#### CSCI 3104 - Algorithms - Spring 2011

### Problem Set #5

#### Due: 12pm, Feb 23rd, 2011

1. Text problem 3.8. (If using on-line book, ignore part (c))
2. Suppose you are trying to buy a digraph from a salesman Joe. You
tell Joe that your graph cannot have any odd-length cycles, and must
be strongly-connected. Joe says he has just the thing, and he shows
you just three edges of it: (a, b), (b, c) and (a, c). Explain why Joe
must be lying. (Note: there might be a LOT more edges, but you
have to base your answer on just the three you can see.)

3. Text problem 3.21.

4. Text problem 3.24. Justify the correctness and running time of your
algorithm. (Note that it says dag and **not** digraph. If we
ask the same problem about a digraph, there is no known polynomial-time
algorithm!)

5. A **chain of words** is a list of words where the i-th word is the (i-1)st
word with one extra character and some mixing of letters. For example,
AN, TAN, RANT, TRAIN, RETINA, NASTIER is a chain of length 6. Find the
longest chain you can in our
wordlist.

In order to do this, first build a dag. The dag will consist of
a node for each word (you might want to collapse words into a single node
when it makes sense to), and an edge from word x to word y if y can follow
x in a chain. Then run DFS from each source node in the dag and keep track
of the maximum depth you reach. Print out an example chain that has
maximum length (there will be a TON... just give one chain).