--------------------------------------------------------------------------------
                         BASIC DATA STRUCTURES IN C++
                                                   -Sanchit Karve
                                                      born2c0de
                                                 "Accept No Limits"
--------------------------------------------------------------------------------

In this Tutorial I assume that all of you have a working knowledge on how to use
Classes in C++ because all of my data structures are going to be based on them.
I realised that there are a lot of Data Structures Tutorials available but it's
rare to find one that uses OOP. So this one will mainly focus on having a data
structure incorporated as a class.
CODE IS COMPILED IN BORLAND C++ UNLESS OTHERWISE MENTIONED.

We shall cover the following Basic Data Structures in this Tutorial:

1. STACKS
2. QUEUES
3. LINKED LISTS
4. BINARY TREES

We shall also combine data structures together later in this tutorial such as 
combining a Linked List along with a Stack etc. We shall also learn about Doubly
Linked Lists and Circular Linked Lists in this Tutorial.

So let's begin without wasting any time.


1)                              STACKS

Stacks are commonly used Data Structures while writing code. It's concept is 
really simple which makes it even simpler to write it in code. Consider this
situation. There are a pile of 5 Books on a Table. You want to add one book to
the pile. What do you do??? You simply add the book on the TOP of the pile. What 
if you want the third book from the new 6 book pile? You then lift each book one
by one from the TOP until the third book reaches the top. Then you take the 
third book and replace all the others back into the pile by adding them from the 
TOP.
If you've noticed I've mentioned the word TOP in Caps. Yes, TOP is the most 
important word as far as stacks are concerned. Data is stored in a Stack where 
adding of data is permitted only from the top. Removing/Deleting Data is also 
done from the top. As Simple as That. Now you may ask where Stacks are used? 
Stacks are infact used on every Processor. Each processor has a stack where data
and addresses are pushed or added to the stack. Again the TOP rule is followed 
here. The ESP Register adds as a Stack Pointer that refers to the top of the
stack in the Processor. Anyway, since the explaination of how the Processor
Stack works is beyond the subject of this Tutorial, let's write our Stack Data
Structure. Remember some Stack Terminology before continuing. Adding Data to the
Stack is known as Pushing and deleting data from the stack is known as Popping.


#include <iostream.h>
#include <conio.h>

#define MAX 10        // MAXIMUM STACK CONTENT


class stack
{

  private:
    int arr[MAX];   // Contains all the Data
    int top;        //Contains location of Topmost Data pushed onto Stack

  public:
	 stack()         //Constructor
	 {
	    top=-1;      //Sets the Top Location to -1 indicating an empty stack
	 }

	 void push(int a)  // Push ie. Add Value Function
	 {
		top++;        // increment to by 1
		if(top<MAX)
		 {
			arr[top]=a;  //If Stack is Vacant store Value in Array
		 }
		 else
		 {
			cout<<"STACK FULL!!"<<endl;
			top--;
		 }
	 }

	int pop()                  // Delete Item. Returns the deleted item
	{
		if(top==-1)
		{
			cout<<"STACK IS EMPTY!!!"<<endl;
			return NULL;
		}
		else
		{
			int data=arr[top];     //Set Topmost Value in data
			arr[top]=NULL;       //Set Original Location to NULL
			top--;               // Decrement top by 1
			return data;         // Return deleted item
		}
	 }
};


void main()
{
 stack a;
 a.push(3);
 cout<<"3 is Pushed\n";
 a.push(10);
 cout<<"10 is Pushed\n";
 a.push(1);
 cout<<"1 is Pushed\n\n";

 cout<<a.pop()<<" is Popped\n";
 cout<<a.pop()<<" is Popped\n";
 cout<<a.pop()<<" is Popped\n";
 getch();
}

Output:
3 is Pushed
10 is Pushed
1 is Pushed

1 is Popped
10 is Popped
3 is Popped

Clearly we can see that the last data pushed is the first one to be popped out.
That's why a Stack is also known as a LIFO Data Structure which stands for "Last
In,First Out" and I guess you know why.

Let us see how we implemented the stack. We first created a variable called top
that points to the top of the stack. It is initialised to -1 to indicate that 
the stack is empty. As Data is entered, the value in top increments itself and
data is stored into an array arr. Now there's one drawback to this Data
Structure. Here we state the Maximum number of elements as 10. What if we need
more than 10 Data Elements? In that case we combine a Stack along with a Linked
List which will be explained later.
Now once you've got this one right, let's proceed to the Queue Data Structure.


