ten42% cat -n RPN.java
     1  /* RPN.java: use parser to convert to RPN
     2   * grammar:
     3   *   P ---> E '#'
     4   *   E ---> T {('+'|'-') T}
     5   *   T ---> S {('*'|'/') S}
     6   *   S ---> F '^' S | F
     7   *   F ---> char | '(' E ')'
     8   */
     9  class RPN {
    10     private int level = 0;
    11     private GetChar getChar = new GetChar();
    12     private char next;
    13
    14     private void P() {
    15        scan();
    16        E();
    17        if (next != '#') error(1);
    18        else System.out.println();
    19     }
    20
    21     private void E() {
    22        T();
    23        while (next == '+' || next == '-') {
    24           char save = next;
    25           scan();
    26           T();
    27           gen(save);
    28        }
    29     }
    30
    31     private void T() {
    32        S();
    33        while (next == '*' || next == '/') {
    34           char save = next;
    35           scan();
    36           S();
    37           gen(save);
    38        }
    39     }
    40
    41     private void S() {
    42        F();
    43        if (next == '^') {
    44           scan();
    45           S();
    46           gen('^');
    47        }
    48     }
    49
    50     private void F() {
    51        if (Character.isLetter(next)) {
    52           gen(next);
    53           scan();
    54        }
    55        else if (next == '(') {
    56           scan();
    57           E();
    58           if (next == ')') scan();
    59           else error(2);
    60        }
    61        else {
    62           error(3);
    63        }
    64     }
    65
    66     private void scan() {
    67        while (Character.isWhitespace(next = 
                    getChar.getNextChar()))
    68           ;
    69     }
    70
    71     private void error(int n) {
    72        System.out.println("\n*** ERROR: " + n);
    73        System.exit(1);
    74     }
    75
    76     private void gen(char ch) {
    77        System.out.print(ch);
    78     }
    79
    80     public static void main(String[] args) {
    81        RPN rpn = new RPN();
    82        rpn.P();
    83     }
    84  }
ten42% cat -n GetChar.java
     1  // GetChar: fetch next char 
     2  import java.io.*;
     3  public class GetChar { 
     4     private Reader in; // name for input stream
     5    
     6     // GetChar: constructor  
     7     public GetChar () { 
     8        in = new InputStreamReader(System.in);
     9     }
    10
    11     // getNextChar: fetches next char
    12     public char getNextChar() {
    13        char ch = ' '; // keep compiler happy
    14        try {
    15           ch = (char)in.read();
    16        } catch (IOException e) {
    17           System.out.println("Reading char");
    18        }
    19        return ch;
    20     }
    21  }

ten42% java RPN
a + b + c + d #
ab+c+d+

ten42% java RPN
a^b^c^d#
abcd^^^

ten42% java RPN
(a + b*c)^(d/e - f)*g#
abc*+de/f-^g*

ten42% java RPN
a + b c #
ab+
*** ERROR: 1

ten42% java RPN
( (a + b)*c #
ab+c*
*** ERROR: 2

ten42% java RPN
a + b ) #
ab+
*** ERROR: 1

ten42% java RPN
((a)+(((b))))*((((c))))#
ab+c*

ten42% java RPN
a + b*c^d + e#
abcd^*+e+

ten42% java RPN
a+b*c^d*e+f#
abcd^*e*+f+

ten42% java RPN
a^b*c+d*e^f#
ab^c*def^*+