Stacks

Stacks in Data Structure

• 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

1. Stack is an ordered list of similar data type.
2. Stack is a LIFO structure. (Last in First out).
3. push() function is used to insert new elements into the Stack and pop() is used to delete an element from the stack. Both insertion and deletion are allowed at only one end of Stack called Top.
4. 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.

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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.

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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.

/*  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

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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)

Let's discuss STACK in details