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decide whether a word is in the word list If we use a linear search, we lose If we use a good data structure, we can expect an efficient search If the word list is sorted, which is to be expected for an online dictionary, we can use a binary search (shown in Figure 612) and perform each check in roughly log W string comparisons For 40,000 words doing so involves perhaps 16 comparisons per check, for a total of less than 3,000,000 string comparisons This number of comparisons can certainly be done in a few seconds and is a factor of 100 better than the previous algorithm We can further improve the algorithm based on the following observation Suppose that we are searching in some direction and see the character sequence qx An English dictionary will not contain any words beginning with q x SO is it worth continuing the innermost loop (over all word lengths) The answer obviously is no: If we detect a character sequence that is not a prefix of any word in the dictionary, we can immediately look in another direction This algorithm is given by the following pseudocode:

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for each row R for each column C for each direction D for each word lengch L cneck if L chars star~inga r row R column C in direction D form a word i f they do not form a prefix, / / the innermost loop break;

If a character Sequence is not a prefix of any word in the dictionary, we can terminatesearching in that direction

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The only remaining algorithmic detail is the implementation of the prefix test: Assuming that the current character sequence is not in the word list, how can we decide whether it is a prefix of some word in the word list The answer turns out to be simple Recall from Section 742 that the lower-bound STL function returns the position of the smallest element that is at least as large as the target The caller can easily check on whether a match is found If a match is not found, verifying that the character sequence is a prefix of some word in the list also is easy, because, if it is, it must be a prefix of the word in the returned position (in Exercise 1 I 3 you are asked to prove this outcome)

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Our C++ implementation follows the algorithm description almost verbatim We design a Puzzle class to store the grid and word list as well as the corresponding input streams The class interface is shown in Figure 1 12 The public part of the class consists of a constructor and a single member function, solvepuzzl e The private part includes the data members and supporting routines

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

/ / Puzzle class interface: solve word search puzzle // / / CONSTRUCTION: with no initializer / / ******************pUBLIC OPERATIGNS********************** / / int Solvepuzzle( i // -->

#include < stream> #include <string> #include <vector> #include <algorithm> #include "matrixhN using namespace std; class Puzzle

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public: Puzzle( ) ; int solvePuzzle(

const;

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