Double Threaded Binary Search Tree
Double Threaded Binary Search Tree: is a binary search tree in which the nodes are not every left NULL pointer points to its inorder predecessor and the right NULL pointer points to the inorder successor.
The threads are also useful for fast accessing the ancestors of a node.
Double Threaded Binary Search Tree is one of the most used types of Advanced data structures used in many real-time applications like places where there are recent insertion and traversal of all elements of the search tree.
Creation algorithm for Double Threaded Binary Search Tree:
- In Double Threaded Binary search tree, there are five fields namely, data fields, left, right pointers, lbit, and rbit where lbit and rbit are boolean value stored to denote the right pointer points to an inorder successor or a new child node. Similarly, lbit denotes that the left pointer points to an inorder predecessor or a new child node.
- Base condition for the creation of the Double Threaded binary search tree is that the root node exists or not, If it doesn’t exist then create a new node and store it.
- Otherwise, compare the data of the current node to the new Data to be inserted, If the new data is less than the current data then traverse to the left child node. Otherwise, traverse to the right child node.
- If the left child or right child doesn’t exist then insert the node to its left and point its left and right child to the inorder predecessor and successor respectively.
Below is the implementation of the above approach:
C++
// C++ implementation of the double // threaded binary searighth tree #include <iostream> using namespace std; // Class of the Node class Node { int lbit, rbit; int value; Node *left, *right; public : // Constructor of the // Node of the Tree Node() { lbit = rbit = 0; value = 0; left = right = NULL; } friend class DTBT; }; // Class of the Threaded // Binary search tree class DTBT { Node* root; public : // Constructor of the // Threaded of the Binary // Search Tree DTBT() { root = new Node(); // Initialise the dummy node // to any random value of // your choice. root->value = 9999; // Considering our whole // tree is at left of // dummy node root->rbit = 1; root->lbit = 0; // Consider your whole tree // lies to the left of // this dummy node. root->left = root; root->right = root; } void create(); void insert( int value); void preorder(); Node* preorderSuccessor(Node*); void inorder(); Node* inorderSuccessor(Node*); }; // Function to create the Binary // search tree void DTBT::create() { int n = 9; // Insertion of the nodes this ->insert(6); this ->insert(3); this ->insert(1); this ->insert(5); this ->insert(8); this ->insert(7); this ->insert(11); this ->insert(9); this ->insert(13); } // Function to insert the nodes // into the threaded binary // search tree void DTBT::insert( int data) { // Condition to check if there // is no node in the binary tree if (root->left == root && root->right == root) { Node* p = new Node(); p->value = data; p->left = root->left; p->lbit = root->lbit; p->rbit = 0; p->right = root->right; // Inserting the node in the // left of the dummy node root->left = p; root->lbit = 1; return ; } // New node Node* cur = new Node; cur = root->left; while (1) { // Condition to check if the // data to be inserted is // less than the current node if (cur->value < data) { Node* p = new Node(); p->value = data; if (cur->rbit == 0) { p->right = cur->right; p->rbit = cur->rbit; p->lbit = 0; p->left = cur; // Inserting the node // in the right cur->rbit = 1; cur->right = p; return ; } else cur = cur->right; } // Otherwise insert the node // in the left of current node if (cur->value > data) { Node* p = new Node(); p->value = data; if (cur->lbit == 0) { p->left = cur->left; p->lbit = cur->lbit; p->rbit = 0; // Pointing the right child // to its inorder Successor p->right = cur; cur->lbit = 1; cur->left = p; return ; } else cur = cur->left; } } } // In Threaded binary search tree // the left pointer of every node // points to its Inorder predecessor, // whereas its right pointer points // to the Inorder Successor void DTBT::preorder() { Node* c = root->left; // Loop to traverse the tree in // the preorder fashion while (c != root) { cout << " " << c->value; c = preorderSuccessor(c); } } // Function to find the preorder // Successor of the node Node* DTBT::preorderSuccessor(Node* c) { if (c->lbit == 1) { return c->left; } while (c->rbit == 0) { c = c->right; } return c->right; } // In Threaded binary search tree // the left pointer of every node // points to its Inorder predecessor // whereas its right pointer points // to the Inorder Successor void DTBT::inorder() { Node* c; c = root->left; while (c->lbit == 1) c = c->left; // Loop to traverse the tree while (c != root) { cout << " " << c->value; c = inorderSuccessor(c); } } // Function to find the inorder // successor of the node Node* DTBT::inorderSuccessor(Node* c) { if (c->rbit == 0) return c->right; else c = c->right; while (c->lbit == 1) { c = c->left; } return c; } // Driver Code int main() { DTBT t1; // Creation of the Threaded // Binary search tree t1.create(); cout << "Inorder Traversal of DTBST\n" ; t1.inorder(); cout << "\nPreorder Traversal of DTBST\n" ; t1.preorder(); return 0; } |
