As an example, Figure 1213 shows how the algorithm processes in Java

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As an example, Figure 1213 shows how the algorithm processes
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Below each stack is the symbol read To the right of each stack, in boldface, is any output
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The Evaluator class will parse and evaluate infix expressions
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We now have the theoretical background required to implement a simple calculator Our calculator supports addition, subtraction, multiplication, division, and exponentiation We write a class template Evaluator that can be instantiated with the type in which the math is to be performed (presumably, int or double or perhaps a HugeInt class) We make a simplifying
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Figure 1213 Infix to postfix conversion
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assumption: Negative numbers are not allowed Distinguishing between the binary minus operator and the unary minus requires extra work in the scanning routine and also complicates matters because it introduces a nonbinary operator Incorporating unary operators is not difficult, but the extra code does not illustrate any unique concepts and thus we leave it for you to do as an exercise Figure 1214 shows the Evaluator class interface, which is used to process a single string of input The basic evaluation algorithm requires two 5tacks The first stack is used to evaluate the infix expression and generate the postfix expression It is the stack of operators declared at line 33 An enumerated type, TokenType,is declared at line 20; note that the symbols are listed in order of precedence Rather than explicitly outputting the postfix expression, we send each postfix symbol to the postfix machine as it is generated Thus we also need a stack that stores operands Consequently, the postfix machine stack, declared at line 34, is instantiated with NumericTypeNote that, if we did not have templates, we would be in trouble because the two
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We need two stacks: an stack and a stack for the postfix machine,
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m-stacks
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Evaluator class interface: evaluate infix expression NumericType: Must have standard set of arithmetic operators CONSTRUCTION: with a string ******************PUBLIC OPERATIONS***********************
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7 / / NumericType getvalue( ) - - > Return value of infix expression 8 / / ******************ERRORS********************************** 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42
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/ / Some error checking is performed
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#include <stdlibh> #include <mathh> #include < fstream> #include <iostream> #include <sstream> #include <vector> #include <string> using namespace std; enum TokenType
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EOL, VALUE, OPAREN, CPAREN, EXP, MULT, DIV, PLUS, MINUS } ;
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template <class NumericType> class Evaluator
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public: Evaluator( const string & s ) { opStackpush-back( EOL ) ; NumericType getvalue(
str( s
/ / Do the evaluation
private: vector<TokenType> opStack; / / Operator stack for conversion vector<NumericType> postFixStack; / / Postfix machine stack istringstream str;
/ / The character stream
/ / Internal routines NumericType getTop ( ) ; / / Get top of postfix stack void binaryOp( TokenType topop ) ; / / Process an operator void processToken( const Token<NumericType> & lastToken ) ;
Figure 1214 The Evaluator class interface
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1 template <class NumericType> 2 class Token 3 I 4 public: 5 Token( TokenType tt = EOL, const NumericType 6 : theType ( tt ) , thevalue ( nt ) { 1
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
TokenType getType( ) const { return theType; } const NumericType & getvalue( { return thevalue; ) private: TokenType theType; NumericType thevalue;
const
template <class NumericType> class Tokenizer
public: Tokenizer ( istream & is ) : in( is Token<NumericType> getToken( ) ; private: istream
Figure 1215 The Token class and Tokenizer class interface
stacks hold items of different types* The remaining data member is an istringstream object used to step through the input line" As was the case with the balanced symbol checker, we can write a Tokenizer class that can be used to give us the token sequence Although we could reuse code, there is in fact little commonality, so we write a Tokenizer class for this application only Here, however, the tokens are a little more complex because, if we read an operand, the type of token is VALUE, but we must also know what the value is that has been read Thus we define both a Tokeni zer class and a Token class, shown in Figure 1215 A Token Stores both a TokenType,and if the token is a VALUE, its numeric value Accessors can be used to obtain information about a token (The
2 We use vector instead of the stack adapter since it provides basic stack operations via push-back,pop-back, and back 3 The istringstream function is not yet available on all compilers The online code has a deprecated replacement for older compilers See the online README file for detalls