RDFS( 2 ) RDFS(8) RDFS(9) RDFS(1) RDFS(3) RDFS(5) RDFS(6) RDFS(7) -> Stop no more unvisited neighbors Recursive calls Mark 7 as visited Mark Pred[7]

18 Graph / Slide 18 Example Adjacency List 0 1 2 3 4 5 6 7 8 9 Visited Table (T/F) T T T T T T T T T T 8 9 - 1 3 3 5 6 2 8 Pred RDFS( 2 ) RDFS(8) RDFS(9) RDFS(1) RDFS(3) RDFS(5) RDFS(6) -> Stop Recursive calls 2 4 3 5 1 7 6 9 8 0 source

19 Graph / Slide 19 Example Adjacency List 0 1 2 3 4 5 6 7 8 9 Visited Table (T/F) T T T T T T T T T T 8 9 - 1 3 3 5 6 2 8 Pred RDFS( 2 ) RDFS(8) RDFS(9) RDFS(1) RDFS(3) RDFS(5) -> Stop Recursive calls 2 4 3 5 1 7 6 9 8 0 source

20 Graph / Slide 20 Example Adjacency List 0 1 2 3 4 5 6 7 8 9 Visited Table (T/F) T T T T T T T T T T 8 9 - 1 3 3 5 6 2 8 Pred RDFS( 2 ) RDFS(8) RDFS(9) RDFS(1) RDFS(3) -> Stop Recursive calls 2 4 3 5 1 7 6 9 8 0 source

21 Graph / Slide 21 Example Adjacency List 0 1 2 3 4 5 6 7 8 9 Visited Table (T/F) T T T T T T T T T T 8 9 - 1 3 3 5 6 2 8 Pred RDFS( 2 ) RDFS(8) RDFS(9) RDFS(1) -> Stop Recursive calls 2 4 3 5 1 7 6 9 8 0 source

22 Graph / Slide 22 Example Adjacency List 0 1 2 3 4 5 6 7 8 9 Visited Table (T/F) T T T T T T T T T T 8 9 - 1 3 3 5 6 2 8 Pred RDFS( 2 ) RDFS(8) RDFS(9) -> Stop Recursive calls 2 4 3 5 1 7 6 9 8 0 source

23 Graph / Slide 23 Example Adjacency List 0 1 2 3 4 5 6 7 8 9 Visited Table (T/F) T T T T T T T T T T 8 9 - 1 3 3 5 6 2 8 Pred RDFS( 2 ) RDFS(8) -> Stop Recursive calls 2 4 3 5 1 7 6 9 8 0 source

24 Graph / Slide 24 Example Adjacency List 0 1 2 3 4 5 6 7 8 9 Visited Table (T/F) T T T T T T T T T T 8 9 - 1 3 3 5 6 2 8 Pred RDFS( 2 ) -> Stop Recursive calls 2 4 3 5 1 7 6 9 8 0 source

25 Graph / Slide 25 Example Adjacency List 0 1 2 3 4 5 6 7 8 9 Visited Table (T/F) T T T T T T T T T T 8 9 - 1 3 3 5 6 2 8 Pred Try some examples. Path(0) -> Path(6) -> Path(7) -> Check our paths, does DFS find valid paths? Yes. 2 4 3 5 1 7 6 9 8 0 source

26 Graph / Slide 26 Time Complexity of DFS (Using adjacency list) * We never visited a vertex more than once * We had to examine all edges of the vertices n We know Σ vertex v degree(v) = 2m where m is the number of edges * So, the running time of DFS is proportional to the number of edges and number of vertices (same as BFS) n O(n + m) * You will also see this written as: n O(|v|+|e|)|v| = number of vertices (n) |e| = number of edges (m)

27 Graph / Slide 27 DFS Tree Resulting DFS-tree. Notice it is much “deeper” than the BFS tree. Captures the structure of the recursive calls - when we visit a neighbor w of v, we add w as child of v - whenever DFS returns from a vertex v, we climb up in the tree from v to its parent

Download ppt "Depth-first search COMP171 Fall 2005. Graph / Slide 2 Depth-First Search (DFS) * DFS is another popular graph search strategy n Idea is similar to pre-order."

Similar presentations

CSE 390B: Graph Algorithms Based on CSE 373 slides by Jessica Miller, Ruth Anderson 1.

