CS208 Week 5 Homework

CS208 Week 5 Homework - in Section 4.2 to justify your...

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D C B A S H G F E K J I M L Q R O N T V U W 4 E B 2 3 1 1 1 3 3 2 2 2 2 1 1 Z G F D C A CS208 - Week 5 Homework November 15, 2010 Discrete Math CS 208 Online 1. (Similar to Exercise 4.2 Question 30 on page 178) The city of Honigsberg, located on the banks of the Rregel River, had  eight bridges that connected islands in the river to the shores as illustrated below. It was the custom of the town people to  stroll on Friday afternoons and, in particular, to cross over the bridges. The people of Honigsberg wanted to know if it was  possible to stroll in such a way that it was possible to go over each bridge exactly once and return to the starting point.  (Question a) Is the problem looking for an Euler circuit or a Hamiltonian circuit? (Question b) Draw a graph with nodes and  edges to show the situation. (Question c) If there is a way, show the detailed circuit; otherwise, use an appropriate theorem 
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Unformatted text preview: in Section 4.2 to justify your answer. A. This problem is looking for a Euler Circuit. B. C. 2. (Similar to Exercise 4.3 Question 4 on page 190) Use the Breadth-first search algorithm to determine the distance and a shortest path from S to T in the graph. Use alphabetical order when there is a choice for a predecessor. To obtain the full credit, you must show the node label for each node (such as the one in Figure 4.31 on page 182). Node Labels S 0(-) H 4(G) Q 5(K) A 1(S) I 3(F) R 6(Q) B 4(G) J 3(F) U 6(O) C 5(B) K 4(G) V 5(K) D 6(C) L 5(H) W 6(Q) E 1(S) M 6(L) T 7(R) F 2(A) N 4(I) G 3(F) O 6(U) Shortest Path: S, A, F, G, K, Q, R, T 3. Node Labels A 0(-) B 2(A) C 5(F) D 3(B) E 4(D) F 3(A) G 5(E) Z 6(G) Shortest Path: A, B, D, E, G, Z...
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CS208 Week 5 Homework - in Section 4.2 to justify your...

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