Friday, 12 April 2013

BINARY SEARCH TREE

A binary search tree (BST), also known as an ordered binary tree, is a node-based data structure in which each node has no more than two child nodes. 

Every binary tree must satisfy the following conditions:-

  • Each child must either be a leaf node or the root of another binary search tree. 
  • The left sub-tree contains only nodes with keys less than the parent node. 
  • The right sub-tree contains only nodes with keys greater than the parent node. 




The BST data structure is the basis for a number of highly efficient sorting and searching algorithm.


The very basic operations that can be performed on a Binary Search Tree are:-
  1. Searching
  2. Insertion
  3. Deletion
  4. Traversal


Traversals:-

  1. Preorder
  2. Inorder
  3. Postorder

The following images explains the different types of traversal in a BST:-

PRE-ORDER




IN-ORDER




POST-ORDER



In my C source code, I have included the following operations:-
  1. printing the preorder
  2. printing the inorder
  3. printing the postorder
  4. addition of a node into the BST
  5. counting the number of levels of tree
  6. calculating the height of the tree
  7. counting the number of leaf nodes
  8. printing all the elements of a particular level
  9. printing all the elements of a particular level
  10. deletion of nodes from the tree


SOURCE CODE:-
/******************************************************************************************************************************/
//COMPLETE PROGRAM ON BINARY SEARCH TREE

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

struct Tree
{
int val;
struct Tree* left,* right;
};

typedef struct Tree tree;


void inorder(tree*);
void preorder(tree*);
void postorder(tree*);
tree*makenode(int);
tree*add(tree*,tree*);
int countheight(tree*);
int countleaf(tree*);
int countnode(tree*);
void expandlevel(tree*,int,int);
tree*deletenode(tree*,int);



static int s=0;

int main()
{
tree*root,*nn;
//int level;
int tmp,ch;
root=NULL;
clrscr();
while(1)
{
printf("ENTER THE VALUE OF NODE");
scanf("%d",&tmp);

if(tmp==0)
break;

nn=makenode(tmp);

root=add(root,nn);

}

while(1)
{
clrscr();
printf("YOU HAVE FOLLOWING CHOICES:\n");
printf("1.PRINT PREORDER\n");
printf("2.PRINT INORDER\n");
printf("3.PRINT POSTORDER\n");
printf("4.ADD A NODE\n");
printf("5.COUNT THE NUMBER OF LEVELS OF TREE\n");
printf("6.COUNT THE HEIGHT\n");
printf("7.COUNT THE NUMBER OF LEAF NODES\n");
printf("8.COUNT THE TOTAL NUMBER OF NODES\n");
printf("9.PRINT ALL THE ELEMENTS OF A PARTICULAR LEVEL\n");
printf("10.DELETE A NODE FROM THE TREE\n");
printf("11.EXIT\n");
printf("ENTER YOUR CHOICE: ");
scanf("%d",&ch);

switch(ch)
{
case 1:
preorder(root);
break;
case 2:
inorder(root);
break;
case 3:
postorder(root);
break;
case 4:
printf("ENTER THE DATA PART OF THE NODE THAT YOU WANT TO ADD");
scanf("%d",&tmp);
nn=makenode(tmp);
root=add(root,nn);
break;
case 5:
//level=countlevel(root);
printf("\n%d",countheight(root)-1);
break;
case 6:
printf("%d",countheight(root));
break;
case 7:
s=0;
printf("%d",countleaf(root));
break;
case 8:
s=0;
printf("%d",countnode(root));
break;
case 9:
printf("ENTER THE LEVEL NUMBER THAT YOU WANT TO EXPAND: ");
scanf("%d",&tmp);
if(countheight(root)<tmp)
printf("THE LEVEL YOU ENTERED DOES NOT EXIST");
else
expandlevel(root,tmp,0);
break;
case 10:
printf("ENTER THE DATA PART OF THE NODE THAT YOU WANT TO DELETE");
scanf("%d",&tmp);
root=deletenode(root,tmp);
break;
case 11:
exit(1);
break;
default:
printf("YOU HAVE ENTERED A WRONG CHOICE");
}
printf("\nPRESS ANY KEY TO CONTINUE...");
getch();
}