2)                              QUEUES

There's a huge crowd at your local grocery store. There are too many people 
trying to buy their respective items and the Shopkeeper doesnt know from where 
to start. Everyone wants their job done quickly and the shopkeeper needs an 
efficient method to solve this problem. What does he do? He introduces a Queue 
System based on the First Come, First Serve System. The Last Person trying to
buy an item stands behind the last person at the END of the queue. The 
Shopkeeper however is present at the FRONT end of the queue. He gives the item
to the person in FRONT of the queue and after the transaction is done, the
person in FRONT of the Queue Leaves. Then the person second in queue becomes the
First person in the Queue.
Do you get the point here? A Queue is similar to a stack except that addition of
data is done in the BACK end and deletion of data is done in the FRONT.
Writing a queue is a lot harder than writing a stack. We maintain 2 Integers in
our Queue Data Structure, one signifying the FRONT end of the Queue and the 
other referring to the BACK end of the Queue.
Let us use the same coding style as we used for the Stack. We first initialise
both the ends to -1 to indicate an empty queue. When Data is added to the queue 
both ends get respective postive values. When New Data is added, the back End is
incremented and when data is deleted the front end is decremented. This works
fine but it has a major drawback. What if the Maximum capacity of the Queue is 5
Items. Suppose the User has added 4 items, deleted 3 items and adds 2 again. The
Stack wont permit him to add the last half of the data as it will report that
the stack is full. The Reason is that we are blindly incrementing/decrementing 
each end depending on addition/deletion not realising that both the ends are
related to each other. I leave this as an excercise for you to answer. Why will
our proposed Stack report the Stack as Full even though it's actually vacant?
So we need another approach.In this method we focus more on the data than on the
addition end and the deletion end.
What we now use is the grocery store example again. Suppose there are 5 items in
a queue and we want to delete them one by one. We first delete the first data
item pointed by the deletion end. Then we shift all data one step ahead so that 
the second item becomes the first, third item becomes second and so on...
Another method would be to maintain the difference between the two ends which is 
not practical. Hence we stick to our previous method. It might be slow in Big
Queues, but it certainly works great. Here's the code.

/*                           QUEUE IMPLEMENTATION
		                       -Sanchit Karve
                                         born2c0de
*/

#include <iostream.h>
#include <conio.h>


#define MAX 5           // MAXIMUM CONTENTS IN QUEUE


class queue
{
 private:
 	int t[MAX];
 	int al;      // Addition End
 	int dl;      // Deletion End

 public:
  queue()
  {
  	dl=-1;
  	al=-1;
  }

  void del()
  {
     int tmp;
     if(dl==-1)
     {
	    cout<<"Queue is Empty";
     }
     else
     {
		for(int j=0;j<=al;j++)
		{
	  		if((j+1)<=al)
	  		{
	  			tmp=t[j+1];
	  			t[j]=tmp;
	  		}
	  		else
	  		{
	  			al--;

	  		if(al==-1)
		 		dl=-1;
		 	else
		 		dl=0;
	  		}
		}
     }
  }

void add(int item)
{
 	if(dl==-1 && al==-1)
 	{
  		dl++;
  		al++;
 	}
   else
   {
  		al++;
  		if(al==MAX)
   	{
			cout<<"Queue is Full\n";
			al--;
			return;
  		}
 	}
 	t[al]=item;

}

  void display()
  {
  	if(dl!=-1)
   {
   	for(int i=0;i<=al;i++)
      	cout<<t[i]<<" ";
   }
   else
   	cout<<"EMPTY";
  }

};

void main()
{
 queue a;
 int data[5]={32,23,45,99,24};

 cout<<"Queue before adding Elements: ";
 a.display();
 cout<<endl<<endl;

 for(int i=0;i<5;i++)
 {
   a.add(data[i]);
   cout<<"Addition Number : "<<(i+1)<<" : ";
   a.display();
   cout<<endl;
 }
 cout<<endl;
 cout<<"Queue after adding Elements: ";
 a.display();
 cout<<endl<<endl;

 for(int i=0;i<5;i++)
 {
   a.del();
   cout<<"Deletion Number : "<<(i+1)<<" : ";
   a.display();
   cout<<endl;
 }
 getch();
}


OUTPUT:
Queue before adding Elements: EMPTY

Addition Number : 1 : 32
Addition Number : 2 : 32 23
Addition Number : 3 : 32 23 45
Addition Number : 4 : 32 23 45 99
Addition Number : 5 : 32 23 45 99 24

Queue after adding Elements: 32 23 45 99 24

Deletion Number : 1 : 23 45 99 24
Deletion Number : 2 : 45 99 24
Deletion Number : 3 : 99 24
Deletion Number : 4 : 24
Deletion Number : 5 : EMPTY

As you can clearly see through the output of this program that addition is
always done at the end of the queue while deletion is done from the front end of 
the queue. Once again the Maximum limit of Data will be extended later when we 
learn Linked Lists.


