Fall 3. CS 241 Data Structures -- Lecture Notes

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• An underlying representation for expressions
• Using and testing a StringTokenizer
• Beware of spaces
• Evaluating postfix expressions:

  while (more input) {
     next = nextToken()
     if (next is operand)
        push(next)
     else apply next to top two operands and push the result
  }
  answer is on top of the stack
  

• converting infix to postfix expressions:

  while (more input) {
     next = nextToken()
     if (next is operator) {
        while (precedence(top) >= precedence(next)) {  // **********not <=!
           emit(top());
        } // while
        push(next)
     } // if
     else emit next
  }
  while !stack.isEmpty()
     emit(pop())
  

• Example: Because of the *ed while loop, 2-3+4 converts to 23-4+ evaluates to 3 instead of 234+- which evaluates to -5!
• parentheses!
  • Insight: parentheses promote the precedence of everything inside them above everything -- thus, must emit all intraparenthetic operators before any following operators
  • Treat ()'s as operators, except you never emit them
  • ( has lower precedence than any operator, so it can be pushed on top of anything
  • ) has higher precedence than any operator, everything on the stack down to the first ( must be popped and emitted
• Input made easy (er) -- StringTokenizer




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