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expression tree A tree in which the leaves contain operands and the other nodes contain operators (p 432) infix expression An expression in which a binary operator has arguments to its left and right When there are several operators, precedence and associativity determine how the operators are processed (P 420) lexical analysis The process of recognizing tokens in a stream of symbols (p 41 1) operator precedence parsing An algorithm that converts an infix expression to a postfix expression in order to evaluate the infix expression (p 422) postfix expression An expression that can be evaluated by a postfix machine without using any precedence rules (p 421) postfix machine Machine used to evaluate a postfix expression The algorithm it uses is as follows: Operands are pushed onto a stack and an operator pops its operands and then pushes the result At the end of the evaluation, the stack should contain exactly one element, which represents the result (p 421)
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precedence table A table used to decide what is removed from the operator stack Left-associative operators have the operator stack precedence set at 1 higher than the input symbol precedence Rightassociative operators go the other way (p 430) state machine A common technique used to parse symbols; at any point, the machine is in some state, and each input character takes it to a new state Eventually, the state machine reaches a state at which a symbol has been recognized (p 414) tokenization The process of generating the sequence of symbols (tokens) from an input stream (p 41 1 )
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1 In production code, input errors must be handled as carefully as possible Being lax in this regard leads to programming errors 2 For the balanced symbol routine, handling quotes incorrectly is a common error 3 For the infix to postfix algorithm, the precedence table must reflect the correct precedence and associativity
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Both application programs are available You should probably download the balancing program; it may help you debug other C++ programs
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Balancecpp Tokeni2erh Tokenizercpp 1nfixcpp
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Contains the balanced symbol program Contains the Tokenizer class interface for checking C++ programs (Figure 122) Contains the Tokenizer class implementation for checking C++ programs Contains the expression evaluator, instantiated for int
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121 Show the result of running the balanced symbol program on a 1 b ( I c [ [ [
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122 Show the postfix expression for a 1 + 2 - 3 " 4 b l A 2 - 3 "4 c 1 + 2 * 3 - 4 ^ 5 + 6 d ( 1 + 2 ) * 3 - ( 4 ^ ( 5 - 6 )
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123 For the infix expression a + b c * d * e f - g - h / ( i + j ) , do the following a Show how the operator precedence parsing algorithm generates the corresponding postfix expression b Show how a postfix machine evaluates the resulting postfix expression c Draw the resulting expression tree
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124 For the balanced symbol program, explain how to print out an error message that is likely to reflect the probable cause 125 In general terms, explain how unary operators are incorporated into expression evaluators Assume that the unary operators precede their operands and have high precedence Include a description of how they are recognized by the state machine
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126 Use of the operator for exponentiation is likely to confuse C++ programmers (because it is the bitwise exclusive-or operator) Rewrite the Evaluator class with * * as the exponentiation operator
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127 The infix evaluator accepts illegal expressions in which the operators are misplaced a What will 1 2 3 + * be evaluated as b How can we detect these illegalities c Modify the Evaluator class to do so
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