CS211-Project 5 Infix Expression Evaluator Solved

Writ a C++ program that will evaluate an infix expression.  The algorithm REQUIRED for this program will use two stacks, an operator stack and a value stack.  Both stacks MUST be implemented using a dynamic array class (not struct) that you write.

 

The commands used by this system are listed below and are to come from standard input.  Your program is to prompt the user for input and display error messages for unknown commands.  The code in proj5Base.cpp already does this for you.   You are expected to use that code as the base for your project.  

 

Command
Description
q 
Quit the program.
? 
List the commands used by this program and a brief description of how to use each one.
<infixExpression  
Evaluate the given infix expression and display its result.
 

The <infixExpression will only use the operators of addition, subtraction, multiplication, division and the parentheses.  It will also only contain unsigned (i.e. positive) integer values.  We obviously could allow for more operators and more types of values, but the purpose of this assignment is to focus on writing C++ classes and not on complicated arithmetic expressions.   

 

Infix Expression are when the operators of addition, subtraction, multiplication and division are listed IN between the values.  Infix Expressions require the use of parentheses to express nonstandard precedence.   Examples of Infix Expressions are:

 

            42 + 64

            60 + 43 * 18 + 57

            (60 + 43) * (18 + 57)

            18 – 12 – 3  

            18 – (12 – 3)  

 

The simplest algorithm to evaluate an Infix Expression includes a translation from an Infix expression to a Postfix Expression and then evaluating the Postfix Expression.  The algorithm that we will use combines the translation and evaluation into a single algorithm.  So the following short discussion of Postfix expression may be useful in understanding our algorithm.  Note that all of these algorithms requires the use of stacks; hence, the reason for the stack class.

 

Postfix Expressions are when the operators of addition, subtraction, multiplication and division are list AFTER (i.e. “post”) the values.  Postfix Expression never require the use of parentheses to express non-standard precedence.  The fact that postfix expressions do not need parentheses makes them much easier to evaluate than infix expressions.   In fact, most computers first convert infix expression to a postfix expression and then evaluate that postfix expression.

 

A postfix expression is evaluated using a stack.  When a value is encountered, it is pushed onto the stack.   When an operator is encountered, two values are popped from the stack.  Those values are evaluated using the operation implied by the operator.  Then the result is pushed back onto the stack.   When the end of a postfix expression is encountered, the value on the top of the stack is the result of the expression.  There should only be one value on the stack when the end of the postfix expression is encountered.  

 

Examples of Postfix Expressions are:

 

            42 64 +

            60 43 18 * + 57 +

            60 43 + 18 57 + *

            18 12 – 3 –   18 12 3 –  –  

 

Both the algorithm to convert an infix expression to a postfix expression and the algorithm to evaluate a postfix expression require the use of stacks.  Note that the conversion algorithm requires a stack of operators, while the evaluation algorithm requires a stack of values.

 

For this program, you are to write the following methods for the dynamic array stack class:

 

            void init( );       
//  initialize the stack for use THIS MAY BE A CONSTRUCTOR
            bool isEmpty ( );    
// return true if the stack has no members
            void push (data);
// add the data to the top of stack; grow dynamic array if needed
            data top ( );       
// return the data value on the top of the stack
            void pop ( );     
// remove the data value from the top of the stack
            void reset ( );  
// “clear” the stack to remove any values it contains  
 

For this program, your dynamic array MUST start with 2 positions in the array. When the array needs to grow, it size MUST grow by 2 additional positions each time (note the array to grow in size from 2 to 4 to 6 to 8 to 10 to ...).  Note the init( ) method to set up the stack should really be a constructor (but could be a normal method).  You can also write a “topPop( )” method that combine both the top and pop operations in a single method.  Also, note that since the values from the infix expressions will all be integer values (we will only do integer division), and since the operators can all be represented as characters (which is a sub-class of integers), you are more than welcome to write a single stack class which store integers to be used for both stacks.   

  

The instance/variable containing for each stack MUST be declared as a local variable to some method (it may be as a local variable to a method other than main( )  ).  It may NOT be global.  Each operation performed on the stack MUST be done in its own method.  ALL data members of the stack class MUST use access modifier of private.  

