Binary Search Tree

Search From a Tree • How much time it takes? • In order to search an element from the tree of n nodes, we may have to perform maximum n comparison. • What are the advantages of storing data in the form of tree? • Move towards search tree.

Binary Search Tree •

A binary tree that is either empty or in which every node contains a key and satisfies the conditions: I.

The key in the left child of a node (if it exists) is less than the key in its parent II. The key in the right child of a node (if it exists) is greater than the key in its parent node. III. The left and right sub-trees of the root are again binary search trees.

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Keys in a binary search tree can be regarded as already sorted into order

Making a Binary Search Tree 4

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Binary Search Tree Examples Binary Search Trees: What about this tree?

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What about this tree?

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Implementation of Binary Search Tree class BTNode{ public: int data; BTNode *left,*right; BTNode (int d,BTNode* l=NULL, BTNode* r=NULL) {data=d;left=l; right=r;} };

Implementation of Binary Search Tree class BST{ BTNode * root; public: BST(){root=NULL;} void InsertKey(int x); void InsertRKey(int x,BTNode* & B); void Inorder(BTNode* bt); void Preorder(BTNode* bt); void Postorder(BTNode* bt); BTNode* &RRoot(){return root;} void deleteNode(BTNode *BT); BTNode* SearchKey(int d); ~ BST( ); }

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Deleting a Binary Search Tree void BST::deleteNode(BTNode *BT) { if(BT!=NULL) { deleteNode(BT->left); deleteNode(BT->right); cout<<"\tdeleting\t"<data; delete BT; } } BST:: ~ BST() { deleteNode(RRoot()); }

Implementation of Binary Search Tree void BST::Inorder(BTNode* bt) { if(bt != NULL) { Inorder(bt->left); cout<<"\t"<data; Inorder(bt->right); } } void BST::Preorder(BTNode* bt) { if(bt != NULL) { cout<<"\t"<data; Preorder(bt->left); Preorder(bt->right); } }

void BST::Postorder(BTNode* bt) { if(bt != NULL) { Postorder(bt->left); Postorder(bt->right); cout<<"\t"<data; } }

Searching a Binary Search Tree • For every node, compare the key to be located with the value stored in the node currently pointed at. • If the key is less than the value, go to the left subtree and try again. • If the key is greater than the value, go to the right subtree and try again. • If the key is equal to the value then, obviously the search can be discontinued. • The search is also aborted if there is no way to go, indicating that key is not in the tree.

Searching a Binary Search Tree BTNode* BST::SearchKey(int d) { BTNode *TN=root; while(TN !=NULL) { if(TN->data == d) return TN; else if( TN->data < d) TN=TN->right; else TN=TN->left; } return NULL; }

BST Insertion void BST::InsertKey( int x) { BTNode* pZ=new BTNode(x); if(root ==NULL) root=pZ; else { BTNode* Pre, *Cur=root; while(Cur!=NULL) { Pre=Cur; if(x < Cur->data) else } if(x < Pre->data) else } }

Cur=Cur->left; Cur=Cur->right; Pre->left =pZ; Pre->right=pZ;

BST Insertion (Recursive) void BST:: InsertRKey(int x, BTNode* & B) { if(B==NULL) B=new BTNode(x); else if(x < B->data) InsertRKey(x,B->left); else InsertRKey(x,B->right); }

Driver int main ( ) { BST b1; int d; BTNode * Temp; while(1) { cout<<"Enter Next Node "; cin>>d; if(d==0) break; b1.InsertRKey(d , b1.RRoot()); } cout<<"\n\n\t\t The Inorder traversal is\n "; b1.Inorder(b1.RRoot()); cout<<"Enter the key to search "; cin>>d; Temp=b1.SearchKey(d); if(Temp!=NULL) cout<<"\n"<data<<" Found at Address "<