CS241: Spring 2010 --Evaluating infix expressions

1. Stacks and Queues - a quick introduction
2. Introduction to expressions: prefix, infix, and postfix
3. Evaluating arbitrary infix expressions; not so easy!!
4. postfix evaluation
   

   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
   

5. converting infix to postfix expressions:

   while (more input) {
      next = nextToken()
      if (next is operator) {
         while (!isEmpty() && precedence(top()) >= precedence(next)) {  
            emit(pop());
         } // while
         push(next)
      } // if
      else emit next
   }
   while !stack.isEmpty()
      emit(pop())
   

6. 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, with the following changes
   • ( has lower precedence than any other operator, but it is pushed without regard to precedence -- i.e. when next is an open parenthesis, simply push it
   • ) has higher precedence than any operator but it is never pushed; when next is an open parenthesis, everything on the stack down to the first ( must be popped and emitted