Threaded Binary Tree | Insertion
We have already discuss the Binary Threaded Binary Tree.
Insertion in Binary threaded tree is similar to insertion in binary tree but we will have to adjust the threads after insertion of each element.
C representation of Binary Threaded Node:
struct Node { struct Node *left, *right; int info; // false if left pointer points to predecessor // in Inorder Traversal boolean lthread; // false if right pointer points to successor // in Inorder Traversal boolean rthread; };
In the following explanation, we have considered Binary Search Tree (BST) for insertion as insertion is defined by some rules in BSTs.
Let tmp be the newly inserted node. There can be three cases during insertion:
Case 1: Insertion in empty tree
Both left and right pointers of tmp will be set to NULL and new node becomes the root.
root = tmp; tmp -> left = NULL; tmp -> right = NULL;
Case 2: When new node inserted as the left child
After inserting the node at its proper place we have to make its left and right threads points to inorder predecessor and successor respectively. The node which was inorder successor. So the left and right threads of the new node will be-
tmp -> left = par ->left; tmp -> right = par;
Before insertion, the left pointer of parent was a thread, but after insertion it will be a link pointing to the new node.
par -> lthread = false; par -> left = temp;
Following example show a node being inserted as left child of its parent.
After insertion of 13,
Predecessor of 14 becomes the predecessor of 13, so left thread of 13 points to 10.
Successor of 13 is 14, so right thread of 13 points to left child which is 13.
Left pointer of 14 is not a thread now, it points to left child which is 13.
Case 3: When new node is inserted as the right child
The parent of tmp is its inorder predecessor. The node which was inorder successor of the parent is now the inorder successor of this node tmp. So the left and right threads of the new node will be-
tmp -> left = par; tmp -> right = par -> right;
Before insertion, the right pointer of parent was a thread, but after insertion it will be a link pointing to the new node.
par -> rthread = false; par -> right = tmp;
Following example shows a node being inserted as right child of its parent.
After 15 inserted,
Successor of 14 becomes the successor of 15, so right thread of 15 points to 16
Predecessor of 15 is 14, so left thread of 15 points to 14.
Right pointer of 14 is not a thread now, it points to right child which is 15.
C++ implementation to insert a new node in Threaded Binary Search Tree:
Like standard BST insert, we search for the key value in the tree. If key is already present, then we return otherwise the new key is inserted at the point where search terminates. In BST, search terminates either when we find the key or when we reach a NULL left or right pointer. Here all left and right NULL pointers are replaced by threads except left pointer of first node and right pointer of last node. So here search will be unsuccessful when we reach a NULL pointer or a thread.
Implementation:
C++
// Insertion in Threaded Binary Search Tree. #include<bits/stdc++.h> using namespace std; struct Node { struct Node *left, *right; int info; // False if left pointer points to predecessor // in Inorder Traversal bool lthread; // False if right pointer points to successor // in Inorder Traversal bool rthread; }; // Insert a Node in Binary Threaded Tree struct Node *insert( struct Node *root, int ikey) { // Searching for a Node with given value Node *ptr = root; Node *par = NULL; // Parent of key to be inserted while (ptr != NULL) { // If key already exists, return if (ikey == (ptr->info)) { printf ( "Duplicate Key !\n" ); return root; } par = ptr; // Update parent pointer // Moving on left subtree. if (ikey < ptr->info) { if (ptr -> lthread == false ) ptr = ptr -> left; else break ; } // Moving on right subtree. else { if (ptr->rthread == false ) ptr = ptr -> right; else break ; } } // Create a new node Node *tmp = new Node; tmp -> info = ikey; tmp -> lthread = true ; tmp -> rthread = true ; if (par == NULL) { root = tmp; tmp -> left = NULL; tmp -> right = NULL; } else if (ikey < (par -> info)) { tmp -> left = par -> left; tmp -> right = par; par -> lthread = false ; par -> left = tmp; } else { tmp -> left = par; tmp -> right = par -> right; par -> rthread = false ; par -> right = tmp; } return root; } // Returns inorder successor using rthread struct Node *inorderSuccessor( struct Node *ptr) { // If rthread is set, we can quickly find if (ptr -> rthread == true ) return ptr->right; // Else return leftmost child of right subtree ptr = ptr -> right; while (ptr -> lthread == false ) ptr = ptr -> left; return ptr; } // Printing the threaded tree void inorder( struct Node *root) { if (root == NULL) printf ( "Tree is empty" ); // Reach leftmost node struct Node *ptr = root; while (ptr -> lthread == false ) ptr = ptr -> left; // One by one print successors while (ptr != NULL) { printf ( "%d " ,ptr -> info); ptr = inorderSuccessor(ptr); } } // Driver Program int main() { struct Node *root = NULL; root = insert(root, 20); root = insert(root, 10); root = insert(root, 30); root = insert(root, 5); root = insert(root, 16); root = insert(root, 14); root = insert(root, 17); root = insert(root, 13); inorder(root); return 0; } |
