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SYNOPSIS OF THE PROJECT

INTRODUCTION:

A stack is alinear data structure.It is an ADT(Abstract Data Type) that contains a sequence of elements.The elements of the stack can be accessed in the following two ways:

  • LIFO(Last-in,First-out)
  • FILO(First-in,Last-out)

The pictorial representation of the stack is shown in the following diagram:

9

8

7

6

5

4

3

2

Fig: stack

Example:

Consider an example of papers stacked over one another on a table.The document placed at the top is the first one to be removed,i.e.,the paper at the bottom remains in the stack for the more substantial period.Hence,the LIFO/FILO order has been followed.

FEATURES OF STACK:

  • Dynamic data structures
  • Variable in size
  • Memory occupied is not fixed

OPERATIONS PERFORMED ON THE STACK:

Below are the given operations which are performed on the stack.

  • Pushoperation:A new element is summed up to the stack by using 'push' operation.The stack is considered as 'overflow' if no more elements can be inserted into the stack.
  • Popoperation:An element from the stack can be removed by using the 'pop'operation.Hence,the elements are popped in the reversemanner in which they were pushed into the stack.The stack is considered as 'underflow' if no more elements are left in the stack.
  • Top:The topmost element of the stack can be obtained by using the 'Top' operation.
  • Is Empty:This operation returns 'true'if the stack is empty else it returns 'False'.

TIME COMPLEXITIES:

The time complexity of all the stack operationsi.e.;push(),pop(),isEmpty() and Top() is O(1).

APPLICATIONS OF THE STACK:

The stack is applicable in:

  • Converting infix to postfix or prefix expressions.
  • Many computer algorithms like Tower Of Hanoi,Tree traversals,etc.
  • Graph algorithms like Topological sorting and strongly connected components.
  • Backtracking,N-Queens problem,Rat in a maze problem and Sudoku solver.
  • Balancing of symbols

STACK IMPLEMENTATION:

The stack can be implemented in two ways:

  • Using arrays
  • Using Linked lists

stack implementation using arrays:

#include<stdio.h>

#include<conio.h>

Using namespace std;

#define  MAX 1000

Class Stackexample

{

            Private:

int top;

             Public:

int s[MAX];    //maximum size of the stack

Stackexample()

                   {

                        Top=-1;

                    }

bool push(inti);

int pop();

boolisEmpty();

};    

boolstackexample::push(inti)

{  

if(top>=(MAX-1))

             {

cout<<"stack overflow occur";

return false;

               }

else

              {

s[++top]=i;

cout<<i<<\n is pushed into the stack";

return true;

               }

}

intstackexample::pop()

{

if(top<0)

          {

cout<<"\n stack underflow occur";

return 0;

}

else

{

inti=s[top--];

returni;

}

}

boolstackexample::isEmpty()

{

return(top<0);

}

void main()

{

classstackexamplest;

st.push(100);

st.push(200);

st.push(300);

cout<<st.pop()<<"popped from the stack \n";

}

OUTPUT:

100 is pushed into the stack

200 is pushed into the stack

300 is pushed into the stack

300 is popped from the stack

ADVANTAGES:

It is easy to implement

DISADVANTAGES:

It is not dynamic.

STACK IMPLEMENTATION USING LINKED LIST:

#include<stdio.h>

#include<conio.h>

Using namespace std;

classstackexample

    public:

    int data; 

    stackexample* nxt; 

}; 

stackexample* newNode(int data) 

  stackexample* stackexample=new Stackexample();

  stackexample->data = data; 

  stackexample->nxt = NULL; 

  returnstackexample; 

intisEmpty(Stackexample *root1) 

    return !root1; 

}

voidpush(Stackexample** root1, int data) 

    Stackexample* stackexample = newNode(data); 

    stackexample->nxt = *root1; 

    *root1 = stackexample; 

    cout<<data<<"is  pushed into the stack\n"; 

}

intpop(Stackexample** root1) 

    if (isEmpty(*root1)) 

      {

        return INT_MIN; 

      }

    Stackexample* temp = *root1; 

    *root1 = (*root1)->nxt; 

    int popped = temp->data; 

    free(temp); 

    return popped; 

inttop(Stackexample* root1) 

    if (isEmpty(root1)) 

        return INT_MIN; 

    return root1->data; 

int main() 

    Stackexample* root1 = NULL; 

    push(&root1, 100); 

    push(&root1, 200); 

    push(&root1, 300); 

    cout<<pop(&root1)<<"  is popped from the stack\n"; 

    cout<<"Top element is "<<top(root1)<<endl; 

    return 0; 

Output:

100is pushed into the stack

200 is pushed into the stack

300 is pushedinto thestack

300is popped from the stack

The top element is 200

ADVANTAGES:

It is dynamic,i.e., the stack can grow and shrink as per the need of the user during the runtime.

DISADVANTAGES:

Additional memory is required because of the use of pointers.

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