1. Lecture 15 CSE 331 Oct 7, 2009

2. Mid-term stuff Chapters 1-3 in [KT] Sample mid-term (and graded HW3) at the END of class The web version has the correct spacing Proctors Hung NgoSwapnoneel Roy Yang Wang

3. BFS Implementation BFS(u) Discovered[u] = T and Discovered[v] = F for every v≠ u Set i = 0 Set L 0 = {u} While L i is not empty L i+1 = Ø For every u in L i Consider every edge (u,v) If Discovered[v] = F then Discovered[v] = T Add v to L i+1 i++ Array Linked List Input graph as Adjacency list

4. Today’s agenda BFS implementation runs in O(m+n) time Can the runtime be improved? Topological sort (?)

5. Reading Assignment Sec 3.3, 3.4 and 3.5 of [KT]

6. Directed graphs Model asymmetric relationships Precedence relationships u needs to be done before v means (u,v) edge

7. Directed graphs Adjacency matrix is not symmetric Each vertex has two lists in Adj. list rep.

8. Directed Acyclic Graph (DAG) No directed cycles Precedence relationships are consistent

9. Topological Sorting of a DAG Order the vertices so that all edges go “forward”