Java
// Java program Insertion in Threaded Binary Search Tree. import java.util.*; public class solution { static class Node { Node left, right; int info; // False if left pointer points to predecessor // in Inorder Traversal boolean lthread; // False if right pointer points to successor // in Inorder Traversal boolean rthread; }; // Insert a Node in Binary Threaded Tree static Node insert( Node root, int ikey) { // Searching for a Node with given value Node ptr = root; Node par = null ; // Parent of key to be inserted while (ptr != null ) { // If key already exists, return if (ikey == (ptr.info)) { System.out.printf( "Duplicate Key !\n" ); return root; } par = ptr; // Update parent pointer // Moving on left subtree. if (ikey < ptr.info) { if (ptr . lthread == false ) ptr = ptr . left; else break ; } // Moving on right subtree. else { if (ptr.rthread == false ) ptr = ptr . right; else break ; } } // Create a new node Node tmp = new Node(); tmp . info = ikey; tmp . lthread = true ; tmp . rthread = true ; if (par == null ) { root = tmp; tmp . left = null ; tmp . right = null ; } else if (ikey < (par . info)) { tmp . left = par . left; tmp . right = par; par . lthread = false ; par . left = tmp; } else { tmp . left = par; tmp . right = par . right; par . rthread = false ; par . right = tmp; } return root; } // Returns inorder successor using rthread static Node inorderSuccessor( Node ptr) { // If rthread is set, we can quickly find if (ptr . rthread == true ) return ptr.right; // Else return leftmost child of right subtree ptr = ptr . right; while (ptr . lthread == false ) ptr = ptr . left; return ptr; } // Printing the threaded tree static void inorder( Node root) { if (root == null ) System.out.printf( "Tree is empty" ); // Reach leftmost node Node ptr = root; while (ptr . lthread == false ) ptr = ptr . left; // One by one print successors while (ptr != null ) { System.out.printf( "%d " ,ptr . info); ptr = inorderSuccessor(ptr); } } // Driver Program public static void main(String[] args) { Node root = null ; root = insert(root, 20 ); root = insert(root, 10 ); root = insert(root, 30 ); root = insert(root, 5 ); root = insert(root, 16 ); root = insert(root, 14 ); root = insert(root, 17 ); root = insert(root, 13 ); inorder(root); } } //contributed by Arnab Kundu // This code is updated By Susobhan Akhuli |
Python3
# Insertion in Threaded Binary Search Tree. class newNode: def __init__( self , key): # False if left pointer points to # predecessor in Inorder Traversal self .info = key self .left = None self .right = None self .lthread = True # False if right pointer points to # successor in Inorder Traversal self .rthread = True # Insert a Node in Binary Threaded Tree def insert(root, ikey): # Searching for a Node with given value ptr = root par = None # Parent of key to be inserted while ptr ! = None : # If key already exists, return if ikey = = (ptr.info): print ( "Duplicate Key !" ) return root par = ptr # Update parent pointer # Moving on left subtree. if ikey < ptr.info: if ptr.lthread = = False : ptr = ptr.left else : break # Moving on right subtree. else : if ptr.rthread = = False : ptr = ptr.right else : break # Create a new node tmp = newNode(ikey) if par = = None : root = tmp tmp.left = None tmp.right = None elif ikey < (par.info): tmp.left = par.left tmp.right = par par.lthread = False par.left = tmp else : tmp.left = par tmp.right = par.right par.rthread = False par.right = tmp return root # Returns inorder successor using rthread def inorderSuccessor(ptr): # If rthread is set, we can quickly find if ptr.rthread = = True : return ptr.right # Else return leftmost child of # right subtree ptr = ptr.right while ptr.lthread = = False : ptr = ptr.left return ptr # Printing the threaded tree def inorder(root): if root = = None : print ( "Tree is empty" ) # Reach leftmost node ptr = root while ptr.lthread = = False : ptr = ptr.left # One by one print successors while ptr ! = None : print (ptr.info,end = " " ) ptr = inorderSuccessor(ptr) # Driver Code if __name__ = = '__main__' : root = None root = insert(root, 20 ) root = insert(root, 10 ) root = insert(root, 30 ) root = insert(root, 5 ) root = insert(root, 16 ) root = insert(root, 14 ) root = insert(root, 17 ) root = insert(root, 13 ) inorder(root) # This code is contributed by PranchalK |
C#
