* * In the language Lisp, each of the four basic arithmetic operators appears *
ID: 3761041 • Letter: #
Question
*
* In the language Lisp, each of the four basic arithmetic operators appears
* before an arbitrary number of operands, which are separated by spaces.
* The resulting expression is enclosed in parentheses. The operators behave
* as follows:
*
* (+ a b c ...) returns the sum of all the operands, and (+) returns 0.
*
* (- a b c ...) returns a - b - c - ..., and (- a) returns -a.
*
* (* a b c ...) returns the product of all the operands, and (*) returns 1.
*
* (/ a b c ...) returns a / b / c / ..., and (/ a) returns 1/a.
*
* Note: + * may have zero operand
* - / must have at least one operand
*
* You can form larger arithmetic expressions by combining these basic
* expressions using a fully parenthesized prefix notation.
* For example, the following is a valid Lisp expression:
*
* (+ (- 6) (* 2 3 4) (/ (+ 3) (* 1) (- 2 3 1)) (+))
*
* This expression is evaluated successively as follows:
*
* (+ (- 6) (* 2 3 4) (/ 3 1 -2) (+))
* (+ -6 24 -1.5 0.0)
* 16.5
*
* Requirements:
*
* - Implement the given MyStack class
* - Design and implement an algorithm that uses MyStack class to evaluate a
* valid Lisp expression composed of the four basic operators and integer values.
* - Valid tokens in an expression are '(',')','+','-','*','/',and positive integers (>=0)
* - Display result as floting point number with at 2 decimal places
* - Negative number is not a valid "input" operand, e.g. (+ -2 3)
* However, you may create a negative number using parentheses, e.g. (+ (-2)3)
* - There may be any number of blank spaces, >= 0, in between tokens
* Thus, the following expressions are valid:
* (+ (-6)3)
* (/(+20 30))
*
* - Must use MyStack class in this project. (*** DO NOT USE Java API Stack class ***)
* - Must throw LispExpressionException to indicate errors in LispExpressionEvaluator class
* - Must not add new or modify existing data fields
* - Must implement methods in MyStack class.
* - Must implement these methods in LispExpressionEvaluator class:
*
* public LispExpressionEvaluator()
* public LispExpressionEvaluator(String inputExpression)
* public void reset(String inputExpression)
* public double evaluate()
* private void evaluateCurrentOperation()
*
* - You may add new private methods
*
*************************************************************************************/
package PJ2;
import java.util.*;
public class LispExpressionEvaluator
{
// Current input Lisp expression
private String currentExpression;
// Main expression stack, see algorithm in evaluate()
private MyStack<Object> tokenStack;
private MyStack<Double> operationStack;
// default constructor
// set currentExpression to ""
// create MyStack objects
public LispExpressionEvaluator()
{
// add statements
}
// constructor with an input expression
// set currentExpression to inputExpression
// create MyStack objects
public LispExpressionEvaluator(String inputExpression)
{
// add statements
}
// set currentExpression to inputExpression
// clear MyStack objects
public void reset(String inputExpression)
{
// add statements
}
// This function evaluates current operator with its operands
// See complete algorithm in evaluate()
//
// Main Steps:
// Pop operands from tokenStack and push them onto
// operationStack until you find an operator
// Apply the operator to the operands on operationStack
// Push the result into tokenStack
//
private void evaluateCurrentOperation()
{
// add statements
}
/**
* This funtion evaluates current Lisp expression in currentExpression
* It return result of the expression
*
* The algorithm:
*
* Step 1 Scan the tokens in the string.
* Step 2 If you see an operand, push operand object onto the tokenStack
* Step 3 If you see "(", next token should be an operator
* Step 4 If you see an operator, push operator object onto the tokenStack
* Step 5 If you see ")" // steps in evaluateCurrentOperation() :
* Step 6 Pop operands and push them onto operationStack
* until you find an operator
* Step 7 Apply the operator to the operands on operationStack
* Step 8 Push the result into tokenStack
* Step 9 If you run out of tokens, the value on the top of tokenStack is
* is the result of the expression.
*/
public double evaluate()
{
// only outline is given...
// you need to add statements/local variables
// you may delete or modify any statements in this method
// use scanner to tokenize currentExpression
Scanner currentExpressionScanner = new Scanner(currentExpression);
// Use zero or more white space as delimiter,
// which breaks the string into single character tokens
currentExpressionScanner = currentExpressionScanner.useDelimiter("\s*");
// Step 1: Scan the tokens in the string.
while (currentExpressionScanner.hasNext())
{
// Step 2: If you see an operand, push operand object onto the tokenStack
if (currentExpressionScanner.hasNextInt())
{
// This force scanner to grab all of the digits
// Otherwise, it will just get one char
String dataString = currentExpressionScanner.findInLine("\d+");
// more ...
}
else
{
// Get next token, only one char in string token
String aToken = currentExpressionScanner.next();
//System.out.println("Other: " + aToken);
char item = aToken.charAt(0);
switch (item)
{
// Step 3: If you see "(", next token shoube an operator
// Step 4: If you see an operator, push operator object onto the tokenStack
// Step 5: If you see ")" // steps in evaluateCurrentOperation() :
default: // error
throw new LispExpressionException(item + " is not a legal expression operator");
} // end switch
} // end else
} // end while
// Step 9: If you run out of tokens, the value on the top of tokenStack is
// is the result of the expression.