Java
public class ThreadedBinarySearchTree { // Class of the Node private static class Node { int lbit, rbit; int value; Node left, right; // Constructor of the Node of the Tree Node() { lbit = rbit = 0 ; value = 0 ; left = right = null ; } } // Class of the Threaded Binary search tree private static class ThreadedBinarySearchTreeImpl { Node root; // Constructor of the Threaded Binary Search Tree ThreadedBinarySearchTreeImpl() { root = new Node(); // Initialize the dummy node to any random value of your choice. root.value = 9999 ; // Considering our whole tree is at the left of the dummy node. root.rbit = 1 ; root.lbit = 0 ; // Consider your whole tree lies to the left of this dummy node. root.left = root; root.right = root; } void create() { // Insertion of the nodes this .insert( 6 ); this .insert( 3 ); this .insert( 1 ); this .insert( 5 ); this .insert( 8 ); this .insert( 7 ); this .insert( 11 ); this .insert( 9 ); this .insert( 13 ); } void insert( int data) { // Condition to check if there is no node in the binary tree if (root.left == root && root.right == root) { Node p = new Node(); p.value = data; p.left = root.left; p.lbit = root.lbit; p.rbit = 0 ; p.right = root.right; // Inserting the node in the left of the dummy node root.left = p; root.lbit = 1 ; return ; } // New node Node cur = root.left; while ( true ) { // Condition to check if the data to be inserted is less than the current node if (cur.value < data) { Node p = new Node(); p.value = data; if (cur.rbit == 0 ) { p.right = cur.right; p.rbit = cur.rbit; p.lbit = 0 ; p.left = cur; // Inserting the node in the right cur.rbit = 1 ; cur.right = p; return ; } else cur = cur.right; } // Otherwise insert the node in the left of the current node if (cur.value > data) { Node p = new Node(); p.value = data; if (cur.lbit == 0 ) { p.left = cur.left; p.lbit = cur.lbit; p.rbit = 0 ; // Pointing the right child to its inorder Successor p.right = cur; cur.lbit = 1 ; cur.left = p; return ; } else cur = cur.left; } } } // In Threaded binary search tree, the left pointer of every node // points to its Inorder predecessor, // whereas its right pointer points to the Inorder Successor void preorder() { Node c = root.left; // Loop to traverse the tree in the preorder fashion while (c != root) { System.out.print( " " + c.value); c = preorderSuccessor(c); } } // Function to find the preorder Successor of the node Node preorderSuccessor(Node c) { if (c.lbit == 1 ) { return c.left; } while (c.rbit == 0 ) { c = c.right; } return c.right; } // In Threaded binary search tree, the left pointer of every // node points to its Inorder predecessor // whereas its right pointer points to the Inorder Successor void inorder() { Node c = root.left; while (c.lbit == 1 ) c = c.left; // Loop to traverse the tree while (c != root) { System.out.print( " " + c.value); c = inorderSuccessor(c); } } // Function to find the inorder successor of the node Node inorderSuccessor(Node c) { if (c.rbit == 0 ) return c.right; else c = c.right; while (c.lbit == 1 ) { c = c.left; } return c; } } // Driver Code public static void main(String[] args) { ThreadedBinarySearchTreeImpl t1 = new ThreadedBinarySearchTreeImpl(); // Creation of the Threaded Binary search tree t1.create(); System.out.println( "Inorder Traversal of DTBST" ); t1.inorder(); System.out.println( "\nPreorder Traversal of DTBST" ); t1.preorder(); } } |
Python3
# Python implementation of the double # threaded binary searighth tree # Class of the Node class Node: def __init__( self ): self .lbit = None self .rbit = None self .value = None self .left = None self .right = None # Class of the Threaded # Binary search tree class DTBT: root = None # Constructor of the # Threaded of the Binary # Search Tree def __init__( self ): self .root = Node() # Initialise the dummy node # to any random value of # your choice. self .root.value = 9999 # Considering our whole # tree is at left of # dummy node self .root.rbit = 1 self .root.lbit = 0 # Consider your whole tree # lies to the left of # this dummy node. self .root.left = self .root self .root.right = self .root def create( self ): n = 9 # Insertion of the nodes self .insert( 6 ) self .insert( 3 ) self .insert( 