Stack is an
abstract data type with a bounded(predefined) capacity. It is a simple data
structure that allows adding and removing elements in a particular order. Every
time an element is added, it goes on the top of the stack, the only element
that can be removed is the element that was at the top of the stack, just like
a pile of objects.
Basic features of Stack
- Stack is an ordered list of similar data type.
- Stack is a LIFO structure. (Last in First out).
- push() function is used to insert new elements into the Stack and pop() function is used to delete an element from the stack. Both insertion and deletion are allowed at only one end of Stack called Top.
- Stack is said to be in Overflow state when it is completely full and is said to be in Underflow state if it is completely empty.
Applications of Stack
The simplest
application of a stack is to reverse a word. You push a given word to stack -
letter by letter - and then pop letters from the stack.
There are other
uses also like : Parsing, Expression Conversion(Infix to Postfix,
Postfix to Prefix etc) and many more.
Implementation of Stack
Stack can be
easily implemented using an Array or a Linked List. Arrays are quick, but are
limited in size and Linked List requires overhead to allocate, link, unlink,
and deallocate, but is not limited in size. Here we will implement Stack using
array.
Algorithm for PUSH operation
- Check if the stack is full or not.
- If the stack is full,then print error of overflow and exit the program.
- If the stack is not full,then increment the top and add the element .
Algorithm for POP operation
- Check if the stack is empty or not.
- If the stack is empty, then print error of underflow and exit the program.
- If the stack is not empty, then print the element at the top and decrement the top.
/* Below program
is written in C++ language */
Class Stack
{
int top;
public:
int a[10]; //Maximum size of Stack
Stack()
{
top = -1;
}
};
void Stack::push(int x)
{
if( top >= 10)
{
cout <<
"Stack Overflow";
}
else
{
a[++top] = x;
cout <<
"Element Inserted";
}
}
int Stack::pop()
{
if(top < 0)
{
cout <<
"Stack Underflow";
return 0;
}
else
{
int d =
a[top--];
return d;
}
}
void Stack::isEmpty()
{
if(top < 0)
{
cout <<
"Stack is empty";
}
else
{
cout << "Stack
is not empty";
}
}
Position of Top
|
Status of Stack
|
-1
|
Stack is
Empty
|
0
|
Only one
element in Stack
|
N-1
|
Stack is Full
|
N
|
Overflow
state of Stack
|
Analysis of Stacks
Below mentioned
are the time complexities for various operations that can be performed on the
Stack data structure.
- Push Operation : O(1)
- Pop Operation : O(1)
- Top Operation : O(1)
- Search Operation : O(n)
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