In the lecture notes and video lectures for Stacks and Queues : Sections 3 7 we discussed an application that evaluates an arithmetic expression written in infix notation such as:
(-1 - -2) * -(3 / 5)
Infix notation is the usual algebraic notation that we are all familiar with where a binary operator (a binary operator is an operator that has two operands) is written between the left-hand and right-hand operands. For example, in the expression above, the left-hand operand of the subtraction operator is -1 and the right-hand operand is -2. Some operators, such as the negation operator, are unary operators meaning there is only one operand. For negation, the operand is written to the right of the negation operator. Therefore, this expression contains six operators: negation, subtraction, negation, multiplication, negation, and division.
In the algorithm that evaluates the expression, we also treat a left parenthesis as an operator, which it is not, but during the evaluation we have to push left parentheses onto the operator stack.
In an infix arithmetic expression, each operator has a precedence level, which for a left parenthesis, is different when it is on the operator stack as opposed to when it is not (this will become clear when you read the trace of the algorithm for the above expression; see page 3):
Operator Normal Precedence Level Stack Precedence Level
( 5 0
– 4 4
* / 3 3
+ – 2 2
) 1 1
Right parentheses really don't have precedence because they are not pushed on the operator stack, but we assign them a precedence level of 1 for consistency. The algorithm discussed in the notes did not handle the negation operator so I have modified it to handle negation. Here is the revised algorithm:
Method evaluate(In: pExpr as an infix expression) Returns Double
Create operatorStack -- Stores Operators
Create operandStack -- Stores Operands
While end of pExpr has not been reached Do
Scan next token in pExpr -- The type of token is Token
If token is an operand Then
Convert token to Operand object named number
operandStack.push(number)
ElseIf token is an InstanceOf LeftParen Then
Convert token to LeftParen object named paren
operatorStack.push(paren)
ElseIf token is an InstanceOf RightParen Then
While not operatorStack.peek() is an InstanceOf LeftParen Do topEval()
operatorStack.pop() -- Pops the LeftParen
ElseIf token is Negation, Addition, Subtraction, Multiplication, or Division Then
Convert token to Operator object named operator
While keepEvaluating() returns True Do topEval()
operatorStack.push(op)
End While
While not operatorStack.isEmpty() Do topEval()
Return operandStack.pop()
End Method evaluate
Method keepEvaluating() Returns True or False
If operatorStack.isEmpty() Then Return False
Else Return stackPrecedence(operatorStack.peek()) ≥ precedence(operator)
End Method keepEvaluating
Method topEval() Returns Nothing
right ← operandStack.pop()
operator ← operatorStack.pop()
If operator is Negation Then operandStack.push(-right)
Else left ← operandStack.pop()
If operator is Addition Then operandStack.push(left + right)
ElseIf operator is Subtraction Then operandStack.push(left - right)
ElseIf operator is Multiplication Then operandStack.push(left * right)
Else operandStack.push(left / right)
End If
End Method topEval
Method precedence(In: Operator pOperator) Returns Int
If pOperator is LeftParen Then Return 5
ElseIf pOperator is Negation Then Return 4
ElseIf pOperator is Multiplication or Division Then Return 3
ElseIf pOperator is Addition or Subtraction Then Return 2
Else Return 1
End Method precedence
Method stackPrecedence(In: Operator pOperator) Returns Int
If pOperator is LeftParen Then Return 0
ElseIf pOperator is Negation Then Return 4
ElseIf pOperator is Multiplication or Division Then Return 3
ElseIf pOperator is Addition or Subtraction Then Return 2
Else Return 1
End Method stackPrecedence
It would be worthwhile to trace the algorithm using the above expression to make sure you understand how it works
1. Create the operand and operator stacks. Both are empty at the beginning.
2. Scan the first token ( and push it onto the operator stack.
3. Scan the next token (negation) and push it onto the operator stack.
4. Scan the next token 1 and push it onto the operand stack.
5. Scan the next token (subtraction). Since the operator on top of the operator stack (negation) has higher precedence than subtraction, evaluate the top (note: negation is a unary operator so there is only one operand to be popped from the operand stack):
a. Pop the top number from the operand stack. Call this right = 1.
b. Pop the top operator from the operator stack. Call this operator = – (negation).
c. Evaluate operator and push the result (-1) onto the operand stack.
d. Now push the subtraction operator onto the operator stack.
6. Scan the next token (negation). Since the operator on top of the stack (subtraction) has precedence less than negation, push the negation operator onto the operator stack
7. Scan the next token 2 and push it onto the operand stack.
8. Scan the next token ). Pop and evaluate operators from the operator stack until the matching ( is reached.
a. The top operator is a unary operator (negation):
Pop the top number from the operand stack. Call this right = 2.
Pop the top operator from the operator stack. Call this operator = – (negation).
Evaluate operator and push the result (-2) onto the operand stack.
b. The top operator is a binary operator (subtraction):
Pop the top number from the operand stack. Call this right = -2.
Pop the top number from the operand stack. Call this left = -1.
Pop the top operator from the operator stack. Call this operator = – (subtraction).
Evaluate operator and push the result (1) onto the operand stack.
c. The top operator is ( so pop it.
