Mutual Recursion

1
Mutual Recursion

• A set of methods calls each other cooperatively
  and repeatedly
• Expression is a term, or sum or difference of
  terms
• Term is a factor, or a product or quotient of
  factors
• Factor is a number, or an expression enclosed in
  parenthesis

2
Using Mutual Recursion

• Problem to compute the value of arithmetic
  expressions such as
• 3 4 5 (3 4) 5 1 - (2 - (3 - (4 -
  5)))

3
Syntax Diagram for Evaluating and Expression
4
Syntax Tree for Two Expressions
5
Evaluator

• ExpressionTokenizer breaks input string into
  tokens (numbers, operators, parenthesis)
• nextToken returns string
• peekToken look at next token without consuming
  it
• (3 4) 6 See without consuming it.

6
Mutually Recursive Methods

• Implement 3 methods that call each other
  recursively
• getExpressionValue calls getTermValue, is next
  token or -, if so call get TermValue again and
  adds or subtracts
• getTermValue calls getFactorValue
• getFactorValue number or getExpressionValue

7
File Evaluator.java

• 01 /
• 02 A class that can compute the value of an
  arithmetic expression.
• 03 /
• 04 public class Evaluator
• 05
• 06 /
• 07 Constructs an evaluator.
• 08 _at_param anExpression a string containing
  the expression
• 09 to be evaluated.
• 10 /
• 11 public Evaluator(String anExpression)
• 12
• 13 tokenizer new ExpressionTokenizer(anEx
  pression)
• 14
• 15
• 16 /
• 17 Evaluates the expression.

8

• 18 _at_return the value of the expression.
• 19 /
• 20 public int getExpressionValue()
• 21
• 22 int value getTermValue()
• 23 boolean done false
• 24 while (!done)
• 25
• 26 String next tokenizer.peekToken()
• 27 if ("".equals(next)
  "-".equals(next))
• 28
• 29 tokenizer.nextToken()
• 30 int value2 getTermValue()
• 31 if ("".equals(next)) value
  value value2
• 32 else value value - value2
• 33
• 34 else done true
• 35
• 36 return value

9

• 38
• 39 /
• 40 Evaluates the next term found in the
  expression.
• 41 _at_return the value of the term.
• 42 /
• 43 public int getTermValue()
• 44
• 45 int value getFactorValue()
• 46 boolean done false
• 47 while (!done)
• 48
• 49 String next tokenizer.peekToken()
• 50 if ("".equals(next)
  "/".equals(next))
• 51
• 52 tokenizer.nextToken()
• 53 int value2 getFactorValue()
• 54 if ("".equals(next)) value
  value value2
• 55 else value value / value2
• 56

10

• 58
• 59 return value
• 60
• 61
• 62 /
• 63 Evaluates the next factor found in the
  expression.
• 64 _at_return the value of the factor.
• 65 /
• 66 public int getFactorValue()
• 67
• 68 int value
• 69 String next tokenizer.peekToken()
• 70 if ("(".equals(next))
• 71
• 72 tokenizer.nextToken()
• 73 value getExpressionValue()
• 74 next tokenizer.nextToken() //
  read ")"
• 75
• 76 else

11

• 78 return value
• 79
• 80
• 81 private ExpressionTokenizer tokenizer
• 82

12
File ExpressionTokenizer.java

• 01 /
• 02 This class breaks up a string describing
  an expression
• 03 into tokens numbers, parentheses, and
  operators
• 04 /
• 05 public class ExpressionTokenizer
• 06
• 07 /
• 08 Constructs a tokenizer.
• 09 _at_param anInput the string to tokenize
• 10 /
• 11 public ExpressionTokenizer(String anInput)
• 12
• 13 input anInput
• 14 start 0
• 15 end 0
• 16 nextToken()
• 17

13

• 18
• 19 /
• 20 Peeks at the next token without
  consuming it.
• 21 _at_return the next token or null if there
  are no more tokens
• 22 /
• 23 public String peekToken()
• 24
• 25 if (start gt input.length()) return
  null
• 26 else return input.substring(start,
  end)
• 27
• 28
• 29 /
• 30 Gets the next token and moves the
  tokenizer to the
• 31 following token.
• 32 _at_return the next token or null if there
  are no more tokens
• 33 /
• 34 public String nextToken()
• 35
• 36 String r peekToken()

14

• 38 if (start gt input.length()) return r
• 39 if (Character.isDigit(input.charAt(start
  )))
• 40
• 41 end start 1
• 42 while (end lt input.length()
  Character.isDigit(input.charAt(end)))
• 43 end
• 44
• 45 else
• 46 end start 1
• 47 return r
• 48
• 49
• 50 private String input
• 51 private int start
• 52 private int end
• 53

15
File EvaluatorTest.java

• 01 import javax.swing.JOptionPane
• 02
• 03 /
• 04 This program tests the expression
  evaluator.
• 05 /
• 06 public class EvaluatorTest
• 07
• 08 public static void main(String args)
• 09
• 10 String input JOptionPane.showInputDial
  og("Enter an expression")
• 11 Evaluator e new Evaluator(input)
• 12 int value e.getExpressionValue()
• 13 System.out.println(input ""
  value)
• 14 System.exit(0)
• 15
• 16