Interface for class TicTacToe in Java

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Interface for class TicTacToe
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/ / Return the static value of the current position int TicTacToe::positionValue( ) const
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return isAWin( COMPUTER isAWin( HUMAN ) boardIsFul1 ( )
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COMPUTER-WIN HUMAN-WIN DRAW
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UNCLEAR;
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Supporting routine for evaluating positions
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Alpha-beta pruning is an improvement to the minimax algorithm
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This approach suggests a recursive algorithm to determine the value of a position Keeping track of the best move is a matter of bookkeeping once the basic algorithm to find the value of the position has been written If the position is a terminal position (ie, we can see right away that tic-tac-toe has been achieved or the board is full without tic-tac-toe), the position's value is immediate Otherwise, we recursively try all moves, computing the value of each resulting position, and choose the maximum value The recursive call then requires that the human player evaluate the value of the position For the human player the value is the minimum of all the possible next moves because the human player is trying to force the computer to lose Thus the recursive function chooseMove,shown in Figure 828 takes a parameter s, which indicates whose turn it is to move Lines 1 1 and 12 handle the base case of the recursion If we have an immediate answer, we can return Otherwise, we set some values at lines 14 to 21, depending on which side is moving The code in lines 28 to 38 is executed once for each available move We try the move at line 28, recursively evaluate the move at line 29 (saving the value), and then undo the move at line 30 Lines 33 and 34 test to determine whether this move is the best seen so far If so, we adjust value at line 36 and record the move at line 37 At line 41 we return the value of the position; the move is stored in the parameters bestRow and bestcolumn,which are passed by reference Although the routine shown in Figure 828 optimally solves tic-tac-toe, it performs a lot of searching Specifically, to choose the first move on an empty board, it makes 549,946 recursive calls (this number is obtained by running the program) By using some algorithmic tricks, we can compute the same information with fewer searches One such technique is known as alpha-beta pruning, which is an improvement to the minimax algorithm We describe this technique in detail in 1 1 Application of alpha-beta pruning reduces the number of recursive calls to only 18,297
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In this chapter we examined recursion and showed that it is a powerful problem-solving tool Following are its fundamental rules, which you should never forget 1 Base cases: Always have at least one case that can be solved without using recursion 2 Make progress: Any recursive call must progress toward the base case 3 "You gotta believe ":Always assume that the recursive call works
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1 / / Routine to compute optimal tic-tac-toe move 2 int TicTacToe::chooseMove( Side s , int & bestRow, 3 int & bestcolumn ) 4 { 5 Side opp; / / The other side 6 int reply; / / value of opponent's reply 7 int dc; / / placeholder 8 int simpleEva1; / / Result of an immediate evaluation 9 int value; 10 11 if( ( simpleEva1 = positionvalue( ) ) ! = UNCLEAR ) 12 return simpleEva1; 13 if ( s == COMPUTER ) 14 15 i 16 opp = HUMAN; value = HUMAN-WIN; 17 1 18 else 19 i 20 opp = COMPUTER; value = COMPUTER-WIN; 21 } 22 23 / / Search for a move 24 for( int row = 0 ; row < 3 ; row++ ) 25 for( int column = 0; column < 3 ; column++ ) 26 if( squareIsEmpty( row, column ) ) 27 { 28 place( row, column, s ) ; / / Try a move; then 29 reply = chooseMove( opp, dc, dc ) ; / / Evaluate; 30 place( row, column, EMPTY ) ; / / then undo 31 32 i/ If s gets a better position; update 33 if( s == COMPUTER && reply > value / / 34 s == HUMAN & & reply < value ) 35 ( 36 value = reply; 37 bestRow = row; bestColumn = column; 38 } 39 1 40 41 return value; 42 1
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