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.

Following is structure of a single-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;  
};

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++

/* C++ program to convert a Binary Tree to 
    Threaded Tree */
#include <bits/stdc++.h> 
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; 
} 

Java

/* 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 

Python3

# 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 

C#

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 

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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