3)                                LINKED LISTS

The Linked List is a more complex data structure than the stack and queue. A
Linked List consists of two parts, one the DATA half and the POINTER half. The
Data half contains the data that we want to store while the pointer half 
contains a pointer that points to the next linked list data structure. This way
we have a dynamic data structure as we can add as much data as we want within
memory restrictions. And yes, pointers play a major role in Data Structures...No 
Pointers, No Data Structures...So Knowledge of Pointers is a basic must before
continuing.
Look at this diagram that explains the Linked List:
                                                      { P = Pointer , N = NULL }
[12|P]-->-->-->-->[15|P]-->-->-->[29|P]-->-->-->[45|N]

Here the data stored within the Data Structure is 12,15,29,45.
As you can see, the pointer with 12 points to the next linked list which is 15 
which points to 29 and so on.
This is just a conceptual idea. In Reality all this data is stored in random 
places in memory. Using Pointers help us to get all the data in order.
While Adding Data to a Linked List we check for previously added Linked Lists.
Then we reach the last node of the List where the pointer value is NULL and
point it to our newly created linked list, else if there is no previously
existing linked list we simply add one and set it's pointer to NULL.
Deletion is more complex. Suppose we want to delete the data 15. Then we first
find 15. Then we point the pointer which is present with 12 to the data in 29.
Then we delete the node which contains 15 as it's data.
Studying the Following Source code will help you understand and Appreciate the
Linked List:

#include <iostream.h>
#include <conio.h>

class linklist
{
	private:

   	 struct node
         {
            int data;
            node *link;
         }*p;

   public:

         linklist();
         void append( int num );
         void add_as_first( int num );
         void addafter( int c, int num );
         void del( int num );
         void display();
         int count();
         ~linklist();
};

linklist::linklist()
{
	p=NULL;
}

void linklist::append(int num)
{
   node *q,*t;

   if( p == NULL )
   {
      p = new node;
      p->data = num;
      p->link = NULL;
   }
   else
   {
      q = p;
      while( q->link != NULL )
     	q = q->link;

      t = new node;
      t->data = num;
      t->link = NULL;
      q->link = t;
   }
}

void linklist::add_as_first(int num)
{
   node *q;

   q = new node;
   q->data = num;
   q->link = p;
   p = q;
}

void linklist::addafter( int c, int num)
{
   node *q,*t;
   int i;
   for(i=0,q=p;i<c;i++)
   {
      q = q->link;
      if( q == NULL )
      {
      	cout<<"\nThere are less than "<<c<<" elements.";
        return;
      }
   }

   t = new node;
   t->data = num;
   t->link = q->link;
   q->link = t;
}

void linklist::del( int num )
{
   node *q,*r;
   q = p;
   if( q->data == num )
   {
      p = q->link;
      delete q;
      return;
   }

   r = q;
   while( q!=NULL )
   {
      if( q->data == num )
      {
      	 r->link = q->link;
         delete q;
         return;
      }

      r = q;
      q = q->link;
   }
   cout<<"\nElement "<<num<<" not Found.";
}

void linklist::display()
{
   node *q;
   cout<<endl;

   for( q = p ; q != NULL ; q = q->link )
   	cout<<endl<<q->data;

}

int linklist::count()
{
   node *q;
   int c=0;
   for( q=p ; q != NULL ; q = q->link )
   	c++;

   return c;
}

linklist::~linklist()
{
   node *q;
   if( p == NULL )
   	return;

   while( p != NULL )
   {
      q = p->link;
      delete p;
      p = q;
   }
}

void main()
{
   linklist ll;
   cout<<"No. of elements = "<<ll.count();
   ll.append(12);
   ll.append(13);
   ll.append(23);
   ll.append(43);
   ll.append(44);
   ll.append(50);

   ll.add_as_first(2);
   ll.add_as_first(1);

   ll.addafter(3,333);
   ll.addafter(6,666);

   ll.display();
   cout<<"\nNo. of elements = "<<ll.count();

   ll.del(333);
   ll.del(12);
   ll.del(98);
   cout<<"\nNo. of elements = "<<ll.count();
   getch();
}

