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References
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If you are interested in computer games, a good starting point for information is the article cited in [ l l In this special issue of the journal, devoted exclusively to the subject, you will also find plenty of information and references to other works covering Chess, Checkers, and other computer games
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1 K Lee and S Mahajan, "The Development of a World Class Othello Program," ArtiJicial Intelligence 43 (1990), 21-36
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12
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Stacks are used extensively in compilers In this chapter we present two simple components of a compiler: a balanced symbol checker and a simple calculator We do so to show simple algorithms that use stacks and to show how the STL classes described in 7 are used In this chapter, we show: how to use a stack to check for balanced symbols, how to use a state machine to parse symbols in a balanced symbol program, and how to use operator precedence parsing to evaluate infix expressions in a simple calculator program
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As discussed in Section 72, compilers check your programs for syntax errors Frequently, however, a lack of one symbol (such as a missing * / comment-ender or 1) causes the compiler to produce numerous lines of diagnostics without identifying the real error A useful tool to help debug compiler error messages is a program that checks whether symbols are balanced In other words, every { must correspond to a 1, every [ to a l , and so on However, simply counting the numbers of each symbol is insufficient For example, the sequence [ ( ) 1 is legal, but the sequence [ ( I ) is wrong
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A stack is useful here because we know that when a closing symbol such as is seen, it matches the most recently seen unclosed ( Therefore, by placing an opening symbol on a stack, we can easily determine whether a closing symbol makes sense Specifically, we have the following algorithm
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A stack can be used detect mismatched symbols
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Symbols: ( [
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eof*
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Errors (indicated by *): (when expecting) (with no matching opening symbol
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[ unmatched at end of input
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Stack operations in a balanced-symbol algorithm
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1 Make an empty stack 2 Read symbols until the end of the file a If the symbol is an opening symbol, push it onto the stack b If it is a closing symbol do the following i If the stack is empty, report an error ii Otherwise, pop the stack If the symbol popped is not the corresponding opening symbol, report an error 3 At the end of the file, if the stack is not empty, report an error
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Symbols in comments, string constants, and character constants need not be balanced
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Line numbers are needed for meaningful error messages
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In this algorithm, illustrated in Figure 121, the fourth, fifth, and sixth symbols all generate errors The > is an error because the symbol popped from the top of stack is a (, so a mismatch is detected The ) is an error because the stack is empty, so there is no corresponding ( The [ is an error detected when the end of input is encountered and the stack is not empty To make this technique work for C++ programs, we need to consider all the contexts in which parentheses, braces, and brackets need not match For example, we should not consider a parenthesis as a symbol if it occurs inside a comment, string constant, or character constant We thus need routines to skip comments, string constants, and character constants A character constant in C++ can be difficult to recognize because of the many escape sequences possible, so we need to simplify things We want to design a program that works for the bulk of inputs likely to occur For the program to be useful, we must not only report mismatches but also attempt to identify where the mismatches occur Consequently, we keep track of the line numbers where the symbols are seen When an error is encountered, obtaining an accurate message is always difficult If there is an extra 1 , does that mean that the > is extraneous Or was a I missing earlier