Abstract Classes, Inheritance, Solving Prefix and Postfix expressions using Queue’s and Stacks and the details on the file
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Program Assignment #3,
Topics: Abstract Classes, Inheritance, Solving Prefix and Postfix
expressions using Queue’s and Stacks
This is a four part assignment.
Consider: Algebraic expressions can be written in 3 notations: infix, prefix, and postfix.
Infix notation is the standard form we commonly use in mathematics,
2 * (3 + 4)
here operators are written between the operands they act upon: op1 operator op2
In prefix notation, an operator is written in front of its two operands in the format
operator op1 op2, IE: + 3 4 this is the same as 3 + 4
In postfix notation, an operator is written after its two operands: op1 op2 operator,
IE: 3 4 + and is again equivalent to 3+4
In both prefix and postfix notation the order of operands is the same as the original infix
expression.
2 * ( 3 + 4)
234+*
*2+34
and operators can be scattered throughout the expression. One thing true of all
expressions regardless of notation is that the number of operands equals the
number of operators plus 1.
For simplicity, we will only consider the operators + – / * and %. Also, all
operands will initially be a number of type double: IE:
* + 9.3 4.5 – 3 1
Each “token” or piece of the expression will always be separated by at least one
space.
Part 1: Class Expression:
This is an abstract class representing those features common all expressions regardless
of notation.
Expression
– expression: String = null
-tokenList: String[] = null
+ Expression( in expr: String): constructor
+ getExpression() : String
+ getTokenList() : String[]
# isOperand( in str: String): boolean
# isOperator( in str: String): boolean
# getOperandValue( in str: String) : double
# evaluateSubExpression( in op1: double, in operator: String,
in op2: double) : double
+ isLegal(): boolean [abstract]
+ evaluate(): double [abstract]
Interface for class Expression
public Expression( String str) : This constructor receives a String containing the
expression text. It will then break the expressions into “tokens” (individual
symbols separated by spaces) and store the resulting String array into the data
member tokenList.
protected static boolean isOperand(String str): returns true if the String parameters
is a valid operand (double number)
protected static double getOperandValue(String str): given a String containing a
valid operand this method returns the value of the operand as type double.
protected static boolean isOperator(String str): returns true if the String parameter
contains one of “+”, “-“, “*”, “/” or “%”.
public String getExpression(): returns the expression string.
public String[] getTokenList(): returns the tokenList.
protected static double evaluateSubExpression( double operand1, String operator,
double operand2): This method evaluates a subexpression as:
operand1 operator operand2
and returns the result as type double.
public abstract boolean isLegal(): abstract method to be implement in each subclass.
public abstract double evaluate(): abstract method to be implement in each subclass.
Part 2: Class PrefixExpression:
This class extends class Expression and represents PrefixExpressions
PrefixExpression
NO ADDITIONAL DATA MEMBERS
+ PrefixExpression( in expr: String): constructor
+ isLegal(): boolean
+ evaluate(): double
Interface for class PrefixExpression
public PrefixExpression( String str) : This constructor receives a String containing
the expression text. It will invoke the constructor for class Expression, passing in
the expression text.
public boolean isLegal(): This method returns true if the first “token” in the tokenList
is an operator, AND the number of operands in the expression is equal to the
number of operators plus 1.
public double evaluate(): This method uses a queue of Strings to evaluate the prefix
expression.
o Ensure the expression is legal, if not Stop and throw an exception,
using class ArithmeticException
o Enqueue all of the tokens in the tokenList into the queue
o if the # of tokens in the queue >= 3,
▪ Dequeue the 1st 3 values. Into 3 String variables: ie: a, b, & c
▪ else Stop and throw an exception, using class
ArithmeticException
o While not done
▪ If A is not an operator, and B & C are not operands, then we do
not have a subexpression. So;
• Enqueue A back onto the queue, and swap values
• A=B
• B=C
• Dequeue a new value into C
• Repeat the previous steps until A is an operator and B & C
operands
▪ Once is we have a subexpression
• Convert the operands into values of type double
• Call the method evaluateSubexpression
• Enqueue the result back onto the queue.
o If the number of elements in the queue equals 1, we
are “done”.
o Else, dequeued 3 new values into a , b, & c and
continue processing.
o When done (one value remaining on the queue) dequeue and return the
result of the expression.
Part 3: Class PostfixExpression:
This class extends class Expression and represents PostfixExpressions
PostfixExpression
NO ADDITIONAL DATA MEMBERS
+ PostfixExpression( in expr: String): constructor
+ isLegal(): boolean
+ evaluate(): double
Interface for class PostfixExpression
public PostfixExpression( String str) : This constructor receives a String containing
the expression text. It will invoke the constructor for class Expression, passing in
the expression text.
public boolean isLegal(): This method returns true if the last “token” in the tokenList
is an operator, AND the number of operands in the expression is equal to the
number of operators plus 1.
public double evaluate(): This method uses a stack of type Double to evaluate the
postfix expression.
o Ensure the expression is legal, if not Stop and throw an exception,
using class ArithmeticException
o Obtain the tokenList
o if the # of tokens in the tokenList < 3, Stop and throw an exception,
using class ArithmeticException
o Iterate through the token list
▪ if the current token is an operand, convert it to type double and
push onto the stack.
▪ if the current token is an operator:
• if the size of the stack is >=2,
o pop a value from the stack into “operand2”, and
pop a second value from the stack into “operand1”
o Evaluate the subexpression.. calling
evaluateSubExpression
o push the result back onto the stack
• else
o Stop and throw an exception, using class
ArithmeticException
o When done (you are at the end of the token list):
o if ONE value remains on the stack, pop and return the value
o else Stop and throw an exception, using class ArithmeticException
Part 4: Testing your program
NOTE: For this assignment you will complete:
1.
2.
3.
4.
5.
A generic Stack either array based or linked.
A generic Queue either array based or linked.
Abstract class Expression
Class PrefixExpression which extends Expression
Class PostfixExpression which extends Expression
6. For testing purposes ONLY you will create a main
program which will create instances of Pre &
Postfix expression (both valid and invalid) and
attempt to evaluate them.
Hint: you may want to search classes String & Double for methods that would help
convert from String to double and back again.
REMEMBER IF YOU GET STUCK ASK FOR HELP EARLY!!!!!!!!!!!
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