OUTPUT:
No. of elements = 0

1
2
12
13
333
23
43
666
44
50
No. of elements = 10
Element 98 not Found.
No. of elements = 8

Here as you see, the class contains a structure node that consists of an integer
type for data and a pointer pointing to another node structure. Here we maintain
a node pointer p that always points to the first item in the list. Here is a
list of the functions that are used in the data structure.
linklist()                           : CONSTRUCTOR
void append( int num );              : ADD AT END OF LIST
void add_as_first( int num );        : ADD TO BEGINNING OF LIST
void addafter( int c, int num );     : ADD DATA num AFTER POSTION c
void del( int num );                 : DELETE DATA num
void display();                      : DISPLAY LINKED LIST
int count();                         : NUMBER OF ITEMS IN LIST
~linklist();                         : DESTRUCTOR

Many places you will see statements like q=q->link inside a loop. This statement 
just shifts the pointer from one node to the other. the Destructor as well as 
the del() function use the delete operator to deallocate space that was
previously allocated by the new operator. The Rest should be clear if you have a 
basic understanding of pointers.
The advantage of using pointers is that you dont have to worry about wasting
space by allocating a lot of memory beforehand. As the need for data increases, 
memory is allocated accordingly. But the flip side is that to access each node
we have to iterate through each node till we reach the desired node. That's why 
linked lists have different forms of themselves for easier access. For example 
Circular and Doubly Linked Lists. Circular Linked Lists are those in which the 
last node always points to the first node in the list. Doubly Linked Lists 
contain two pointers, one that points to the next node and the other that points 
to the previous node.
I shall only give source code for Circular Linked List, while code for doubly 
linked lists is given as an excercise. However, if you cant write it...you are
free to contact me at born2c0de@hotmail.com

3.A)             STACK DATA STRUCTURE IMPLEMENTING LINKED LISTS

Here, we use the same concept of the stack but eliminate the MAXIMUM data items
constraint. Since we shall be using Linked Lists to store data in the stack,
the Stack can hold as much as data as it wants as long as the data is within
Memory Limits.Here's the code:

#include <iostream.h>

struct node
{
   int data;
   node *link;
};

class lstack
{
      private:
              node* top;
              
      public:
             lstack()
             {
             	top=NULL;
             }
             
             void push(int n)
             {
             	node *tmp;
             	tmp=new node;
             	if(tmp==NULL)
             	   cout<<"\nSTACK FULL";
             	   
             	tmp->data=n;
             	tmp->link=top;
             	top=tmp;
             }

             int pop()
             {
             	if(top==NULL)
             	{
             		cout<<"\nSTACK EMPTY";
             		return NULL;
             	}
                node *tmp;
                int n;
                tmp=top;
                n=tmp->data;
                top=top->link;
                delete tmp;
                return n;
             }

             ~lstack()
             {
             	if(top==NULL)
             	   return;

             	node *tmp;
             	while(top!=NULL)
             	{
             	   tmp=top;
             	   top=top->link;
             	   delete tmp;
             	}
             }
};

void main()
{
	lstack s;
	s.push(11);
	s.push(101);
	s.push(99);
	s.push(78);
	cout<<"Item Popped = "<<s.pop()<<endl;
	cout<<"Item Popped = "<<s.pop()<<endl;
	cout<<"Item Popped = "<<s.pop()<<endl;
}	



3.B)             QUEUES WITH LINKED LIST IMPLEMENTATION

Similar to the one above, the queued linked list removes the maximum data limit
as well. Here is the code:

#include <iostream.h>

struct node
{
   int data;
   node *link;
};

class lqueue
{
 private:
    node *front,*rear;
    
 public:
    lqueue()
    {
    	front=NULL;
    	rear=NULL;
    }
    
    void add(int n)
    {
    	node *tmp;
    	tmp=new node;
    	if(tmp==NULL)
    	   cout<<"\nQUEUE FULL";
    	   
    	tmp->data=n;
    	tmp->link=NULL;
    	if(front==NULL)
    	{
    		rear=front=tmp;
    		return;
    	}
            rear->link=tmp;
            rear=rear->link;
    }
    
    int del()
    {
    	if(front==NULL)
    	{
    		cout<<"\nQUEUE EMPTY";
    		return NULL;
    	}
        node *tmp;
        int n;
        n=front->data;
        tmp=front;
        front=front->link;
        delete tmp;
        return n;
    }
    
