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

Given a binary tree. Modify it in such a way that after modification you can have a preorder traversal of it using only the right pointers. During modification, you can use right as well as left pointers. 

Examples: 

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

Method 1 (Recursive):

One needs to make the right pointer of root point to the left subtree. 
If the node has just left child, then just moving the child to right will complete the processing for that node. 
If there is a right child too, then it should be made right child of the right-most of the original left subtree.
The above function used in the code process a node and then returns the rightmost node of the transformed subtree.

Implementation:

C++

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

using namespace std;

// A binary tree node has data,
// left child and right child
struct Node {
    int data;
    struct Node* left;
    struct Node* right;
};

// function that allocates a new node
// with the given data and NULL left
// and right pointers.
struct Node* newNode(int data)
{
    struct Node* node = new struct Node;
    node->data = data;
    node->left = NULL;
    node->right = NULL;
    return (node);
}

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

    // 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;
}

// printing using right pointer only
void printpre(struct Node* root)
{
    while (root != NULL) {
        cout << root->data << " ";
        root = root->right;
    }
}

// Driver program to test above functions
int main()
{
    /* Constructed binary tree is
         10
        / \
       8   2
      / \
     3   5     */
    struct Node* root = newNode(10);
    root->left = newNode(8);
    root->right = newNode(2);
    root->left->left = newNode(3);
    root->left->right = newNode(5);

    modifytree(root);
    printpre(root);

    return 0;
}

Java

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

// A binary tree node has data,
// left child and right child
static class Node
{
    int data;
    Node left;
    Node right;
};

// function that allocates a new node
// with the given data and null left
// and right pointers.
static Node newNode(int data)
{
    Node node = new Node();
    node.data = data;
    node.left = null;
    node.right = null;
    return (node);
}

// 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 exists we are done!
    if (right == null)
        return rightMost;

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

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

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

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

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

// This code is contributed by Arnab Kundu

Python3

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

class newNode():

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


# Function to modify tree
def modifytree(root):

    right = root.right
    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 = None


    # if the right subtree does
    # not exists we are done!
    if (not 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


# printing using right pointer only
def printpre(root):

    while (root != None):
        print(root.data,end=" ")
        root = root.right

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

    modifytree(root)
    printpre(root)

# This code is contributed by SHUBHAMSINGH10

C#

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

class GFG
{

// A binary tree node has data,
// left child and right child
public class Node
{
    public int data;
    public Node left;
    public Node right;
};

// function that allocates a new node
// with the given data and null left
// and right pointers.
static Node newNode(int data)
{
    Node node = new Node();
    node.data = data;
    node.left = null;
    node.right = null;
    return (node);
}

// 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 exists we are done!
    if (right == null)
        return rightMost;

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

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

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

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

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

// This code is contributed by 29AjayKumar

Javascript

<script>

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

    // A binary tree node has data,
    // left child and right child
    class Node
    {
        constructor(data) {
           this.left = null;
           this.right = null;
           this.data = data;
        }
    }

    // function that allocates a new node
    // with the given data and null left
    // and right pointers.
    function newNode(data)
    {
        let node = new Node(data);
        return (node);
    }

    // Function to modify tree
    function modifytree(root)
    {
        let right = root.right;
        let 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 exists we are done!
        if (right == null)
            return rightMost;

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

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

    // printing using right pointer only
    function printpre(root)
    {
        while (root != null)
        {
            document.write( root.data + " ");
            root = root.right;
        }
    }

    /* Constructed binary tree is
        10
        / \
        8 2
        / \
        3 5 */
    let root = newNode(10);
    root.left = newNode(8);
    root.right = newNode(2);
    root.left.left = newNode(3);
    root.left.right = newNode(5);

    modifytree(root);
    printpre(root);

</script>

Output:

10 8 3 5 2 

Time Complexity : O(n)
Auxiliary Space : O(n)

Method 2 (Iterative): This can be easily done using iterative preorder traversal. See here. 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.