CSE 390B: Graph Algorithms Based on CSE 373 slides by Jessica Miller, Ruth Anderson 1.
Depth-First Search1 Part-H2 Depth-First Search DB A C E.

Depth-First Search1 Part-H2 Depth-First Search DB A C E.
Graphs CSC 220 Data Structure. Introduction One of the Most versatile data structures like trees. Terminology –Nodes in trees are vertices in graphs.

Graphs CSC 220 Data Structure. Introduction One of the Most versatile data structures like trees. Terminology –Nodes in trees are vertices in graphs.
Analysis of Algorithms Depth First Search. Graph A representation of set of objects Pairs of objects are connected Interconnected objects are called “vertices.

Analysis of Algorithms Depth First Search. Graph A representation of set of objects Pairs of objects are connected Interconnected objects are called “vertices.
1 Graphs Traversals In many graph problems, we need to traverse the vertices of the graph in some order Analogy: Binary tree traversals –Pre-order Traversal.

1 Graphs Traversals In many graph problems, we need to traverse the vertices of the graph in some order Analogy: Binary tree traversals –Pre-order Traversal.
Graph Theory, DFS & BFS Kelly Choi 08-07-2006. 08-07-20062 What is a graph? A set of vertices and edges –Directed/Undirected –Weighted/Unweighted –Cyclic/Acyclic.

Graph Theory, DFS & BFS Kelly Choi What is a graph? A set of vertices and edges –Directed/Undirected –Weighted/Unweighted –Cyclic/Acyclic.
Graph Search Methods A vertex u is reachable from vertex v iff there is a path from v to u. 2 3 8 10 1 4 5 9 11 6 7.

Graph Search Methods A vertex u is reachable from vertex v iff there is a path from v to u
CSE 373: Data Structures and Algorithms Lecture 19: Graphs III 1.

CSE 373: Data Structures and Algorithms Lecture 19: Graphs III 1.
Graph Search Methods A vertex u is reachable from vertex v iff there is a path from v to u. 2 3 8 10 1 4 5 9 11 6 7.

Graph Search Methods A vertex u is reachable from vertex v iff there is a path from v to u
Breadth-First and Depth-First Search

Breadth-First and Depth-First Search
1 Graphs: Traversal Searching/Traversing a graph = visiting the vertices of a graph by following the edges in a systematic way Example: Given a highway.

1 Graphs: Traversal Searching/Traversing a graph = visiting the vertices of a graph by following the edges in a systematic way Example: Given a highway.
Graph Search Methods Spring 2007 CSE, POSTECH. Graph Search Methods A vertex u is reachable from vertex v iff there is a path from v to u. A search method.

Graph Search Methods Spring 2007 CSE, POSTECH. Graph Search Methods A vertex u is reachable from vertex v iff there is a path from v to u. A search method.
© 2006 Pearson Addison-Wesley. All rights reserved14 A-1 Chapter 14 excerpts Graphs (breadth-first-search)

© 2006 Pearson Addison-Wesley. All rights reserved14 A-1 Chapter 14 excerpts Graphs (breadth-first-search)
CS 206 Introduction to Computer Science II 11 / 07 / 2008 Instructor: Michael Eckmann.

CS 206 Introduction to Computer Science II 11 / 07 / 2008 Instructor: Michael Eckmann.
Graphs By JJ Shepherd. Introduction Graphs are simply trees with looser restrictions – You can have cycles Historically hard to deal with in computers.

Graphs By JJ Shepherd. Introduction Graphs are simply trees with looser restrictions – You can have cycles Historically hard to deal with in computers.
Discrete Structures Lecture 13: Trees Ji Yanyan United International College Thanks to Professor Michael Hvidsten.

Discrete Structures Lecture 13: Trees Ji Yanyan United International College Thanks to Professor Michael Hvidsten.
Graph Traversals Visit vertices of a graph G to determine some property: Is G connected? Is there a path from vertex a to vertex b? Does G have a cycle?

Graph Traversals Visit vertices of a graph G to determine some property: Is G connected? Is there a path from vertex a to vertex b? Does G have a cycle?
Applications of graph traversals

Applications of graph traversals
Implementation of Graph Decomposition and Recursive Closures Graph Decomposition and Recursive Closures was published in 2003 by Professor Chen. The project.

Implementation of Graph Decomposition and Recursive Closures Graph Decomposition and Recursive Closures was published in 2003 by Professor Chen. The project.
Graph & BFS.

Graph & BFS.

Similar presentations

Ads by Google