a. Implement the word puzzle program using the algorithm described at the end of the chapter.
b. We can get a big speed increase by storing, in addition to each word W, all of W’s prefixes. (If one of W’s prefixes is another word in the dictionary, it is stored as a real word.) Although this may seem to increase the size of the hash table drastically, it does not, because many words have the same prefixes. When a scan is performed in a particular direction, if the word that is looked up is not even in the hash table as a prefix, then the scan in that direction can be terminated early. Use this idea to write an improved program to solve the word puzzle.
c. If we are willing to sacrifice the sanctity of the hash table ADT, we can speed up the program in part (b) by noting that if, for example, we have just computed the hash function for “excel,” we do not need to compute the hash function for “excels” from scratch. Adjust your hash function so that it can take advantage of its previous calculation.
d. In Chapter 2, we suggested using binary search. Incorporate the idea of using prefixes into your binary search algorithm. The modification should be simple. Which algorithm is faster?
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