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Homework answers / question archive / CMSC 351 (JWG) Homework 10 1

**CMSC 351 (JWG) Homework 10**

1. Given the adjacency matrix *AM *for a graph with *n *vertices and a list *V *of *k *vertices, write [25 pts] the pseudocode for a function istrail(AM,n,V,k) which would determine whether *V *specifies a trail, returning either TRUE or FALSE. What is the best- and worst-case Θ time complexity of your pseudocode?

**Solution:**

Given the adjacency list *AL *for a graph with *n *vertices and a list *V *of *k *vertices, write the [25 pts] pseudocode for a function iswalk(AL,n,V,k) which would determine whether *V *specifies a walk, returning either TRUE or FALSE. What is the best- and worst-case Θ time complexity of your pseudocde?

**Solution:**

Show the functioning of the shortest-path algorithm applied to the following graph with *s *= 1 [13 pts] and *t *= 3. Show the steps as we did in class (and in the notes) and show the queue at each step.

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**Solution:**

In the shortest path algorithm suppose the graph were weighted instead of unweighted. If the [12 pts]

line

dist[y] = dist[x] + 1

were replaced by

dist[y] = dist[x] + edgeweight(x to y)

would this effectively find the shortest total weighted distance from *s *to *t*? If so, explain why.

If not, explain why not and give an example graph to support your argument.

**Solution:**

5. Modify the shortest path algorithm so that it finds the shortest path from *s *to itself (a cycle) [25 pts] and returns FALSE if no such cycle exists.

**Solution:**

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