Implementation:

C++

// C++ code to modify binary tree for
// traversal using only right pointer
#include <iostream>
#include <stack>
#include <stdio.h>
#include <stdlib.h>

using namespace std;

// A binary tree node has data,
// left child and right child
struct Node {
    int data;
    struct Node* left;
    struct Node* right;
};

// Helper function that allocates a new
// node with the given data and NULL
// left and right  pointers.
struct Node* newNode(int data)
{
    struct Node* node = new struct Node;
    node->data = data;
    node->left = NULL;
    node->right = NULL;
    return (node);
}

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

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

    /* Pop all items one by one.
        Do following for every popped item
       a) print it
       b) push its right child
       c) push its left child
    Note that right child is pushed first
    so that left is processed first */
    struct Node* pre = NULL;
    while (nodeStack.empty() == false) {

        // Pop the top item from stack
        struct 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 != NULL) {

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

        // set previous node as current node
        pre = node;
    }
}

// printing using right pointer only
void printpre(struct Node* root)
{
    while (root != NULL) {
        cout << root->data << " ";
        root = root->right;
    }
}

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

    modifytree(root);
    printpre(root);

    return 0;
}

Java

// Java code to modify binary tree for
// traversal using only right pointer
import java.util.*;
class GfG {

// A binary tree node has data,
// left child and right child
static class Node {
    int data;
    Node left;
    Node right;
}

// Helper function that allocates a new
// node with the given data and NULL
// left and right pointers.
static Node newNode(int data)
{
    Node node = new Node();
    node.data = data;
    node.left = null;
    node.right = null;
    return (node);
}

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

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

    /* Pop all items one by one.
        Do following for every popped item
    a) print it
    b) push its right child
    c) push its left child
    Note that right child is pushed first
    so that left is processed first */
    Node pre = null;
    while (nodeStack.isEmpty() == false) {

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

        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;
        }

        // set previous node as current node
        pre = node;
    }
}

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

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

    modifytree(root);
    printpre(root);

}
}

Python

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

# A binary tree node has data,
# left child and right child
class newNode():

    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):

    # Base Case
    if (root == None):
        return

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

    ''' Pop all items one by one.
    Do following for every popped item
    a) print
    b) append its right child
    c) append its left child
    Note that right child is appended first
    so that left is processed first '''
    pre = None
    while (len(nodeStack)):

        # Pop the top item from stack
        node = nodeStack[-1]
        nodeStack.pop()

        # append 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 != None):

            # set the right pointer of
            # previous node to current
            pre.right = node

        # set previous node as current node
        pre = node

# printing using right pointer only
def printpre( root):
    while (root != None):
        print(root.data, end = " ")
        root = root.right

# Driver code

''' Constructed binary tree is
        10
    / \
    8     2
/ \
3     5
'''
root = newNode(10)
root.left = newNode(8)
root.right = newNode(2)
root.left.left = newNode(3)
root.left.right = newNode(5)

modifytree(root)
printpre(root)

# This code is contributed by SHUBHAMSINGH10

C#

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

class GfG
{

// A binary tree node has data,
// left child and right child
public class Node
{
    public int data;
    public Node left;
    public Node right;
}

// Helper function that allocates a new
// node with the given data and NULL
// left and right pointers.
static Node newNode(int data)
{
    Node node = new Node();
    node.data = data;
    node.left = null;
    node.right = null;
    return (node);
}

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

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

    /* Pop all items one by one.
        Do following for every Popped item
    a) print it
    b) Push its right child
    c) Push its left child
    Note that right child is Pushed first
    so that left is processed first */
    Node pre = null;
    while (nodeStack.Count !=0)
    {

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

        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;
        }

        // set previous node as current node
        pre = node;
    }
}

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

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

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

// This code is contributed by
// Arnab Kundu

Javascript

<script>

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

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

    // Helper function that allocates a new
    // node with the given data and NULL
    // left and right pointers.
    function newNode(data)
    {
        let node = new Node(data);
        return (node);
    }

    // An iterative process to set the right
    // pointer of Binary tree
    function modifytree(root)
    {
        // Base Case
        if (root == null)
            return;

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

        /* Pop all items one by one.
            Do following for every popped item
        a) print it
        b) push its right child
        c) push its left child
        Note that right child is pushed first
        so that left is processed first */
        let pre = null;
        while (nodeStack.length > 0) {

            // Pop the top item from stack
            let node = nodeStack[nodeStack.length - 1];

            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;
            }

            // set previous node as current node
            pre = node;
        }
    }

    // printing using right pointer only
    function printpre(root)
    {
        while (root != null) {
            document.write(root.data + " ");
            root = root.right;
        }
    }

    /* Constructed binary tree is
            10
            / \
            8  2
           / \
          3   5
    */
    let root = newNode(10);
    root.left = newNode(8);
    root.right = newNode(2);
    root.left.left = newNode(3);
    root.left.right = newNode(5);

    modifytree(root);
    printpre(root);

</script>

Output:

10 8 3 5 2 

Time Complexity : O(n)
Auxiliary Space : O(n)