Assignment 2: Ordered Word Ladders

An ordered word ladder ('owl') is an alphabetically-ordered sequence of words where each word in the sequence differs from its predecessor by one action:

1. changing one letter, e.g. barn→born

2. adding or removing one letter, e.g. band→brand and bran→ran

The following are examples of word ladders of different length:

• ban→bar→boar→boat→goat, length 5

• an→can→cane→dane→date→mate→mite→site→size, length 9

Phase 1

At the heart of the assignment is a function that compares 2 arbitrary null-terminated strings and returns true if the strings satisfy one of the 2 conditions above, and false otherwise. This function has signature:

   1 bool differByOne(char *, char *)

Write such a function and of course test it.

Phase 2

Generate a graph that represents all the words in the input that differ by one. Each word is represented by a vertex in the graph, and vertices are adjacent if the corresponding words differ by one. The words can be found on stdin, and are in dictionary order, and will have white space between them (which means they may be all on one line, or spread out over many lines). You may assume that they consist of just lower-case letters (a-z) in this assignment (so no punctuation, hyphens, capital letters ...). As you will be building graphs, you must use the graph ADT provided in lectures (use the Adjacency Matrix version).

For example, if a dictionary consists of the 7 words an ban bean ben hen mean men then the graph that represents all ordered word ladders would be drawn as:

             0
             |
             1 
           /   \
          2 --- 3
          |    / \
          5   6---4

where the vertices 0..6 represent the 7 words in the given order. There are lots of ordered word ladders in this graph: for example, 0→1→2→5 representing an→ban→bean→mean. Any path between any two vertices in the graph is an owl, but notice although the edges are undirected, you can select only vertices in ascending order (hence the term 'ordered' in 'owl'). There is only one ladder of length 6 for this dictionary, and that is 0→1→2→3→4→6.

In this phase you are asked to create a graph for a dictionary, and print the graph.

• Input The words in the dictionary should be read from stdin. They may appear along the line, or spread over many lines, but must be sorted in dictionary order. For example:

   an ban bean ben hen mean men

• Output Print the dictionary and the resulting graph. As you will be using the Graph ADT you should simply call showGraph(). For the example above, the output would look like:

   Dictionary
   0: an
   1: ban
   2: bean
   3: ben
   4: hen
   5: mean
   6: men
   Ordered Word Ladder Graph
   V=7, E=9
   <0 1> 
   <1 0> <1 2> <1 3> 
   <2 1> <2 3> <2 5> 
   <3 1> <3 2> <3 4> <3 6> 
   <4 3> <4 6> 
   <5 2> <5 6>
   <6 3> <6 4> <6 5>  

Phase 3

Now a more 'formal' specification:

• input Your program should read the format described in lectures: a #integer followed by an arbitrary number of pair of edges

For example, if a dictionary consists of the 12 words case cast cat cats cave cost cove love post sale save suave then the graph that represents all ordered word ladders would be drawn as:

             0         9
           /   \       |
          1     4      10
         / \   / \
        2   5 6  10
        |   | |   |
        3   8 7  11

where the vertices 0..11 represent the 12 words in the given order.