1. MATH 310, FALL 2003 (Combinatorial Problem Solving) Lecture 14, Wednesday, October 1

2. Binary Search Tree Traversals (p.110) Binary search tree: r – Root L – left subtree R – right subtree Preorder: r,L,R cbafde Postorder: L,R,r abedfc Inorder: L,r,R abcdef c b a f d e

3. Review We will spend most of the time answering questions and solving problems for Test 1. Some terms to be used in Test 1: degree sequence graphical sequence Graphs Q(n),K(n),R(n),B(n) on the chessboard. Grid graph G(m,n) Generalized Petersen graph P(n,r) Triangle = C_3. Cubic graph Truncation of a vertex Triangle contraction S – set of binary strings. Graph G(S)

4. 4.1. Shortest Paths Homework (MATH 310#5W): Read 4.2. Do Exercise 4.1: 1,3,5,7,9 Volunteers: ____________ Problem: 9. No Section of Chapter 4 will be on Test 1. No Section of Chapter 4 will be on Test 1. Challenge (up to 5+5 pts.) Exercise 4.1. 13. Challenge (up to 5+5 pts.) Exercise 4.1. 13.

5. Dijkstra’s Algorithm At each step of the algorithm the (green) edge e between a labeled vertex p and unlabeled vertex q is selected in such a way, that d(p) + k(e) is minimal. a Labeled verticesb Unlabeled vertices p q a