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Lecture 11

Lecture 11. CSE 331 Sep 20, 2019. Mini Project group due week from Monday!. Please respect the TAs. HW 3 is out!. Solutions to HW 2. Handed out at the end of the lecture. Graded HW 1. Should be released by tonight. Formally define everything.

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Lecture 11

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  1. Lecture 11 CSE 331 Sep 20, 2019

  2. Mini Project group due week from Monday!

  3. Please respect the TAs

  4. HW 3 is out!

  5. Solutions to HW 2 Handed out at the end of the lecture

  6. Graded HW 1 Should be released by tonight

  7. Formally define everything http://imgs.xkcd.com/comics/geeks_and_nerds.png

  8. Distance between u and v Length of the shortest length path between u and v 1 Distance between RM and BO?

  9. Tree Connected undirected graph with no cycles

  10. Rooted Tree

  11. A rooted tree AC’s child=SG Pick any vertex as root SG’s parent=AC Let the rest of the tree hang under “gravity”

  12. Every n vertex tree has n-1 edges

  13. Every n vertex tree has n-1 edges Let G be an undirected graph on n nodes Then ANY two of the following implies the third: T is connected T has no cycles T has n-1 edges

  14. Rest of Today’s agenda Algorithms for checking connectivity

  15. Checking by inspection

  16. What about large graphs? s t Are s and t connected?

  17. Brute-force algorithm? List all possible vertex sequences between s and t nn such sequences Check if any is a path between s and t

  18. Algorithm motivation all

  19. Breadth First Search (BFS)

  20. Connectivity Problem Input: Graph G = (V,E) and s in V Output: All t connected to s in G

  21. Breadth First Search (BFS) Build layers of vertices connected to s L0= {s} Assume L0,..,Ljhave been constructed Lj+1set of vertices not chosen yet but are connected by an edge to Lj Stop when new layer is empty

  22. BFS Tree BFS naturally defines a tree rooted at s Add non-tree edges Lj forms the jth “level” in the tree u in Lj+1is child of v in Lj from which it was “discovered” L0 1 7 1 9 2 3 L1 2 3 8 0 4 7 8 L2 5 5 4 6 6 L3

  23. Today’s agenda Computing Connected component

  24. Computing Connected Component Explore(s) Start with R = {s} While exists (u,v) edge v not in R and u in R Add v to R Output R* = R

  25. Questions?

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