Parsing Expressions in VS .NET

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Parsing Expressions
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char expstr[80]; cout << "Enter a period to stop\n"; parser ob; // instantiate a parser for(;;) { cout << "Enter expression: "; cingetline(expstr, 79); if(*expstr=='') break; cout << "Answer is: " << obeval_exp(expstr) << "\n\n"; }; return 0; }
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Enter a period to stop Enter expression: 10-2*3 Answer is: 4 Enter expression: (10-2)*3 Answer is: 24 Enter expression: 10/3 Answer is: 333333 Enter expression:
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Understanding the Parser
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To understand exactly how the parser evaluates an expression, work through the following expression (Assume that exp_ptr points to the start of the expression) 10 3 * 2 When eval_exp( ), the entry point into the parser, is called, it gets the first token If the token is null, the function prints the message No Expression Present and returns However, in this case, the token contains the number 10 Since the first token is not null, eval_exp2( ) is called As a result, eval_exp2( ) calls eval_exp3( ), and eval_exp3( ) calls
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eval_exp4( ), which in turn calls eval_exp5( ) Then eval_exp5( ) checks whether the token is a unary plus or minus, which in this case it is not, so eval_exp6( ) is called At this point eval_exp6( ) either recursively calls eval_exp2( ) (in the case of a parenthesized expression) or calls atom( ) to find the value of a number Since the token is not a left parentheses, atom( ) is executed and result is assigned the value 10 Next, another token is retrieved, and the functions begin to return up the chain Since the token is now the operator , the functions return up to eval_exp2( ) What happens next is very important Because the token is , it is saved in op The parser then gets the next token, which is 3, and the descent down the chain begins again As before, atom( ) is entered The value 3 is returned in result, and the token * is read This causes a return back up the chain to eval_exp3( ), where the final token 2 is read At this point, the first arithmetic operation occurs the multiplication of 2 and 3 The result is returned to eval_exp2( ), and the subtraction is performed The subtraction yields the answer 4 Although the process may at first seem complicated, work through some other examples to verify that this method functions correctly every time This parser would be suitable for use by a simple desktop calculator, as is illustrated by the previous program Before it could be used in a computer language, database, or in a sophisticated calculator, however, it would need the ability to handle variables This is the subject of the next section
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Adding Variables to the Parser
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All programming languages, many calculators, and spreadsheets use variables to store values for later use Before the parser can be used for such applications, it needs to be expanded to include variables To accomplish this, you need to add several things to the parser First, of course, are the variables themselves As stated earlier, we will use the letters A through Z for variables The variables will be stored in an array inside the parser class Each variable uses one array location in a 26-element array of doubles Therefore, add the following to the parser class:
double vars[NUMVARS]; // holds variables' values
You will also need to change the parser constructor, as shown here
// parser constructor parser::parser() { int i; exp_ptr = NULL;
40:
Parsing Expressions
for(i=0; i<NUMVARS; i++) vars[i] = 00; }
As you can see, the variables are initialized to 0 as a courtesy to the user You will also need a function to look up the value of a given variable Because the variables are named A through Z, they can easily be used to index the array vars by subtracting the ASCII value for A from the variable name The member function find_var( ), shown here, accomplishes this:
// Return the value of a variable double parser::find_var(char *s) { if(!isalpha(*s)){ serror(1); return 00; } return vars[toupper(*token)-'A']; }
As this function is written, it will actually accept long variable names, but only the first letter is significant You may modify this to fit your needs You must also modify the atom( ) function to handle both numbers and variables The new version is shown here:
// Get the value of a number or a variable void parser::atom(double &result) { switch(tok_type) { case VARIABLE: result = find_var(token); get_token(); return; case NUMBER: result = atof(token); get_token(); return; default: serror(0); } }
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