//
// return result
return 0.0; // return result here
}
//=====================================================================
// DO NOT MODIFY ANY STATEMENTS BELOW
//=====================================================================
// This static method is used by main() only
private static void evaluateExprTest(String s, LispExpressionEvaluator expr, String expect)
{
Double result;
System.out.println("Expression " + s);
System.out.printf("Expected result : %s ", expect);
expr.reset(s);
try {
result = expr.evaluate();
System.out.printf("Evaluated result : %.2f ", result);
}
catch (LispExpressionException e) {
System.out.println("Evaluated result :"+e);
}
System.out.println("-----------------------------");
}
// define few test cases, exception may happen
public static void main (String args[])
{
LispExpressionEvaluator expr= new LispExpressionEvaluator();
//expr.setDebug();
String test1 = "(+ (- 6) (* 2 3 4) (/ (+ 3) (* 1) (- 2 3 1)) (+))";
String test2 = "(+ (- 632) (* 21 3 4) (/ (+ 32) (* 1) (- 21 3 1)) (+))";
String test3 = "(+ (/ 2) (* 2) (/ (+ 1) (+ 1) (- 2 1 ))(*))";
String test4 = "(+ (/2)(+))";
String test5 = "(+ (/2 3 0))";
String test6 = "(+ (/ 2) (* 2) (/ (+ 1) (+ 3) (- 2 1 ))))";
evaluateExprTest(test1, expr, "16.50");
evaluateExprTest(test2, expr, "-378.12");
evaluateExprTest(test3, expr, "4.50");
evaluateExprTest(test4, expr, "0.5");
evaluateExprTest(test5, expr, "Infinity or LispExpressionException");
evaluateExprTest(test6, expr, "LispExpressionException");
}
}
Explanation / Answer
package PJ2;
import java.util.*;
public class LispExpressionEvaluator
{
private String inputExpr;
private Stack<Object> exprStack;
private Stack<Double> currentOpStack;
public LispExpressionEvaluator()
{
inputExpr = "";
exprStack = new Stack<Object>();
currentOpStack = new Stack<Double>();
}
public LispExpressionEvaluator(String inputExpression)
{
if(inputExpression == null)
{
throw new LispExpressionEvaluatorException();
}
inputExpr = inputExpression;
exprStack = new Stack<Object>();
currentOpStack = new Stack<Double>();
}
public void reset(String inputExpression)
{
if(inputExpression == null)
{
throw new LispExpressionEvaluatorException();
}
inputExpr = inputExpression;
exprStack.clear();
currentOpStack.clear();
}
private void evaluateCurrentOperation()
{
String currOp;
boolean numeric = true;
do
{
currOp = (String.valueOf(exprStack.pop()));
try
{
Double number = Double.parseDouble(currOp);
currentOpStack.push(number);
}
catch(NumberFormatException nfe)
{
numeric = false;
}
}
while(numeric);
double result;
switch (currOp)
{
case "*":
result = currentOpStack.pop();
while(!currentOpStack.isEmpty())
{
result *= currentOpStack.pop();
}
break;
case "/":
result = currentOpStack.pop();
while(!currentOpStack.isEmpty())
{
result /= currentOpStack.pop();
}
break;
case "+":
result = currentOpStack.pop();
while(!currentOpStack.isEmpty())
{
result += currentOpStack.pop();
}
break;
case "-":
result = currentOpStack.pop();
while(!currentOpStack.isEmpty())
{
result -= currentOpStack.pop();
}
break;
default:
result = currentOpStack.pop();
break;
}
exprStack.push(result);
}
public double evaluate()
{
Scanner inputExprScanner = new Scanner(inputExpr);
inputExprScanner = inputExprScanner.useDelimiter("\s*");
while (inputExprScanner.hasNext())
{
if (inputExprScanner.hasNextInt())
{
String dataString = inputExprScanner.findInLine("\d+");
exprStack.push(Double.parseDouble(dataString));
}
else
{
String aToken = inputExprScanner.next();
char item = aToken.charAt(0);
switch (item)
{
case '(':
break;
case ')':
evaluateCurrentOperation();
break;
case'*':
exprStack.push("*");
break;
case'+':
exprStack.push("+");
break;
case'/':
exprStack.push("/");
break;
case'-':
exprStack.push("-");
break;
throw new LispExpressionEvaluatorException(item + " is not a legal expression operator");
}
}
}
return Double.parseDouble(String.valueOf(exprStack.pop()));
}
private static void evaluateExprTest(String s, LispExpressionEvaluator expr)
{
Double result;
System.out.println("Expression " + s);
expr.reset(s);
result = expr.evaluate();
System.out.printf("Result %.2f ", result);
System.out.println("-----------------------------");
}
public static void main (String args[])
{
SimpleLispExpressionEvaluator expr= new SimpleLispExpressionEvaluator();
String test1 = "(+ (- 6) (* 2 3 4) (/ (+ 3) (* 1) (- 2 3 1)))";
String test2 = "(+ (- 632) (* 21 3 4) (/ (+ 32) (* 1) (- 21 3 1)))";
String test3 = "(+ (/ 2) (* 2) (/ (+ 1) (+ 1) (- 2 1 )))";
String test4 = "(+ (/2))";
String test5 = "(+ (/2 3 0))";
String test6 = "(+ (/ 2) (* 2) (/ (+ 1) (+ 3) (- 2 1 ))))";
evaluateExprTest(test2, expr, "-378.12");
evaluateExprTest(test3, expr, "4.50");
evaluateExprTest(test4, expr, "0.5");
evaluateExprTest(test5, expr, "Infinity or LispExpressionException");
evaluateExprTest(test6, expr, "LispExpressionException");
}
}
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