ADT Stack:

• Domain: an ordered list of homogeneous data.
• Operations
  • void Push(element)
  • void Pop(void)
  • element Top(void)
  • bool IsEmpty (void)
  • bool IsFull(void)
• It is an error to pop/top an empty stack
• LIFO - last in first out or
• FILO - first in last out
• A stack can be implemented as a list, all operations are performed at the head of the list.
• An array can be used as well, the first element at position 0, the last at position n. Insert at position n+1, pop to position n-1
• Some Applications:
  • Balanced Expressions:
    • Given an expression with [] () <> or any set of expressions <a href=...> </a>, determine if the expressions are balanced, or does every set match, and have an opening and closing expression.
    • ([<>]){} is fine
    • {[}] is not.
    • Algorithm

      Balanced Expression:
      
       Create a new stack S
       while more text
          get next symbol  t
          If t ∈{opening symbol}
                  S.push(t)
          If t ∈{closing symbols} 
                  q = S.Top();
                  if (q != t) 
                      return error
       if !S.Empty()
            return error
       return no-error
      
      

    • Argue that it works.
    • Argue performance.
  • Evaluating a postfix expression
    • A postfix expression is an expression where operands are given before the operators.
    • 3 5 + is the same as the infix expression 3+5
    • 3 4 + 5 * is (3+4)5
    • 3 4 5 + * is 3(4+5)
    • The nice thing about postfix is that any expression can be written without parentheses.
    • This is also called reverse polish notation (or rpn)
    • Give an algorithm to evaluate an RPN expression.
  • Function Calls.
    • Each time a routine is called the activation record is pushed onto the run time stack.
    • This is how we know which routine to return to