getch();
return 1;
}

tree*deletenode(tree*root,int sval)
{
int dir;
tree*ptr,*prev,*temp;
prev=NULL;
ptr=root;
if(!root)
return root;

while(ptr)
{
if(ptr->val==sval)
break;
prev=ptr;
if(ptr->val>sval)
{
ptr=ptr->left;
dir=0;
}
else
{
ptr=ptr->right;
dir=1;
}
}

if(ptr)
{
if(ptr->left==NULL&&ptr->right==NULL)  //FOR LEAF NODE
{
if(ptr==root)           //LEAF NODE THAT IS ROOT
root=NULL;
else
if(dir==0)            //LEAF NODE THAT IS LEFT CHILD
prev->left=NULL;
else
prev->right=NULL;   //LEAF NODE THAT IS RIGHT CHILD

}
else                          //NODE THAT IS NOT A LEAF NODE
{
if(ptr->left&&ptr->right==NULL)
{
if(ptr==root)
root=root->left;
else
if(dir==0)
prev->left=ptr->left;
else
prev->right=ptr->left;
}
else
{
if(ptr==root)
root=root->right;
else
if(dir==0)
prev->left=ptr->right;
else
prev->right=ptr->right;
}

temp=ptr->right;
while(temp->left)
temp=temp->left;
temp->left=ptr->left;
}
free(ptr);
}
return root;
}


void expandlevel(tree*root,int level,int clevel)
{
if(!root&&clevel>level)
return;
if(clevel==level&&root)
{
printf("%d\t",root->val);
return;
}
if(clevel==level)
return;

expandlevel(root->left,level,clevel+1);
expandlevel(root->right,level,clevel+1);
}



int countnode(tree*root)
{
if(root)
{
countnode(root->left);
countnode(root->right);
s++;
}
return s;
}

int countleaf(tree*root)
{
if(root)
{
countleaf(root->left);
countleaf(root->right);
if((!(root->left))&&((!root->right)))
s++;
}
return s;
}


int countheight(tree*root)
{
int l,r;
if(!root)
return 0;
l=1+countheight(root->left);
r=1+countheight(root->right);

if(l>r)
return l;
return r;
}




void inorder(tree*root)
{
if(root)
{
inorder(root->left);
printf("%d\t",root->val);
inorder(root->right);
}
}

void postorder(tree*root)
{
if(root)
{
postorder(root->left);
postorder(root->right);
printf("%d\t",root->val);
}
}

void preorder(tree*root)
{
if(root)
{
printf("%d\t",root->val);
preorder(root->left);
preorder(root->right);
}
}



tree*makenode(int tmp)
{
tree*nn;
nn=(tree*)malloc(sizeof(tree));
nn->val=tmp;
nn->left=nn->right=NULL;
return nn;
}

tree*add(tree*root,tree*nn)
{
int dir;
tree*ptr,*prev;

if(!root)
return nn;
ptr=root;

while(ptr)
{
prev=ptr;
if(ptr->val>nn->val)
{
dir=0;
ptr=ptr->left;
}
else
{
dir=1;
ptr=ptr->right;
}
}

if(dir)
prev->right=nn;
else
prev->left=nn;

return root;
}
/*****************************************************************************************************************************/

OUTPUT:-

2 comments:

  1. Hi, Lavish i need help in binary tree can i expect logic but code in PHP ... I need your help :)
    Thanks for sharing this ...
    Thank you
    Sandeep Kumar dan

    ReplyDelete
  2. hey Sandeep,
    actually, I'm not that perfect in php, but i can give you the full logic/algorithm explained in detail.
    I apologize for this issue, presently its not possible for me to give the source code in php.

    ReplyDelete