Convert a Binary Tree to Threaded binary tree | Set 2 (Efficient)

Idea of Threaded Binary Tree is to make inorder traversal faster and do it without stack and without recursion. In a simple threaded binary tree, the NULL right pointers are used to store inorder successor. Where-ever a right pointer is NULL, it is used to store inorder successor.

Following diagram shows an example Single Threaded Binary Tree. The dotted lines represent threads.
threadedBT

Following is structure of a single-threaded binary tree.

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struct Node
{
    int key;
    Node *left, *right;
  
    // Used to indicate whether the right pointer is a normal right 
    // pointer or a pointer to inorder successor.
    bool isThreaded; 
};

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How to convert a Given Binary Tree to Threaded Binary Tree?
We have discussed a Queue-based solution here. In this post, space-efficient solution is discussed that doesn’t require a queue.

The idea is based on the fact that we link from inorder predecessor to a node. We link those inorder predecessor which lie in subtree of node. So we find inorder predecessor of a node if its left is not NULL. Inorder predecessor of a node (whose left is NULL) is a rightmost node in the left child. Once we find the predecessor, we link a thread from it to the current node.
Following is the implementation of the above idea.

C++



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/* C++ program to convert a Binary Tree to
    Threaded Tree */
#include <iostream>
#include <queue>
using namespace std;
  
/* Structure of a node in threaded binary tree */
struct Node
{
    int key;
    Node *left, *right;
  
    // Used to indicate whether the right pointer
    // is a normal right pointer or a pointer
    // to inorder successor.
    bool isThreaded;
};
  
// Converts tree with given root to threaded
// binary tree.
// This function returns rightmost child of
// root.
Node *createThreaded(Node *root)
{
    // Base cases : Tree is empty or has single
    //              node
    if (root == NULL)
        return NULL;
    if (root->left == NULL &&
        root->right == NULL)
        return root;
  
    // Find predecessor if it exists
    if (root->left != NULL)
    {
        // Find predecessor of root (Rightmost
        // child in left subtree)
        Node* l = createThreaded(root->left);
  
        // Link a thread from predecessor to
        // root.
        l->right = root;
        l->isThreaded = true;
    }
  
    // If current node is rightmost child
    if (root->right == NULL)
        return root;
  
    // Recur for right subtree.
    return createThreaded(root->right);
}
  
// A utility function to find leftmost node
// in a binary tree rooted with 'root'.
// This function is used in inOrder()
Node *leftMost(Node *root)
{
    while (root != NULL && root->left != NULL)
        root = root->left;
    return root;
}
  
// Function to do inorder traversal of a threadded
// binary tree
void inOrder(Node *root)
{
    if (root == NULL) return;
  
    // Find the leftmost node in Binary Tree
    Node *cur = leftMost(root);
  
    while (cur != NULL)
    {
        cout << cur->key << " ";
  
        // If this Node is a thread Node, then go to
        // inorder successor
        if (cur->isThreaded)
            cur = cur->right;
  
        else // Else go to the leftmost child in right subtree
            cur = leftMost(cur->right);
    }
}
  
// A utility function to create a new node
Node *newNode(int key)
{
    Node *temp = new Node;
    temp->left = temp->right = NULL;
    temp->key = key;
    return temp;
}
  
// Driver program to test above functions
int main()
{
    /*       1
            / \
           2   3
          / \ / \
         4  5 6  7   */
    Node *root = newNode(1);
    root->left = newNode(2);
    root->right = newNode(3);
    root->left->left = newNode(4);
    root->left->right = newNode(5);
    root->right->left = newNode(6);
    root->right->right = newNode(7);
  
    createThreaded(root);
  
    cout << "Inorder traversal of created "
            "threaded tree is\n";
    inOrder(root);
    return 0;
}

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Java

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/* Java program to convert a Binary Tree to 
    Threaded Tree */
import java.util.*;
class solution
{
   
    
/* structure of a node in threaded binary tree */
static class Node 
    int key; 
    Node left, right; 
    
    // Used to indicate whether the right pointer 
    // is a normal right pointer or a pointer 
    // to inorder successor. 
    boolean isThreaded; 
}; 
    
// Converts tree with given root to threaded 
// binary tree. 
// This function returns rightmost child of 
// root. 
static Node createThreaded(Node root) 
    // Base cases : Tree is empty or has single 
    //              node 
    if (root == null
        return null
    if (root.left == null && 
        root.right == null
        return root; 
    
    // Find predecessor if it exists 
    if (root.left != null
    
        // Find predecessor of root (Rightmost 
        // child in left subtree) 
        Node l = createThreaded(root.left); 
    
        // Link a thread from predecessor to 
        // root. 
        l.right = root; 
        l.isThreaded = true
    
    
    // If current node is rightmost child 
    if (root.right == null
        return root; 
    
    // Recur for right subtree. 
    return createThreaded(root.right); 
    
// A utility function to find leftmost node 
// in a binary tree rooted with 'root'. 
// This function is used in inOrder() 
static Node leftMost(Node root) 
    while (root != null && root.left != null
        root = root.left; 
    return root; 
    
// Function to do inorder traversal of a threadded 
// binary tree 
static void inOrder(Node root) 
    if (root == null) return
    
    // Find the leftmost node in Binary Tree 
    Node cur = leftMost(root); 
    
    while (cur != null
    
        System.out.print(cur.key + " "); 
    
        // If this Node is a thread Node, then go to 
        // inorder successor 
        if (cur.isThreaded) 
            cur = cur.right; 
    
        else // Else go to the leftmost child in right subtree 
            cur = leftMost(cur.right); 
    
    
// A utility function to create a new node 
static Node newNode(int key) 
    Node temp = new Node(); 
    temp.left = temp.right = null
    temp.key = key; 
    return temp; 
    
