The solvepuzz le routine for searching in all directions from all starting points in Java

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The solvepuzz le routine for searching in all directions from all starting points
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and extend the string while ensuring that we do not go past the grid's boundary At line 28 we tack on the next character, using operator+=,and perform a binary search at line 31 If we do not have a prefix, we can stop looking and return Otherwise, we know that we have to continue after checking at line 36 for a possible exact match Line 44 returns the number of matches found when the call to solvenirect ion can find no more words A simple main program is shown in Figure 1 19
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112 The Game of Tic-Tac-Toe
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Recall from Section 87 a simple algorithm, known as the minimax strategy, allows the computer to select an optimal move in a game of Tic-TacToe This recursive strategy involves the following decisions
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1 A terminal position can immediately be evaluated, so if the position is terminal return its value 2 Otherwise, if it is the computer's turn to move, return the maximum value of all positions reachable by making one move The reachable values are calculated recursively 3 Otherwise, it is the human player's turn to move Return the minimum value of all positions reachable by making one move The reachable values are calculated recursively
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The minimaxstrategy examines lots Of positions We can get by with less without losing any information
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/ / Return true if prefix is a prefix of word boo1 isprefix( const string & prefix, const string
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word
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if( wordlength( ) < prefixlength( return false; for( int i = 0 ; i < prefixlength( if( prefix[ i I !=word[ i I ) return false; return true;
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/ / Search the grid from a starting point and direction int Puzzle::solveDirection( int baseRow, int baseCol, int rowDelta, int colDelta ) const i string word; int numatches = 0;
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word
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theBoard[ baseRow I[ baseCol
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for( int i = baseRow + rowDelta, j = baseCol + colDelta; i >= 0 & & j > = 0 && i < theBoardnumrows( ) & & j < theBoardnumcols( ) ; i + = rowDelta, j += colDelta )
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word + = theBoard[ i I
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vector~string~::const~iterator itr; itr = lower-bound( theWordsbegin( ) if( itr == theWordsend( break; if ( *itr == word
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theWordsend(
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!isprefix( word, *itr
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numatches++; cout < < "Found " << word << " at " << baseRow << " " < < baseCol << " to " << i << " " << j << endl;
return numMatches;
Implementation of a single search
The Game of Tic-Tac-Toe
1 / / Simple main routine for word search puzzle problem 2 int main( )
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Puzzle p; cout << "Found " < < psolvePuzzle( return 0 ;
<< " matches" << endl;
A simple main routine for the word search puzzle problem
1121 Alpha-Beta Pruning
Although the minimax strategy gives an optimal tic-tac-toe move, it performs a lot of searching Specifically, to choose the first move, it makes roughly a half-million recursive calls One reason for this large number of calls is that the algorithm does more searching than necessary Suppose that the computer is considering five moves: C,, C,, C3,C4,and C, Suppose also that the recursive evaluation of C, reveals that C, forces a draw Now C2 is evaluated At this stage, we have a position from which it would be the human player's turn to move Suppose that in response to C,, the human player can consider H2a,H2b, H2c,and HZdFurther, suppose that an evaluation of H2, shows a forced draw Automatically, C2 is at best a draw and possibly even a loss for the computer (because the human player is assumed to play optimally) Because we need to improve on C,, we do not have to evalis uate any of H,,, H,,, and Hz, We say that H2n a refutation, meaning that it proves that C, is not a better move than what has already been seen Thus we return that C, is a draw and keep C , as the best move seen so far, as shown in Figure 1 110 In general, then, a refutation is a countermove that proves that a proposed move is not an improvement over moves previously considered We do not need to evaluate each node completely; for some nodes, a refutation suffices and some loops can terminate early Specifically, when the human player evaluates a position, such as C2,a refutation, if found, is just as good as the absolute best move The same logic applies to the computer At anv ~ o i nin the search a l ~ h a the value that the human laver has to refute t is , , and beta is the value that the computer has to refute When a search is done on the human player's side, any move less than alpha is equivalent to alpha; when a search is done on the computer side, any move greater than beta is equivalent to beta This strategy of reducing the number of positions evaluated in a minimax search is commonly called alpha-beta pruning As Figure 1 I 1 1 shows, alpha-beta pruning requires only a few changes to chooseMove Both alpha and beta are passed as additional parameters
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A refutation is a Countermovethat proves that a proposed move is not an improvement over moves previously considered If we find a refutation, we do not have to examine any more moves and the recursive call can return
Alpha-beta pruning Is to reduce the number of positions evaluated in a minimax search Alpha is thevaluethat the human player has to refute, and beta is the value that the computer has to