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Lecture 14

Lecture 14. CSE 331 Sep 27, 2013. HW 3 due today. Place Q1, Q2 and Q3 in separate piles. I will not accept HWs after 1:15pm. Other HW related stuff. HW 4 has been posted online: see piazza. Solutions to HW 3 at the END of the lecture. Graded HW 2 available from Monday onwards.

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Lecture 14

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  1. Lecture 14 CSE 331 Sep 27, 2013

  2. HW 3 due today Place Q1, Q2 and Q3 in separate piles I will not accept HWs after 1:15pm

  3. Other HW related stuff HW 4 has been posted online: see piazza Solutions to HW 3 at the END of the lecture Graded HW 2 available from Monday onwards

  4. 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

  5. Questions?

  6. HW 3 due today Place Q1, Q2 and Q3 in separate piles I will not accept HWs after 1:15pm

  7. BFS all

  8. Depth First Search (DFS) http://xkcd.com/761/

  9. DFS(u) Mark u as explored and add u to R For each edge (u,v) If v is not explored then DFS(v)

  10. Why is DFS a special case of Explore?

  11. A DFS run DFS(u) Every non-tree edge is between a node and its ancestor 1 u is explored 1 7 For every unexplored neighbor v of u 2 2 3 DFS(v) 8 4 4 5 5 DFS tree 6 6 3 8 7

  12. Questions?

  13. Connected components are disjoint Either Connected components of s and t are the same or are disjoint Algorithm to compute ALL the connected components? Run BFS on some node s. Then run BFS on t that is not connected to s

  14. Reading Assignment Sec 3.2 in [KT]

  15. Rest of today’s agenda Run-time analysis of BFS (DFS)

  16. Stacks and Queues Last in First out First in First out

  17. But first… How do we represent graphs?

  18. Graph representations 1 0 1 0 1 0 Better for sparse graphs and traversals 0 1 0 Adjacency matrix Adjacency List O(1) O(n) [ O(nv) ] (u,v) in E? All neighbors of u? O(n) O(nu) O(n2) Space? O(m+n)

  19. 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 to Lj Stop when new layer is empty Use CC[v] array Use linked lists

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