    ~lqueue()
    {
    	if(front==NULL)
    	   return;
    	node *tmp;
    	while(front!=NULL)
    	{
    		tmp=front;
    		front=front->link;
    		delete tmp;
    	}
     }
};

void main()
{
	lqueue q;
	q.add(11);
	q.add(22);
	q.add(33);
	q.add(44);
	q.add(55);
	cout<<"\nItem Deleted = "<<q.del();
	cout<<"\nItem Deleted = "<<q.del();
	cout<<"\nItem Deleted = "<<q.del();
}


3.C)                     CIRCULAR LINKED LISTS

Circular Linked Lists are just like normal linked lists except that the pointer
of the last item in the list points to the first item in the list. You must be
wondering...Why would anyone ever want to do such a thing? Well...did you know
that circular linked lists are used almost in every situation, they are infact
used in Electronic Advertisements where each ad is added to the list and is
displayed. After the last ad is displayed the linked list will automatically
display the first ad in the List.
Now let us see how we can implement the Circular Linked List. I've written this
code in much more detail plus I've included a SLIDESHOW Feature that shows the
Data in the List after a time-period is elapsed. It goes on displaying the data
until a key is pressed. Have a look:

#include <windows.h>
#include <stdio.h>
#include <iostream.h>
#include <conio.h>


class CL_list
{
   private:
      struct node
      {
      	int data;
        node *link;
      };
      struct node *p;

   public:
      CL_list();
      CL_list(CL_list& l);
      ~CL_list();
      void add(int);
      void del();
      void addatbeg(int);
      void display();
      void slideshow(float,int,int);
      int count();
      void wait(float);
      bool operator ==(CL_list);
      bool operator !=(CL_list);
      void operator =(CL_list);
};

   CL_list::CL_list()
   {
      p=NULL;
   }

   CL_list::CL_list(CL_list& l)
   {
      node *x;
      p=NULL;
      x=l.p;
      if(x==NULL)
      	return;
      for(int i=1;i<=l.count();i++)
      {
      	add(x->data);
         x=x->link;
      }
   }

   CL_list::~CL_list()
   {
   	node *q,*t;
      q=p;
      t=p;
      if(p==NULL)
      	return;
      while(q->link!=t)
      {
      	p=q;
         q=q->link;
         delete p;
      }
      p=q;
      delete p;
   }

   void CL_list::add(int n)
   {
      if(p==NULL)
      {
      	 node *q;
         q=new node;
         q->data=n;
         q->link=q;
         p=q;
         return;
      }
      node *q;
      q=p;
      while(q->link != p)
      	q=q->link;

      node *t;
      t=new node;
      t->data=n;
      t->link=p;
      q->link=t;
   }

   void CL_list::display()
   {
      if(p==NULL)
      {
      	cout<<"EMPTY LIST\n";
         return;
      }
      node *q;
      q=p;
      for(int i=1;i<=this->count();i++)
      {
       	 cout<<q->data<<endl;
         q=q->link;
      }
   }

   int CL_list::count()
   {
      node *q;
      q=p;
      int c=0;
      if(p==NULL)
      	return 0;
      else
      	c++;
      while(q->link != p)
      {
         c++;
         q=q->link;
      }
      return c;
   }

   void CL_list::del()
   {
      if(p==NULL)
      	return;
      if(p->link==p)
      {
      	p=NULL;
      }
      else
      {
      node *q;
      q=p;
      while(q->link != p )
      	q=q->link;

      q->link=p->link;
      q=p;
      p=(q->link == NULL ? NULL : p->link);
      delete q;
      }

   }

   void CL_list::addatbeg(int n)
   {
      node *q,*t;
      q=p;
      while(q->link!=p)
      	q=q->link;

      t=new node;
      t->data=n;
      t->link=p;
      q->link=t;
      p=t;
   }

   void CL_list::slideshow(float dlay,int x,int y)
   {
      if(p==NULL)
      {
         gotoxy(x,y);
      	cout<<"EMPTY LIST\n";
         return;
      }
      node *q;
      q=p;
      while(!kbhit())
      {
      	 gotoxy(x,y);
         cout<<"               ";
         gotoxy(x,y);
         cout<<q->data;
         wait(dlay);
         q=q->link;
      }
   }

   void CL_list::wait(float t)
   {
      long time=GetTickCount()+(t*1000L);
      while(GetTickCount()<=time)
      {
      /*        WAIT !!! */
      }
   }

   bool CL_list::operator ==(CL_list t)
   {
      if(t.p==NULL && p==NULL)
      	return 1;

      if(this->count() != t.count())
      	return 0;
      node *q;
      q=p;
      int flag;
      flag=1;
      node *a;
      a=t.p;
      for(int i=1;i<=count();i++)
      {
      	if(a->data!=q->data)
           flag=0;
         a=a->link;
         q=q->link;
      }
      if(a->data!=q->data)
      	flag=0;
      return flag;
   }

   bool CL_list::operator !=(CL_list t)
   {
   	return !(this->operator==(t));
   }


   void main()
   {

      CL_list a;
      a.add(1);
      a.add(2);
      a.add(3);
      a.add(4);
      a.addatbeg(128);
      a.del(); // 128 is deleted
      cout<<"\nLIST DATA:\n";
      a.display();

