Modify a binary tree to get preorder traversal using right pointers only

Last Updated : 29 Oct, 2024

Given a binary tree. The task is to modify it in such a way that after modification preorder traversal of it can get only with the right pointers. During modification, we can use right as well as left pointers.

Examples:

Input :

Output :

Explanation: The preorder traversal of given binary tree is 10 8 3 5 2.

Table of Content

[Expected Approach - 1] Using recursion - O(n) Time and O(h) Space
[Expected Approach - 2] Using Iterative Preorder Traversal - O(n) Time and O(n) Space

[Expected Approach - 1] Using recursion - O(n) Time and O(h) Space

The idea is to use recursion to transform the tree, the right pointer of the root is made to point to the left subtree. If the node has only a left child, the left child is moved to the right, completing the processing for that node. However, if the node has both left and right children, the original right child is moved to the rightmost node of the left subtree. This process ensures that the entire left subtree is shifted to the right, and the rightmost node of the transformed subtree is returned after the node is processed.

Below is the implementation of the above approach:

C++

// C++ code to modify binary tree for
// traversal using only right pointer
#include <bits/stdc++.h>

using namespace std;

class Node {
public:    
  	int data;
    Node* left;
    Node* right;
  	Node(int x){
    	data = x;
      	left = right = nullptr;
    }
};

// Function to modify tree
Node* modifytree(Node* root) {
    Node* right = root->right;
    Node* rightMost = root;

    // if the left tree exists
    if (root->left) {

        // get the right-most of the
        // original left subtree
        rightMost = modifytree(root->left);

        // set root right to left subtree
        root->right = root->left;
        root->left = nullptr;
    }

    // if the right subtree does
    // not exists we are done!
    if (!right) 
        return rightMost;

    // set right pointer of right-most
    // of the original left subtree
    rightMost->right = right;

    // modify the rightsubtree
    rightMost = modifytree(right);
    return rightMost;
}

void printpre(Node* curr) {
    while (curr != nullptr) {
        cout << curr->data << " ";
        curr = curr->right;
    }
}

int main() {
  
    // Constructed binary tree is
    //     10
    //    / \
    //   8   2
    //  / \  
    // 3   5     
    Node* root = new Node(10);
    root->left = new Node(8);
    root->right = new Node(2);
    root->left->left = new Node(3);
    root->left->right = new Node(5);

    modifytree(root);
    printpre(root);

    return 0;
}

Java

// Java code to modify binary tree for traversal
// using only right pointer
class Node {
    int data;
    Node left, right;

    public Node(int x) {
        data = x;
        left = right = null;
    }
}

class GfG {

    // Function to modify tree
    static Node modifytree(Node root) {
      
        Node right = root.right;
        Node rightMost = root;

        // If the left tree exists
        if (root.left != null) {

            // Get the right-most of the original left
            // subtree
            rightMost = modifytree(root.left);

            // Set root right to left subtree
            root.right = root.left;
            root.left = null;
        }

        // If the right subtree does not
      	// exist we are done!
        if (right == null)
            return rightMost;

        // Set right pointer of right-most of the original
        // left subtree
        rightMost.right = right;

        // Modify the right subtree
        rightMost = modifytree(right);
        return rightMost;
    }
  
    static void printpre(Node curr) {
        while (curr != null) {
            System.out.print(curr.data + " ");
            curr = curr.right;
        }
    }

    public static void main(String[] args) {
      
        // Constructed binary tree is
        //     10
        //    / \
        //   8   2
        //  / \  
        // 3   5
        Node root = new Node(10);
        root.left = new Node(8);
        root.right = new Node(2);
        root.left.left = new Node(3);
        root.left.right = new Node(5);

        modifytree(root);
        printpre(root);
    }
}

Python

# Python code to modify binary tree for traversal using
# only right pointer

class Node:
    def __init__(self, data):
        self.data = data
        self.left = None
        self.right = None

# Function to modify tree
def modifytree(root):
    right = root.right
    right_most = root

    # If the left tree exists
    if root.left:
      
        # Get the right-most of the original 
        # left subtree
        right_most = modifytree(root.left)

        # Set root right to left subtree
        root.right = root.left
        root.left = None

    # If the right subtree does not exist
    # we are done!
    if not right:
        return right_most

    # Set right pointer of right-most of the 
    # original left subtree
    right_most.right = right

    # Modify the right subtree
    right_most = modifytree(right)
    return right_most

def printpre(curr):
    while curr:
        print(curr.data, end=" ")
        curr = curr.right

if __name__ == "__main__":
  
    # Constructed binary tree is
    #     10
    #    / \
    #   8   2
    #  / \
    # 3   5
    root = Node(10)
    root.left = Node(8)
    root.right = Node(2)
    root.left.left = Node(3)
    root.left.right = Node(5)

    modifytree(root)
    printpre(root)