// Driver program to test above functions 
public static void main(String args[])
   /*       1 
            / \ 
           2   3 
          / \ / \ 
         4  5 6  7   */
    Node root = newNode(1); 
    root.left = newNode(2); 
    root.right = newNode(3); 
    root.left.left = newNode(4); 
    root.left.right = newNode(5); 
    root.right.left = newNode(6); 
    root.right.right = newNode(7); 
    
    createThreaded(root); 
    
    System.out.println("Inorder traversal of created "+"threaded tree is\n"); 
    inOrder(root);  
}
//contributed by Arnab Kundu

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Python3

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# Python3 program to convert a Binary Tree to 
# Threaded Tree 
  
# A utility function to create a new node 
class newNode:
    def __init__(self, key):
        self.left = self.right = None
        self.key = key 
        self.isThreaded = None
          
# Converts tree with given root to threaded 
# binary tree. 
# This function returns rightmost child of 
# root. 
def createThreaded(root):
      
    # Base cases : Tree is empty or has  
    #               single node 
    if root == None
        return None
    if root.left == None and root.right == None
        return root 
  
    # Find predecessor if it exists 
    if root.left != None:
          
        # Find predecessor of root (Rightmost 
        # child in left subtree) 
        l = createThreaded(root.left) 
  
        # Link a thread from predecessor 
        # to root. 
        l.right = root 
        l.isThreaded = True
  
    # If current node is rightmost child 
    if root.right == None
        return root 
  
    # Recur for right subtree. 
    return createThreaded(root.right)
  
# A utility function to find leftmost node 
# in a binary tree rooted with 'root'. 
# This function is used in inOrder() 
def leftMost(root):
    while root != None and root.left != None
        root = root.left 
    return root
  
# Function to do inorder traversal of a 
# threaded binary tree 
def inOrder(root):
    if root == None:
        return
  
    # Find the leftmost node in Binary Tree 
    cur = leftMost(root) 
  
    while cur != None:
        print(cur.key, end = " "
  
        # If this Node is a thread Node, then
        # go to inorder successor 
        if cur.isThreaded: 
            cur = cur.right 
  
        else: # Else go to the leftmost child
              # in right subtree 
            cur = leftMost(cur.right)
  
# Driver Code
if __name__ == '__main__':
      
    #         1 
    #     / \ 
    #     2 3 
    #     / \ / \ 
    #     4 5 6 7 
    root = newNode(1
    root.left = newNode(2
    root.right = newNode(3
    root.left.left = newNode(4
    root.left.right = newNode(5
    root.right.left = newNode(6
    root.right.right = newNode(7
  
    createThreaded(root) 
  
    print("Inorder traversal of created",
                      "threaded tree is"
    inOrder(root)
  
# This code is contributed by PranchalK

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C#

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using System;
  
/* C# program to convert a Binary Tree to  
    Threaded Tree */
public class solution
{
  
  
/* structure of a node in threaded binary tree */
public class Node
{
    public int key;
    public Node left, right;
  
    // Used to indicate whether the right pointer  
    // is a normal right pointer or a pointer  
    // to inorder successor.  
    public bool isThreaded;
}
  
// Converts tree with given root to threaded  
// binary tree.  
// This function returns rightmost child of  
// root.  
public static Node createThreaded(Node root)
{
    // Base cases : Tree is empty or has single  
    //              node  
    if (root == null)
    {
        return null;
    }
    if (root.left == null && root.right == null)
    {
        return root;
    }
  
    // Find predecessor if it exists  
    if (root.left != null)
    {
        // Find predecessor of root (Rightmost  
        // child in left subtree)  
        Node l = createThreaded(root.left);
  
        // Link a thread from predecessor to  
        // root.  
        l.right = root;
        l.isThreaded = true;
    }
  
    // If current node is rightmost child  
    if (root.right == null)
    {
        return root;
    }
  
    // Recur for right subtree.  
    return createThreaded(root.right);
}
  
// A utility function to find leftmost node  
// in a binary tree rooted with 'root'.  
// This function is used in inOrder()  
public static Node leftMost(Node root)
{
    while (root != null && root.left != null)
    {
        root = root.left;
    }
    return root;
}
  
// Function to do inorder traversal of a threadded  
// binary tree  
public static void inOrder(Node root)
{
    if (root == null)
    {
        return;
    }
  
    // Find the leftmost node in Binary Tree  
    Node cur = leftMost(root);
  
    while (cur != null)
    {
        Console.Write(cur.key + " ");
  
        // If this Node is a thread Node, then go to  
        // inorder successor  
        if (cur.isThreaded)
        {
            cur = cur.right;
        }
  
        else // Else go to the leftmost child in right subtree
        {
            cur = leftMost(cur.right);
        }
    }
}
  
// A utility function to create a new node  
public static Node newNode(int key)
{
    Node temp = new Node();
    temp.left = temp.right = null;
    temp.key = key;
    return temp;
}
  
// Driver program to test above functions  
public static void Main(string[] args)
{
   /*       1  
            / \  
           2   3  
          / \ / \  
         4  5 6  7   */
    Node root = newNode(1);
    root.left = newNode(2);
    root.right = newNode(3);
    root.left.left = newNode(4);
    root.left.right = newNode(5);
    root.right.left = newNode(6);
    root.right.right = newNode(7);
  
    createThreaded(root);
  
    Console.WriteLine("Inorder traversal of created " + "threaded tree is\n");
    inOrder(root);
}
}
  
  // This code is contributed by Shrikant13

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Output:

Inorder traversal of created threaded tree is
4 2 5 1 6 3 7

This algorithm works in O(n) time complexity and O(1) space other than function call stack.

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