CS 1723-001 Data Structures
Fall 2001 -- Lectures for Week 6

RPN Evaluation and
Translator of Arithmetic Expressions to RPN

Week's Objectives:
  1. Exercise to implement RPN evaluator.
  2. Study translator from arithmetic expressions to RPN.
  3. Exercise to implement translator.
  4. Put the two above programs together to get an evaluator of arithmetic expressions.
  5. Talk about input/output using copy programs.
Details About the Objectives:

  1. Exercise to implement RPN evaluator. Exercise 2.

  2. Translator from arithmetic expressions to RPN. Here is the list of rules we developed in class to translate arithmetic expressions to RPN, using a stack for the translation. (Note that the RPN evaluator uses a stack of doubles for intermediate values. The translator described here uses a stack of chars to hold pending operators.)

    Rules to translate an arithmetic expression to RPN:

      Rules for each input char (go on to next input char unless otherwise stated)
      Fetch next char, call it ch
    1. if ch is an operand, move it to output.
      From now on ch is an operator or '(' or ')'.
    2. if stack is empty, add ch to stack.
    3. if ch is '(', add ch to stack.
      From now on, stack is not empty. Use top for its top char (just peeked at, not popped).
    4. if ch is ')', remove chars from stack and output down to '(' on stack, which is thrown away.
    5. if top is '(', add ch to stack. From now on, both ch and top are regular operators.
    6. if prec(ch) > prec(top), add ch to stack.
    7. if prec(ch) < prec(top), move top to output, and DO NOT MOVE ON TO NEXT INPUT CHAR.
    8. if prec(ch) == prec(top) and left-to-right associativity, move top to output, and DO NOT MOVE ON TO NEXT INPUT CHAR.
    9. if prec(ch) == prec(top) and right-to-left associativity, add top to stack.
    10. at end, move everything on stack to output.

  3. Exercise to implement translator. Exercise 3.

  4. Evaluator of arithmetic expressions. This is just a matter of feeding a string containing an arithmetic expression into the translator to produce a string containing RPN. Then this string is fed into the RPN evaluator to get a final value. The Java code could look something like: 
          GetNext getNext = new GetNext(); // input class
      Trans trans = new Trans(); // new translater
      Eval eval = new Eval(); // new evaluator
      String s = getNext.getNextString(); // fetch string
      System.out.println("Input: " + s);
      String resStr = trans.translate(s); // produce RPN
      System.out.println("RPN string: " + resStr); // print RPN
      double res = eval.evaluateRPN(resStr);
      System.out.println("Value: " + res); // print value

  5. Here is some material about file I/O and copying, showing programs in C, C++, and Java. file copy.

    Here is material about the standard input, output and error files: error output.

Revision date: 2001-09-29. (Please use ISO 8601, the International Standard.)