Binary Search Tree
Download as PPTX, PDF5 likes2,249 views
The document explains the concept of a binary search tree (BST), detailing its structure and properties, such as how the left and right subtrees are organized in relation to the parent node. It outlines the key operations performed in a BST, including searching, inserting, and various traversal methods (pre-order, in-order, post-order), along with implementation code in C++. It also provides an example of inserting and searching for elements in the binary search tree.
![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]](https://image.slidesharecdn.com/bst-copy-171118141913/85/Binary-Search-Tree-3-320.jpg)
![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;](https://image.slidesharecdn.com/bst-copy-171118141913/85/Binary-Search-Tree-13-320.jpg)
Binary Search Tree
- 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-OrderPost-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 TreeSearching 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; Click here to download Source Code
- 15. Thank You For Your Attention ! Any Question