      CL_list b=a;
      if(b!=a)
      	printf("\nunEQUAL");
      else
      	printf("\nEQUAL\n");
      a.slideshow(1,13,13);

      getch();
}

Here once again we have made sure that the last node always points to the first 
node. Everything else seems fine. Comments should be enough to explain the code.
The interesting part of this code is the slideshow() function. It plainly 
displays the list in an infinite loop which can be terminated by pressing a key.
The wait() function allows the delay while the kbhit() function checks for a
keypress.
Now comes the test. Write a similar linked list only with the following changes:
1) Structure node should be like this:
       struct node
       {
         int data;
         node *next;  // Pointer to Next Node
         node *prev;  // Pointer to Previous Node
       };

2)  Remember that while adding and deleting the next and previous pointers have
to be set up accordingly.

3) Include a display function with a parameter like this:
      void linklist::display(int type)
      {
           if(type==1)
           {
            // Code for output from First Node to Last node
           }
           else
           {
            // Code for output from Last Node to First
           }
      }
This function is really easy to write if you understand how to use both the next
and previous pointers.

If you still cant write the code mail me with your difficulties at my email add: 
born2c0de@hotmail.com

4)                                 BINARY TREES

Uptil now all data structures that we have covered (Stack,Queue,Linked List) are 
linear in nature ie. they have a definate order of placement. Now we shall study
Binary Trees which requires a different thought process as it is a non linear
data structure.

A Binary Tree consists of a main node known as the Root. The Root then has two 
sub-sections, ie. the left and the right half. The data subsequently stored 
after the root is created depends on it's value compared to the root.
Suppose the root value is 10 and the Value to be added is 15, then the data is 
added to the right section of the root.
The Basic idea is that every node can be thought of a binary tree itself. Each 
node has two pointers, one to the left and the other to the right. Depending on
the value to be stored, it is placed after a node's right pointer if the value
of the node is lesser than the one to be added or the node's left pointer if
viceversa.

Let's take an Example. To add the Following List of Numbers, we end up with a
Binary Tree like this:

32 16 34 1 87 13 7 18 14 19 23 24 41 5 53

KEY:
      [X]              X = Root   L/R = Data at Left/Right Node of X
[L]<---|--->[R]


                            ROOT
                            [32]
                             |
                     [16]<---|--->[34]
                      |            |
               [1]<---|--->[18]    |--->[87]
                |           |            |
                |           |    [41]<---|
                |           |     |
                |           |     |--->[53]
                |           |
                |           |--->[19]
                |                  |--->[23]
                |                        |--->[24]
                |
                |--->[13]
                       |
                [7]<---|--->[14]
          [5]<---|

Here's How:
**: KEEP ADDING DATA IN THE TREE ON PAPER AFTER EACH STEP BELOW TO UNDERSTAND
    HOW THE TREE IS FORMED.

1) Since 32 is the First Number to be added, 32 becomes the root of the tree.
2) Next Number is 16 which is lesser than 32 Hence 16 becomes left node of 32.
3) 34. Since 34 > 32 , 34 becomes the right node of the ROOT.

4) 1. Since 1 < 32 we jump to the left node of the ROOT. But since the left node
   has already been taken we test 1 once again. Since 1 < 16, 1 becomes the left
   node of 16.

5) 87. Since 87 > 32 we jump to the right node of the root. Once again this
   space is occupied by 34. Now since 87 > 34, 87 becomes the right node of 34.

6) 13. Since 13 < 32 we jump to left node of the root. There, 13 < 16 so we
   continue towards the left node of 16. There 13 > 1, so 13 becomes the right
   node of 1.

7) Similarly work out addition till the end ie. before Number 53.

8) 53. Since 53 > 32 we jump to the right node of the root. There 53 > 34 so we
   continue to the right node of 34. There 53 < 87 so we continue towards the
   left node of 87. There 53 > 41 so we jump to the right node of 41. Since the
   Right node of 41 is empty 53 becomes the right node of 41.