9. Scan the next token * (multiplication). The operator stack is empty so push *.
10. Scan the next token (negation). Since negation has higher precedence than the operator on top of the operator stack (multiplication) push the negation operator onto the operator stack
11. Scan the next token ( and push it onto the operator stack.
12. Scan the next token 3 and push it onto the operand stack.
13. Scan the next token / (division). Since the operator on top of the stack (left parenthesis) has higher precedence than division push / onto the operator stack. Now do you see why the precedence of ( changes when it is on the operator stack?
14. Scan the next token 5 and push it onto the operand stack.
15. Scan the next token ). Pop and evaluate operators from the operator stack until the matching ( is reached.
a. The top operator is binary operator (division):
Pop the top number from the operand stack. Call this right = 5.
Pop the top number from the operand stack. Call this left = 3.
Pop the top operator from the operator stack. Call this operator = /.
Evaluate operator and push the result (0.6) onto the operand stack.
b. The top operator is ( so pop it.
16. The end of the infix expression string has been reached. Pop and evaluate operators from the operator stack until the operator stack is empty
a. The top operator is a unary operator (negation):
Pop the top number from the operand stack. Call this right = 0.6.
Pop the top operator from the operator stack. Call this operator = – (negation).
Evaluate operator and push the result (-0.6) onto the operand stack.
b. The top operator is a binary operator (multiplication):
Pop the top number from the operand stack. Call this right = -0.6.
Pop the top number from the operand stack. Call this left = 1.
Pop the top operator from the operator stack. Call this operator = *.
Evaluate operator and push the result (-0.6) onto the operand stack.
17. The operator stack is empty. Pop the result from the operand stack (-0.6) and return it.
The project shall implement a GUI calculator which accepts as input a syntactically correct arithmetic expression written in infix notation and displays the result of evaluating the expression. The program shall meet these requirements.
1. The program shall implement a GUI which permits the user to interact with the calculator. Watch the Project 4 video lecture for a demonstration of how the application works.
2. When the Clear button is clicked, the input text field and the result label shall be configured to display nothing.
3. When a syntactically correct infix arithmetic expression is entered in the input text field and the Evaluate button is clicked, the program shall evaluate the expression and display the result in the label of the GUI.
4. When the Exit button is clicked, the application shall terminate.
5. Note: you do not have to be concerned with syntactically incorrect infix expressions. We will not test your program with such expressions.
Refer to the UML class diagram in Section 5.21. Your program shall implement this design.
Main Class
The Main class shall contain the main() method which shall instantiate an object of the Main class and call run() on that object. Main is completed for you.
AddOperator
Implements the addition operator which is a binary operator. AddOperator is completed for you.
BinaryOperator
The abstract superclass of all binary operators. BinaryOperator is completed for you.
DivOperator
Implements the division operator which is a binary operator. Complete the code in this file by using the AddOperator code as an example.
DList< E>
Implements a generic doubly linked list where the type of each element is E. This file contains the same DList class that was provided in the Week 6 Source zip archive, except I have changed it to be a generic class so we can use it to store any class of objects. DList is completed for you.
Expression
Represents an infix expression to be evaluated. Use the provided pseudocode as a guide in completing this class.
LeftParen
Represents a left parenthesis in the expression. LeftParen is completed for you.
MultOperator
Implements the multiplication operator which is a binary operator. Complete the code in this file by using the Add Operator code as an example.
NegOperator
Implements the negation operator which is a unary operator. Complete the code in this file by using the AddOperator code as an example. Note, however, that negation is a unary operator.
Operand
An operand is a numeric value represented as a Double. Implement the class using the UML class diagram as a guide.
Operator
Operator is the superclass of all binary and unary operators. Implement the class using the UML class diagram as a guide. Note that all of the non-constructor methods are abstract, i.e., none of them are implemented in Operator.
Parenthesis
Parenthesis is the superclass of LeftParen and RightParen. These are treated as a weird sort of Operator because we need to be able to push LeftParens on the operator stack when evaluating the expression. Parenthesis is completed for you.
Queue< E>
Implements a generic queue data structure using a DList
RightParen
Represents a right parenthesis in the expression. RightParen is completed for you.
Stack< E>
Implements a generic stack data structure using a DList
SubOperator
Implements the subtraction operator which is a binary operator. Complete the code in this file by using the AddOperator code as an example.
Token
Token is the abstract superclass of the different types of tokens that can appear in an infix expression. Token is completed for you.
Tokenizer
The Tokenizer class scans a string containing an infix expression and breaks it into tokens. For this project, a token will be either an Operand (a double value), a LeftParen or RightParen, or an arithmetic UnaryOperator (NegOperator) or BinaryOperator (one of AddOperator, SubOperator, MultOperator, or DivOperator). Tokenizer is completed for you.
UnaryOperator
UnaryOperator is the superclass of all unary operators. UnaryOperator is completed for you.
View
The View implements the GUI. Read the comments and implement the pseudocode.
UML Class Diagram
The UML class diagram is provided in the zip archive in UMLet format and as a PNG image. Your program shall implement this design. see image.
UML Class Diagram (continued) see image.