1. CSC 172 DATA STRUCTURES

2. Traversing graphs Depth-First Search Breath-First Search
like a post-order traversal of a tree
Breath-First Search
Less like tree traversal

3. Traversing graphs Depth-First Search Breath-First Search
like a post-order traversal of a tree
Breath-First Search
Less like tree traversal
Priority-First Search
Good for Shortest Path
Dijkstra's Algorithm

4. Breadth-First Search Unweighted Shortest Path
Starting vertex has level 0 (anchor vertex)
Visit (mark) all vertices that are only one edge away
mark each vertex with its “level”
One edge away from level 0 is level 1
One edge away from level 1 is level 2
Etc

5. Example A B C D E F G H I J K L M N O P

6. Example A B C D E F G H I J K L M N O P

7. Example A B C D E F G H I J K L M N O P

8. Example 1 A B C D E F G H I J K L M N O P

9. Example 1 A B C D E F G H I J K L M N O P

10. Example 2 1 A B C D E F G H I J K L M N O P

11. Example 2 1 A B C D E F G H I J K L M N O P

12. Example 2 1 3 A B C D E F G H I J K L M N O P

13. Example 2 1 3 A B C D E F G H I J K L M N O P

14. Example 2 1 3 A B C D E F G H I J K 4 L M N O P

15. Example 2 1 3 A B C D E F G H I J K 4 L M N O P

16. Example 2 1 3 A B C D E F G H I J K 4 L M N O P

17. Example 2 1 3 A B C D E F G H I J K 4 L M N O P

18. Example 2 1 3 A B C D E F G H I J K 4 L 5 M N O P

19. Example 2 1 3 A B C D E F G H I J K 4 L 5 M N O P

20. BFS Tree 2 1 3 A B C D E F G H I J K 4 L 5 M N O P

21. Dijkstra's Algorithm // for each Vertex v { v.dist = infinity ;
v.known = false ; }

22. Dijkstra's Algorithm while (there is an unknown vertex) {
v = delMin() ; // get the next one off the queue
v.known = true ;
for each Vertex w adjacent to v {
if (!w.known) {
if (v.dist + dist_v2w < w.dist){
w.dist = vdist + dist_v2w ;
enqueue(w) ]