C#

// C# code to modify binary tree for traversal using only
// right pointer
using System;

class Node {
    public int data;
    public Node left, right;

    public Node(int x) {
        data = x;
        left = right = null;
    }
}

class GfG {
  
    // Function to modify tree
    static Node modifytree(Node root) {
        Node right = root.right;
        Node rightMost = root;

        // If the left tree exists
        if (root.left != null) {
          
            // Get the right-most of the original left
            // subtree
            rightMost = modifytree(root.left);

            // Set root right to left subtree
            root.right = root.left;
            root.left = null;
        }

        // If the right subtree does 
      	// not exist we are done!
        if (right == null)
            return rightMost;

        // Set right pointer of right-most of the original
        // left subtree
        rightMost.right = right;

        // Modify the right subtree
        rightMost = modifytree(right);
        return rightMost;
    }

    static void printpre(Node curr) {
        while (curr != null) {
            Console.Write(curr.data + " ");
            curr = curr.right;
        }
    }

    static void Main(string[] args) {
      
        // Constructed binary tree is
        //     10
        //    / \
        //   8   2
        //  / \  
        // 3   5
        Node root = new Node(10);
        root.left = new Node(8);
        root.right = new Node(2);
        root.left.left = new Node(3);
        root.left.right = new Node(5);

        modifytree(root);
        printpre(root);
    }
}

JavaScript

// JavaScript code to modify binary tree for traversal using
// only right pointer

class Node {
    constructor(data) {
        this.data = data;
        this.left = null;
        this.right = null;
    }
}

// Function to modify tree
function modifytree(root) {

    let right = root.right;
    let rightMost = root;

    // If the left tree exists
    if (root.left) {
    
        // Get the right-most of the original
        // left subtree
        rightMost = modifytree(root.left);

        // Set root right to left subtree
        root.right = root.left;
        root.left = null;
    }

    // If the right subtree does not 
    // exist we are done!
    if (!right)
        return rightMost;

    // Set right pointer of right-most of
    //the original left subtree
    rightMost.right = right;

    // Modify the right subtree
    rightMost = modifytree(right);
    return rightMost;
}

function printpre(curr) {
    while (curr != null) {
        console.log(curr.data + " ");
        curr = curr.right;
    }
}

let root = new Node(10);
root.left = new Node(8);
root.right = new Node(2);
root.left.left = new Node(3);
root.left.right = new Node(5);

modifytree(root);
printpre(root);

Output

10 8 3 5 2

[Expected Approach - 2] Using Iterative Preorder Traversal - O(n) Time and O(n) Space

This can be easily done using Iterative preorder traversal. The idea is to maintain a variable prev which maintains the previous node of the preorder traversal. Every-time a new node is encountered, the node set its right to previous one and prev is made equal to the current node. In the end we will have a sort of linked list whose first element is root then left child then right, so on and so forth.

Below is the implementation of the above approach:

C++

// C++ code to modify binary tree for
// traversal using only right pointer

#include <bits/stdc++.h>
using namespace std;

class Node {
public: 
  	int data;
    Node* left;
    Node* right;
	Node(int x){
    	data = x;
      	left = right = nullptr;
    }
};	

// An iterative process to set the right
// pointer of Binary tree
void modifytree(Node* root) {
  
    if (root == nullptr)
        return;

    // Create an empty stack and 
  	// push root to it
    stack<Node*> nodeStack;
    nodeStack.push(root);

    Node* pre = nullptr;
    while (nodeStack.empty() == false) {

        // Pop the top item from stack
        Node* node = nodeStack.top();

        nodeStack.pop();

        // Push right and left children of
        // the popped node to stack
        if (node->right)
            nodeStack.push(node->right);
        if (node->left)
            nodeStack.push(node->left);

        // check if some previous node
      	// exists
        if (pre != nullptr) {

            // set the right pointer of
            // previous node to current
            pre->right = node;
        }
      
        pre = node;
    }
}

void printpre(Node* root) {
    while (root != nullptr) {
        cout << root->data << " ";
        root = root->right;
    }
}

int main() {
  
    // Constructed binary tree is
    //         10
    //        /   \
    //       8      2
    //      /  \    
    //     3     5  
    Node* root = new Node(10);
    root->left = new Node(8);
    root->right = new Node(2);
    root->left->left = new Node(3);
    root->left->right = new Node(5);

    modifytree(root);
    printpre(root);

    return 0;
}

Java

// Java code to modify binary tree for
// traversal using only right pointer

import java.util.Stack;

class Node {
    int data;
    Node left, right;

    public Node(int x) {
        data = x;
        left = right = null;
    }
}

class GfG {
  
    // An iterative process to set the right
  	// pointer of Binary tree
    static void modifytree(Node root) {
    
        if (root == null)
            return;

        // Create an empty stack and push 
      	// root to it
        Stack<Node> nodeStack = new Stack<>();
        nodeStack.push(root);