using System; // C# program Insertion in Threaded Binary Search Tree. public class solution { public class Node { public Node left, right; public int info; // False if left pointer points to predecessor // in Inorder Traversal public bool lthread; // False if right pointer points to successor // in Inorder Traversal public bool rthread; } // Insert a Node in Binary Threaded Tree public static Node insert(Node root, int ikey) { // Searching for a Node with given value Node ptr = root; Node par = null ; // Parent of key to be inserted while (ptr != null ) { // If key already exists, return if (ikey == (ptr.info)) { Console.Write( "Duplicate Key !\n" ); return root; } par = ptr; // Update parent pointer // Moving on left subtree. if (ikey < ptr.info) { if (ptr.lthread == false ) { ptr = ptr.left; } else { break ; } } // Moving on right subtree. else { if (ptr.rthread == false ) { ptr = ptr.right; } else { break ; } } } // Create a new node Node tmp = new Node(); tmp.info = ikey; tmp.lthread = true ; tmp.rthread = true ; if (par == null ) { root = tmp; tmp.left = null ; tmp.right = null ; } else if (ikey < (par.info)) { tmp.left = par.left; tmp.right = par; par.lthread = false ; par.left = tmp; } else { tmp.left = par; tmp.right = par.right; par.rthread = false ; par.right = tmp; } return root; } // Returns inorder successor using rthread public static Node inorderSuccessor(Node ptr) { // If rthread is set, we can quickly find if (ptr.rthread == true ) { return ptr.right; } // Else return leftmost child of right subtree ptr = ptr.right; while (ptr.lthread == false ) { ptr = ptr.left; } return ptr; } // Printing the threaded tree public static void inorder(Node root) { if (root == null ) { Console.Write( "Tree is empty" ); } // Reach leftmost node Node ptr = root; while (ptr.lthread == false ) { ptr = ptr.left; } // One by one print successors while (ptr != null ) { Console.Write( "{0:D} " ,ptr.info); ptr = inorderSuccessor(ptr); } } // Driver Program public static void Main( string [] args) { Node root = null ; root = insert(root, 20); root = insert(root, 10); root = insert(root, 30); root = insert(root, 5); root = insert(root, 16); root = insert(root, 14); root = insert(root, 17); root = insert(root, 13); inorder(root); } } // This code is contributed by Shrikant13 |
Javascript
<script> // javascript program Insertion in Threaded Binary Search Tree. class Node { constructor(){ this .left = null , this .right = null ; this .info = 0; // False if left pointer points to predecessor // in Inorder Traversal this .lthread = false ; // False if right pointer points to successor // in Inorder Traversal this .rthread = false ; } } // Insert a Node in Binary Threaded Tree function insert(root , ikey) { // Searching for a Node with given value var ptr = root; var par = null ; // Parent of key to be inserted while (ptr != null ) { // If key already exists, return if (ikey == (ptr.info)) { document.write( "Duplicate Key !\n" ); return root; } par = ptr; // Update parent pointer // Moving on left subtree. if (ikey < ptr.info) { if (ptr.lthread == false ) ptr = ptr.left; else break ; } // Moving on right subtree. else { if (ptr.rthread == false ) ptr = ptr.right; else break ; } } // Create a new node var tmp = new Node(); tmp.info = ikey; tmp.lthread = true ; tmp.rthread = true ; if (par == null ) { root = tmp; tmp.left = null ; tmp.right = null ; } else if (ikey < (par.info)) { tmp.left = par.left; tmp.right = par; par.lthread = false ; par.left = tmp; } else { tmp.left = par; tmp.right = par.right; par.rthread = false ; par.right = tmp; } return root; } // Returns inorder successor using rthread function inorderSuccessor(ptr) { // If rthread is set, we can quickly find if (ptr.rthread == true ) return ptr.right; // Else return leftmost child of right subtree ptr = ptr.right; while (ptr.lthread == false ) ptr = ptr.left; return ptr; } // Printing the threaded tree function inorder(root) { if (root == null ) document.write( "Tree is empty" ); // Reach leftmost node var ptr = root; while (ptr.lthread == false ) ptr = ptr.left; // One by one print successors while (ptr != null ) { document.write(ptr.info+ " " ); ptr = inorderSuccessor(ptr); } } // Driver Program var root = null ; root = insert(root, 20); root = insert(root, 10); root = insert(root, 30); root = insert(root, 5); root = insert(root, 16); root = insert(root, 14); root = insert(root, 17); root = insert(root, 13); inorder(root); // This code contributed by aashish1995 </script> |
5 10 13 14 16 17 20 30
Time Complexity: O(log N)
Space Complexity: O(1), since no extra space used.