1 ) self .insert( 5 ) self .insert( 8 ) self .insert( 7 ) self .insert( 11 ) self .insert( 9 ) self .insert( 13 ) # Function to insert the nodes # into the threaded binary # search tree def insert( self , data): # Condition to check if there # is no node in the binary tree if ( self .root.left = = self .root and self .root.right = = self .root): # New node p = Node() p.value = data p.left = self .root.left p.lbit = self .root.lbit p.rbit = 0 p.right = self .root.right # Inserting the node in the # left of the dummy node self .root.left = p self .root.lbit = 1 return # New node cur = self .root.left while ( 1 ): # Condition to check if the # data to be inserted is # less than the current node if (cur.value < data): p = Node() p.value = data if (cur.rbit = = 0 ): p.right = cur.right p.rbit = cur.rbit p.lbit = 0 p.left = cur # Inserting the node # in the right cur.rbit = 1 cur.right = p return else : cur = cur.right # Otherwise insert the node # in the left of current node if (cur.value > data): p = Node() p.value = data if (cur.lbit = = 0 ): p.left = cur.left p.lbit = cur.lbit p.rbit = 0 # Pointing the right child # to its inorder Successor p.right = cur cur.lbit = 1 cur.left = p return else : cur = cur.left # In Threaded binary search tree # the left pointer of every node # points to its Inorder predecessor, # whereas its right pointer points # to the Inorder Successor def preorder( self ): c = self .root.left # Loop to traverse the tree in # the preorder fashion while (c ! = self .root): print (c.value, end = ' ' ) c = self .preorderSuccessor(c) # Function to find the preorder # Successor of the node def preorderSuccessor( self , c): if (c.lbit = = 1 ): return c.left while (c.rbit = = 0 ): c = c.right return c.right # In Threaded binary search tree # the left pointer of every node # points to its Inorder predecessor # whereas its right pointer points # to the Inorder Successor def inorder( self ): c = self .root.left while (c.lbit = = 1 ): c = c.left # Loop to traverse the tree while (c ! = self .root): print (c.value, end = ' ' ) c = self .inorderSuccessor(c) # Function to find the inorder # successor of the node def inorderSuccessor( self , c): if (c.rbit = = 0 ): return c.right else : c = c.right while (c.lbit = = 1 ): c = c.left return c # Driver Code if __name__ = = '__main__' : t1 = DTBT() # Creation of the Threaded # Binary search tree t1.create() print ( "Inorder Traversal of DTBST" ) t1.inorder() print ( "\nPreorder Traversal of DTBST" ) t1.preorder() |
C#
using System; // Class of the Node class Node { public int lbit, rbit; public int value; public Node left, right; // Constructor of the Node of the Tree public Node() { lbit = rbit = 0; value = 0; left = right = null ; } } // Class of the Threaded Binary search tree class DTBT { Node root; // Constructor of the Threaded Binary Search Tree public DTBT() { root = new Node(); // Initialise the dummy node to any random value of your choice. root.value = 9999; // Considering our whole tree is at the left of dummy node root.rbit = 1; root.lbit = 0; // Consider your whole tree lies to the left of this dummy node. root.left = root; root.right = root; } public void Create() { // Insertion of the nodes this .Insert(6); this .Insert(3); this .Insert(1); this .Insert(5); this .Insert(8); this .Insert(7); this .Insert(11); this .Insert(9); this .Insert(13); } // Function to insert the nodes into the threaded binary search tree public void Insert( int data) { // Condition to check if there is no node in the binary tree if (root.left == root && root.right == root) { Node p = new Node(); p.value = data; p.left = root.left; p.lbit = root.lbit; p.rbit = 0; p.right = root.right; // Inserting the node in the left of the dummy node root.left = p; root.lbit = 1; return ; } // New node Node cur = new Node(); cur = root.left; while ( true ) { // Condition to check if the data to be inserted is less than the current node if (cur.value < data) { Node p = new Node(); p.value = data; if (cur.rbit == 0) { p.right = cur.right; p.rbit = cur.rbit; p.lbit = 0; p.left = cur; // Inserting the node in the right cur.rbit = 1; cur.right = p; return ; } else { cur = cur.right; } } // Otherwise insert the node in the left of the current node if (cur.value > data) { Node p = new Node(); p.value = data; if (cur.lbit == 0) { p.left = cur.left; p.lbit = cur.lbit; p.rbit = 0; // Pointing the right child to its inorder Successor p.right = cur; cur.lbit = 1; cur.left = p; return ; } else { cur = cur.left; } } } } // In Threaded binary search tree, the left pointer of every node points to its Inorder predecessor, // whereas its right pointer points to the Inorder Successor public void Preorder() { Node c = root.left; // Loop to traverse