        Node pre = null;
        while (!nodeStack.isEmpty()) {
          
            // Pop the top item from stack
            Node node = nodeStack.pop();

            // Push right and left children of the
          	// popped node to stack
            if (node.right != null)
                nodeStack.push(node.right);
            if (node.left != null)
                nodeStack.push(node.left);

            // Check if some previous node exists
            if (pre != null) {
              
                // Set the right pointer of
              	// previous node to current
                pre.right = node;
            }
            pre = node;
        }
    }

    static void printpre(Node root) {
        while (root != null) {
            System.out.print(root.data + " ");
            root = root.right;
        }
    }

    public static void main(String[] args) {
      
        // Constructed binary tree is
        //         10
        //        /   \
        //       8      2
        //      /  \    
        //     3     5  
        Node root = new Node(10);
        root.left = new Node(8);
        root.right = new Node(2);
        root.left.left = new Node(3);
        root.left.right = new Node(5);

        modifytree(root);
        printpre(root);
    }
}

Python

# Python code to modify binary tree 
# for traversal using only right pointer

class Node:
    def __init__(self, data):
        self.data = data
        self.left = None
        self.right = None

# An iterative process to set the right
# pointer of Binary tree
def modifytree(root):
    
    if root is None:
        return

    # Create an empty stack and push
    # root to it
    nodeStack = []
    nodeStack.append(root)

    pre = None
    while nodeStack:
      
        # Pop the top item from stack
        node = nodeStack.pop()

        # Push right and left children of 
        # the popped node to stack
        if node.right:
            nodeStack.append(node.right)
        if node.left:
            nodeStack.append(node.left)

        # Check if some previous node exists
        if pre is not None:
          
            # Set the right pointer of 
            # previous node to current
            pre.right = node
        pre = node

def printpre(root):
    while root is not None:
        print(root.data, end=" ")
        root = root.right

if __name__ == "__main__":
  
    # Constructed binary tree is
    #         10
    #        /   \
    #       8      2
    #      /  \    
    #     3     5  
    root = Node(10)
    root.left = Node(8)
    root.right = Node(2)
    root.left.left = Node(3)
    root.left.right = Node(5)

    modifytree(root)
    printpre(root)

C#

// C# code to modify binary tree for 
// traversal using only right pointer

using System;
using System.Collections.Generic;

class Node {
    public int data;
    public Node left, right;

    public Node(int x) {
        data = x;
        left = right = null;
    }
}

class GfG {
  
    // An iterative process to set the 
  	// right pointer of Binary tree
    static void modifytree(Node root) {

        if (root == null)
            return;

        // Create an empty stack and push root to it
        Stack<Node> nodeStack = new Stack<Node>();
        nodeStack.Push(root);

        Node pre = null;
        while (nodeStack.Count > 0) {
          
            // Pop the top item from stack
            Node node = nodeStack.Pop();

            // Push right and left children of
          	// the popped node to stack
            if (node.right != null)
                nodeStack.Push(node.right);
            if (node.left != null)
                nodeStack.Push(node.left);

            // Check if some previous node exists
            if (pre != null) {
                pre.right = node;
            }
            pre = node;
        }
    }

    static void printpre(Node root) {
        while (root != null) {
            Console.Write(root.data + " ");
            root = root.right;
        }
    }

    static void Main(string[] args) {
      
        // Constructed binary tree is
        //         10
        //        /   \
        //       8      2
        //      /  \    
        //     3     5  
        Node root = new Node(10);
        root.left = new Node(8);
        root.right = new Node(2);
        root.left.left = new Node(3);
        root.left.right = new Node(5);

        modifytree(root);
        printpre(root);
    }
}

JavaScript

// JavaScript code to modify binary tree 
// for traversal using only right pointer

class Node {
    constructor(data) {
        this.data = data;
        this.left = null;
        this.right = null;
    }
}

// An iterative process to set the right
// pointer of Binary tree
function modifytree(root) {

    if (root === null) return;

    // Create an empty stack and push
    // root to it
    const nodeStack = [];
    nodeStack.push(root);

    let pre = null;
    while (nodeStack.length > 0) {
    
        // Pop the top item from stack
        const node = nodeStack.pop();

        // Push right and left children of 
        // the popped node to stack
        if (node.right !== null) nodeStack.push(node.right);
        if (node.left !== null) nodeStack.push(node.left);

        // Check if some previous node exists
        if (pre !== null) {
            pre.right = node;
        }
        pre = node;
    }
}

function printpre(root) {
    while (root !== null) {
        console.log(root.data + " ");
        root = root.right;
    }
}

const root = new Node(10);
root.left = new Node(8);
root.right = new Node(2);
root.left.left = new Node(3);
root.left.right = new Node(5);

modifytree(root);
printpre(root);

Output

10 8 3 5 2

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