Stack - THE STACK Contents Definition and Examples...

1
THE STACK
Contents:
Definition and Examples
Representing stacks in C
Example: infix, prefix, and postfix
Exercises
Definition and Examples
A stack is an ordered collection of items into which new items may be
inserted and from which items may be deleted at one end, called the top of the
stack.
A stack is a dynamic, constantly changing object as the definition of the stack
provides for the insertion and deletion of items. It has single end of the stack as
top of the stack, where both insertion and deletion of the elements takes place.
The last element inserted into the stack is the first element deleted- last in first
out list (LIFO). After several insertions and deletions, it is possible to have the
same frame again.
Primitive Operations
When an item is added to a stack, it is push ed onto the stack. When an item is
removed, it is pop ped from the stack.
Given a stack s , and an item i , performing the operation push(s,i) adds an
item i to the top of stack s.
push(s, H);
push(s, I);
push(s, J);
Operation pop(s) removes the top element. That is, if i=pop(s) , then the
removed element is assigned to i.
pop(s);

2
Because of the push operation which adds elements to a stack, a stack is
sometimes called a pushdown list.
Conceptually, there is no upper limit on the number of items that may be kept
in a stack.
If a stack contains a single item and the stack is popped, the resulting stack
contains no items and is called the empty stack.
Push operation is applicable to any stack. Pop operation cannot be applied to
the empty stack. If so, underflow happens. A Boolean operation empty(s) , returns
TRUE if stack is empty. Otherwise FALSE, if stack is not empty
Example
To check the parentheses in any mathematical expression, are nested
correctly, we need to ensure that,
• There are an equal number of right and left parentheses
• Every right parentheses is preceded by a matching left parentheses
• For instance,
((A+B)
A+B(
)A+B(-C
(A+B))-(C+D
Each left parentheses opens the scope and right parentheses closes the scope.
The nesting depth at a particular point in an expression is the number of scopes
that have been opened but not yet closed at that point. The parentheses count at
a particular point in an expression is the number of left parentheses minus the
number of right parentheses that have been encountered in scanning the
expression from its left end up to that particular point. The two conditions that
must hold if the parentheses in an expression form an admissible pattern are as
follows:
• The parentheses count at the end of the expression is 0.

3
• The parentheses count at each point in the expression is nonnegative.
A scope ender must be of the same type as its scope opener. Thus, the