This should give you an idea of how a Binary Tree works. You must know that:
1) The linking of nodes to nodes in a Binary Tree is one to one in nature
   ie. a node cannot be pointed by more than 1 node.
2) A Node can point to two different sub-nodes at the most.

Here in the binary tree above there are a few nodes whose left and right
pointers are empty ie. they have no sub-node attached to them. So Nodes 5,14,18,
19,23,24,41 have their left nodes empty.

There are three popular ways to display a Binary Tree. Displaying the trees
contents is known as transversal. There are three ways of transversing a tree iw.
in inorder,preorder and postorder transversal methods. Description of each is
shown below:

PREORDER:
1) Visit the root.
2) Transverse the left leaf in preorder.
3) Transverse the right leaf in preorder.

INORDER:
1) Transverse the left leaf in inorder.
2) Visit the root.
3) Transverse the right leaf in inorder.

POSTORDER:
1) Transverse the left leaf in postorder.
2) Transverse the right leaf in postorder.
3) Visit the root.

Writing code for these three methods are simple if we understand the recursive
nature of a binary tree. Binary tree is recursive, as in each node can be
thought of a binary tree itself. It's just the order of displaying data that
makes a difference for transversal.

Deletion from a Binary Tree is a bit more difficult to understand. For now just
remember that for deleting a node, it is replaced with it's next inorder
successor. I'll explain everything after the Binary Tree code.
Now that you've got all your Binary Tree Fundas clear, let's move on with the
Source code.

#include <iostream.h>

#define YES 1
#define NO 0

class tree
{
	private:
		struct leaf
		{
			int data;
			leaf *l;
			leaf *r;
		};
		struct leaf *p;

	public:
		tree();		
		~tree();
		void destruct(leaf *q);
		tree(tree& a);
		void findparent(int n,int &found,leaf* &parent);
		void findfordel(int n,int &found,leaf *&parent,leaf* &x);
		void add(int n);
		void transverse();
		void in(leaf *q);
		void pre(leaf *q);
		void post(leaf *q);
		void del(int n);
};
		
tree::tree()
{
	p=NULL;
}

tree::~tree()
{
	destruct(p);
}

void tree::destruct(leaf *q)
{
	if(q!=NULL)
	{
		destruct(q->l);
		del(q->data);
		destruct(q->r);
	}
}
void tree::findparent(int n,int &found,leaf *&parent)
{
	leaf *q;
	found=NO;
	parent=NULL;

	if(p==NULL)
		return;

	q=p;
	while(q!=NULL)
	{
		if(q->data==n)
		{
			found=YES;
			return;
		}
		if(q->data>n)
		{
			parent=q;
			q=q->l;
		}
		else
		{
			parent=q;
			q=q->r;
		}
	}
}

void tree::add(int n)
{
	int found;
	leaf *t,*parent;
	findparent(n,found,parent);
	if(found==YES)
		cout<<"\nSuch a Node Exists";
	else
	{
		t=new leaf;
		t->data=n;
		t->l=NULL;
		t->r=NULL;

		if(parent==NULL)
			p=t;
		else
			parent->data > n ? parent->l=t : parent->r=t;
	}
}

void tree::transverse()
{
	int c;
	cout<<"\n1.InOrder\n2.Preorder\n3.Postorder\nChoice: ";
	cin>>c;
	switch(c)
	{
		case 1:
			in(p);
			break;

		case 2:
			pre(p);
			break;

		case 3:
			post(p);
			break;
	}
}

void tree::in(leaf *q)
{
	if(q!=NULL)
	{
		in(q->l);
		cout<<"\t"<<q->data<<endl;
		in(q->r);
	}
	
}

void tree::pre(leaf *q)
{
	if(q!=NULL)
	{
		cout<<"\t"<<q->data<<endl;
		pre(q->l);
		pre(q->r);
	}
	
}

void tree::post(leaf *q)
{
	if(q!=NULL)
	{
		post(q->l);
		post(q->r);
		cout<<"\t"<<q->data<<endl;		
	}
	
}

void tree::findfordel(int n,int &found,leaf *&parent,leaf *&x)
{
	leaf *q;
	found=0;
	parent=NULL;
	if(p==NULL)
		return;

	q=p;
	while(q!=NULL)
	{
		if(q->data==n)
		{
			found=1;
			x=q;
			return;
		}
		if(q->data>n)
		{
			parent=q;
			q=q->l;
		}
		else
		{
			parent=q;
			q=q->r;
		}
	}
}

void tree::del(int num)
{
	leaf *parent,*x,*xsucc;
	int found;

