Stacks

1
Stacks A stack is an ordered set of elements, for
which only the last element placed into the stack
is accessible. The stack data type is also known
as a first-in first-out data structure or a
pushdown list. Stacks have many applications but
in this case we are interested in stack register
as is used in the Pentium processor. The Pentium
uses an 8 word (extended 80 bit floating-point)
stack register to hold numeric values. In order
to evaluate an expression using a stack, we must
represent it in postfix or reverse Polish
notation. To convert an infix (standard
mathematical notation) expression into postfix we
move the operators to the right of each operand
pair in order of precedence.
A(BC/(D-E)) A(BC/DE-) A(BCDE-/) ABCDE
-/ ABCDE-/
(AB)(C-D)/E ABCD-/E
ABCD-/E ABCD-E/
ABCD-E/ ABCD-E/
2
Algorithm for Converting an Infix Expression to
Postfix
Examine infix string from left to right 1. If
next element is an operand, output it. 2. If next
element is '(' push it onto a stack. 3. If next
element is an operator a. If top of stack is
'(' then push operator b. If top of stack is
operator with higher precedence then push
the operator c. Else pop operator from stack
and output then repeat Step 3. 4. If next
element is ')' pop and output until '(' is
found, then pop and discard. 5. If more input,
return to Step 1 else pop and output
remaining operators.