the tree in the preorder fashion while (c != root) { Console.Write( " " + c.value); c = PreorderSuccessor(c); } } // Function to find the preorder Successor of the node public Node PreorderSuccessor(Node c) { if (c.lbit == 1) { return c.left; } while (c.rbit == 0) { c = c.right; } return c.right; } // In Threaded binary search tree, the left pointer of every node points to its Inorder predecessor // whereas its right pointer points to the Inorder Successor public void Inorder() { Node c; c = root.left; while (c.lbit == 1) c = c.left; // Loop to traverse the tree while (c != root) { Console.Write( " " + c.value); c = InorderSuccessor(c); } } // Function to find the inorder Successor of the node public Node InorderSuccessor(Node c) { if (c.rbit == 0) return c.right; else c = c.right; while (c.lbit == 1) { c = c.left; } return c; } } // Driver Code class Program { static void Main() { DTBT t1 = new DTBT(); // Creation of the Threaded Binary search tree t1.Create(); Console.WriteLine( "Inorder Traversal of DTBST" ); t1.Inorder(); Console.WriteLine( "\nPreorder Traversal of DTBST" ); t1.Preorder(); } } // Contributed by Siddhesh |
Javascript
// JavaScript implementation of the double // threaded binary search tree // Class of the Node class Node { constructor() { this .lbit = null ; this .rbit = null ; this .value = null ; this .left = null ; this .right = null ; } } // Class of the Threaded // Binary search tree class DTBT { constructor() { this .root = new Node(); // Initialise the dummy node // to any random value of // your choice. this .root.value = 9999; // Considering our whole // tree is at left of // dummy node this .root.rbit = 1; this .root.lbit = 0; // Consider your whole tree // lies to the left of // this dummy node. this .root.left = this .root; this .root.right = this .root; } create() { const n = 9; // Insertion of the nodes this .insert(6); this .insert(3); this .insert(1); this .insert(5); this .insert(8); this .insert(7); this .insert(11); this .insert(9); this .insert(13); } // Function to insert the nodes // into the threaded binary // search tree insert(data) { // Condition to check if there // is no node in the binary tree if ( this .root.left === this .root && this .root.right === this .root ) { // New node const p = new Node(); p.value = data; p.left = this .root.left; p.lbit = this .root.lbit; p.rbit = 0; p.right = this .root.right; // Inserting the node in the // left of the dummy node this .root.left = p; this .root.lbit = 1; return ; } // New node let cur = this .root.left; while ( true ) { // Condition to check if the // data to be inserted is // less than the current node if (cur.value < data) { const p = new Node(); p.value = data; if (cur.rbit === 0) { p.right = cur.right; p.rbit = cur.rbit; p.lbit = 0; p.left = cur; // Inserting the node // in the right cur.rbit = 1; cur.right = p; return ; } else { cur = cur.right; } } // Otherwise insert the node // in the left of current node if (cur.value > data) { const p = new Node(); p.value = data; if (cur.lbit === 0) { p.left = cur.left; p.lbit = cur.lbit; p.rbit = 0; // Pointing the right child // to its inorder Successor p.right = cur; cur.lbit = 1; cur.left = p; return ; } else { cur = cur.left; } } } } // In Threaded binary search tree // the left pointer of every node // points to its Inorder predecessor, // whereas its right pointer points // to the Inorder Successor preorder() { let c = this .root.left; // Loop to traverse the tree in // the preorder fashion while (c != this .root) { process.stdout.write(c.value + " " ); c = this .preorderSuccessor(c); } } // Function to find the preorder // Successor of the node preorderSuccessor(c) { if (c.lbit == 1) { return c.left; } while (c.rbit == 0) { c = c.right; } return c.right; } // In Threaded binary search tree // the left pointer of every node // points to its Inorder predecessor // whereas its right pointer points // to the Inorder Successor inorder() { let c = this .root.left; while (c.lbit == 1) { c = c.left; } // Loop to traverse the tree while (c != this .root) { process.stdout.write(c.value + " " ); c = this .inorderSuccessor(c); } } // Function to find the inorder // successor of the node inorderSuccessor(c) { if (c.rbit == 0) { return c.right; } else { c = c.right; } while (c.lbit == 1) { c = c.left; } return c; } } let t1 = new DTBT(); // Creation of the Threaded Binary search tree t1.create(); console.log( "Inorder Traversal of DTBST" ); t1.inorder(); console.log( "\nPreorder Traversal of DTBST" ); t1.preorder(); // The code is contributed by Nidhi goel. |
Output
Inorder Traversal of DTBST 1 3 5 6 7 8 9 11 13 Preorder Traversal of DTBST 6 3 1 5 8 7 11 9 13
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