	// If EMPTY TREE
	if(p==NULL)
	{
		cout<<"\nTree is Empty";
		return;
	}
	parent=x=NULL;
	findfordel(num,found,parent,x);
	if(found==0)
	{
		cout<<"\nNode to be deleted NOT FOUND";
		return;
	}

	// If the node to be deleted has 2 leaves
	if(x->l != NULL && x->r != NULL)
	{
		parent=x;
		xsucc=x->r;

		while(xsucc->l != NULL)
		{
			parent=xsucc;
			xsucc=xsucc->l;
		}
		x->data=xsucc->data;
		x=xsucc;
	}

	// if the node to be deleted has no child
	if(x->l == NULL && x->r == NULL)
	{
		if(parent->r == x)
			parent->r=NULL;
		else
			parent->l=NULL;

		delete x;
		return;
	}

	// if node has only right leaf
	if(x->l == NULL && x->r != NULL )
	{
		if(parent->l == x)
			parent->l=x->r;
		else
			parent->r=x->r;

		delete x;
		return;
	}

	// if node to be deleted has only left child
	if(x->l != NULL && x->r == NULL)
	{
		if(parent->l == x)
			parent->l=x->l;
		else
			parent->r=x->l;

		delete x;
		return;
	}
}





void main()
{
	tree t;
	int data[]={32,16,34,1,87,13,7,18,14,19,23,24,41,5,53};
	for(int i=0;i<15;i++)
		t.add(data[i]);

	t.transverse();
	t.del(16);
	t.transverse();
	t.del(41);
	t.transverse();
}

OUTPUT:

1.InOrder
2.Preorder
3.Postorder
Choice: 1
        1
        5
        7
        13
        14
        16
        18
        19
        23
        24
        32
        34
        41
        53
        87

1.InOrder
2.Preorder
3.Postorder
Choice: 2
        32
        18
        1
        13
        7
        5
        14
        19
        23
        24
        34
        87
        41
        53

1.InOrder
2.Preorder
3.Postorder
Choice: 3
        5
        7
        14
        13
        1
        24
        23
        19
        18
        53
        87
        34
        32
Press any key to continue

NOTE: Visual C++ may give Runtime Errors with this code. Compile with Turbo C++.

Just by looking at the output you might realise that we can print out the whole
tree in ascending order by using inorder transversal. Infact Binary Trees are
used for Searching [ Binary Search Trees {BST} ] as well as in Sorting.
The Addition of data part seems fine. Only the deletion bit needs to be
explained.

For deletion of data there are a few cases to be considered:
1) If the leaf to be deleted is not found.
2) If the leaf to be deleted has no sub-leafs.
3) If the leaf to be deleted has 1 sub-leaf.
4) If the leaf to be deleted has 2 sub-leafs.

Dealing with the first case is simple, we just mention an error message and
leave it out there.
In the second case since the node has no sub-nodes, the memory occupied by this
should be freed and either the left link or the right link of the parent of this
node should be set to NULL. Which of these should be set to NULL depends upon
whether the node being deleted is a left child or a right child of its parent.
In the third case we just adjust the pointer of the parent of the leaf to be
deleted such that after deletion it points to the child of the node being
deleted.
The last case in which the leaf to be deleted has to sub-leaves of its own is
rather complicated.The whole logic is to locate the inorder successor, copy it's
data and reduce the problem to simple deletion of a node with one or zero leaves.
Consider in the above program...(Refer to the previous tree as well) when we are
deleting 16 we search for the next inorder successor. So we simply set the data
value to 5 and delete the node with value 5 as shown for cases 2 and 3.

That's all for Binary Trees. Binary Trees are used for various other things
which even include Compression algorithms,binary searching,sorting etc. A lot of
Huffman,Shannon-Fano and other Compression algorithms use Binary Trees. If you
want source code of these Compression codes you can freely contact me at my mail
address.

That wraps up this Data Structure Tutorial. There are a lot more structures that
i'd love to mention such as Sparse Matrices, Graphs etc. but since the aim of
this tutorial was to give an introduction to Data Structures i decided not to
include them in this Tutorial. Maybe I can save them for another Tutorial that
starts from this point itself...later...

If you have any problems in understanding the text or the source code do let me
know. Any valuable comments and suggestions are welcome.

                                                   -Sanchit Karve
                                                      born2c0de
                                                 "Accept No Limits"
--------------------------------------------------------------------------------
[EOF]