bTS

1. Binary Search Tree
Aakash Montheiro - 161702
Abhishek.L.R - 161704
Deelan Jostan Monthero - 161726
I Sem - M.C.A
Aloysius Institute Of Management &
Information Technology

2. What is …?
• A Binary tree is a non-linear data structure which is a collection of elements
called nodes.
• A Binary Search Tree (BST) is a Binary tree in which all the nodes follow the
below-mentioned properties :
The left sub-tree of a node has a key less than or equal to its parent node's key.
The right sub-tree of a node has a key greater than to its parent node's key.
• Thus, BST divides all its sub-trees into two segments;
 Left sub-tree
 Right sub-tree

3. Operations Performed in a BST:
Search − Searches an element in a tree.
Insert − Inserts an element in a tree.
Traversal :
Pre-order Traversal − Traverses a tree in a pre-order manner. [Root->Left->Right]
In-order Traversal − Traverses a tree in an in-order manner. [Left->Root->Right]
Post-order Traversal − Traverses a tree in a post-order manner.[Left->Right->Root]

4. Example:
Given : 37 ,24 ,45 ,20 ,29 ,41,52
37
24 45
20 29 41 52

5. Binary Tree v/s Binary Search Tree
Given : 37 ,45 ,24 ,29 ,41 ,20 ,24 ,52
24
37
24 45
20 29 41 52
37
24 45
20 29 41 52
37
24 45
20 29 41 52

6. Implementation:
• Creating the Structure
typedef struct Tree{
int Data;
struct Tree *Right;
struct Tree * Left;
}TREENODE;
Data *Right
*Left
Null Null

7. Implementation Contd..
class BSTree{
TREENODE *Root;
public:
BTree();//--Constructor
TREENODE *MakeTreeNode(int Num);
void InsertTreeNode(int Num);
void Preorder(TREENODE *Root);
void Postorder(TREENODE *Root);
void Inorder(TREENODE *Root);
TREENODE *GetRoot();
int TreeSearch(int Num);
};
Creating the Class:

8. Implementation Contd…
BTree::BTree()
{
Root=NULL;
}
TREENODE *BTree::MakeTreeNode(int Num)
{
TREENODE *New;
New=(TREENODE *)malloc(sizeof(TREENODE));
New->Data=Num;
New->Right=NULL;
New->Left=NULL;
return New;
}
TREENODE *BTree::GetRoot()
{
return Root;
}
Constructor
Getting the Root Node
Creating the Node

9. Implementation Contd…
void BTree::InsertTreeNode(int Num)
{
TREENODE *New,*Cur,*Prev;
Cur=Prev=Root;
New=MakeTreeNode(Num);
if(Root==NULL){
Root=New;
return;
}
Inserting a Element to a tree:

10. Implementation Contd…
Inserting a Element to a tree Contd:
while(Cur){
if(Num>Cur->Data){
Prev=Cur;
Cur=Cur->Right;
}else{
Prev=Cur;
Cur=Cur->Left;
}
}
if(Num>Prev->Data){
Prev->Right=New;
}else{
Prev->Left=New;
}
return;
}

11. Implementation Contd…
void BTree::Preorder(TREENODE *Root)
{
if(Root){
cout<<Root->Data<<"t""";
Preorder(Root->Left);
Preorder(Root->Right);
}
}
void BTree::Postorder(TREENODE *Root)
{
if(Root){
Postorder(Root->Left);
Postorder(Root->Right);
cout<<Root->Data<<"t";
}
}
void BTree::Inorder(TREENODE *Root)
{
if(Root){
Inorder(Root->Left);
cout<<Root->Data<<"t";
Inorder(Root->Right);
}
}
Pre-Order
In-Order
Post-Order
Traversing the Tree

12. int BTree::TreeSearch(int Num)
{
TREENODE *Cur;
Cur=Root;
while(Cur){
if(Num==Cur->Data){
return 1;
}else if(Num>Cur->Data){
Cur=Cur->Right;
}else{
Cur=Cur->Left;
}
}
}
Implementation Contd…
Searching the Element

13. Implementation Contd…
Inserting elements in Main Program cout<<"Enter the value of N : ";
cin>>N;
cout<<"Enter the elements n";
for(i=1;i<=N;i++){
cout<<"Enter the element A["<<i<<"] : ";
cin>>Num;
BT.InsertTreeNode(Num);
}
Declaration in Main Program
TREENODE *Root;
BTree BT;

14. Implementation Contd…
Root=BT.GetRoot();
cout<<"Pre-order traverse is : ";
BT.Preorder(Root);
cout<<"n";
break;
Traversing the Tree
Searching of Elements
cout<<"Enter the Search element : ";
cin>>Search;
Res=BT.TreeSearch(Search);
if(Res==1){
cout<<"Element "<<Search<<" Found...n";
}else{
cout<<"Element "<<Search<<" Not-found....n";
}
break;
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15. Thank You
For
Your
Attention !
Any Question