             

Algorithm for Infix to Postfix Conversation and Postfix Evaluation 
When getting the input for an infix expression, the program proj5Base.cpp breaks everything down into “tokens”.  There are 3 types of tokens we are mostly concerned with: an OPERATOR token, a VALUE token and the EndOfLine token.  The code in the function processExpression() already checks for these token but you will need to add the code how to interact with the stacks.

First step:  

     Empty both the OperatorStack and the ValueStack  

Second Step:  

     While (the current token is not the EndOfLine Token)     if  ( the current token is a VALUE )                   push the value onto the ValueStack   if  ( the current token is an OPERATOR )                         if  ( the current operator is an Open Parenthesis )                              push the Open Parenthesis onto the OperatorStack                if ( the current operator is + or - )                               while ( the OperatorStack is not Empty   &&

                                                the top of the OperatorStack is +, -, * or / )

                                                            popAndEval (  )

                                    push the current operator on the OperatorStack                         if ( the current operator is * or / )                            while ( the OperatorStack is not Empty  &&

                                                the top of the OperatorStack is * or / )

                                                            popAndEval (  )

                                    push the current operator on the OperatorStack                         if ( the current operator is a Closing Parenthesis )                           while ( the Operator Stack is not Empty &&

                                                the top of the OperatorStack is not an Open Parenthesis )

                                                            popAndEval (  )

                                    if (the OperatorStack is Empty )

                                                            print an error message

else pop the Open Parenthesis from the OperatorStack

            get the next token from the input

 

Third Step:

     Once the EndOfLine token is encountered    while (the OperatorStack is not Empty )

                        popAndEval (  )

            Print out the top of the ValueStack at the result of the expression

            Popping the ValueStack should make it empty, print error if not empty

 

The error statements in the above algorithm should only occur if an invalid infix expression is given as input.  You are not required to check for any other errors in the input.

 

The above algorithm calls another algorithm called popAndEval ( ) which is shown below.  This algorithm plays a critical role in the overall Evaluation of our expressions.

 

            op = top (OperatorStack)          pop (OperatorStack)

v2 = top (ValueStack) pop (ValueStack) v1 = top (ValueStack) pop (ValueStack) v3 = eval ( v1, op, v2 )  

push (ValueStack, v3)

 

To keep some of the error handling/recovery simple for this project, if you are trying to perform a top operation on an empty ValueStack, print out an error message and return the value of -999.  If the operator op for eval ( ) is not one of *, /, + or -, print out and error message and return the value of -999.

 

Command Line Argument: Debug Mode  
 

Your program is to be able to take one optional command line argument, the -d flag. When this flag is given, your program is to run in "debug" mode. When in this mode, your program should display the operators and values as they are encountered in the input.  The printf statements for these are already included in the program proj5Base.cpp, so you just need to make them print only if the –d flag is given.

When the flag is not given, this debugging information should not be displayed. One simple way to set up a "debugging" mode is to use a boolean variable which is set to true when debugging mode is turned on but false otherwise. This variable may be a global variable.  Then using a simple if statement controls whether information should be output or not.  

if ( debugMode == TRUE )  printf (" Debugging Information \n");  

Provided Code for the User Inteface  
The code given in proj5Base.cpp should properly provide for the user interface for this program including all command error checking.  This program has no code for the stacks. It is your job to write the methods for the specified operations and make the appropriate calls.  Most of the changes to the existing program need to be made in the processExpression ( ) method.  

 

 

Note: the instances containing the operator stack and value stack are required to be a local variable in a function.  The function processExpression() is strongly suggested as the function in which to declared the instances of these stacks.

             

Use of Existing C++ Libraries
You are responsible to write the code for the dynamic array stacks yourself!  This is the primary purpose of this project.  Since the C++ Standard Template Libraries already contain a class called Stack, you should name your class something like MyStack to avoid confusion.

 

You are not allowed to use any of the classes from the C++ Standard Template Libraries in this program.  These classes include ArrayList, Vector, LinkedList, List, Set, Stack, HashMap, etc.  If you need such a class, you are to write it yourself.  These are sometimes called the C++ Standard Container Library.  A full listing of the C++ Standard Template Libraries can be found