Convert a Generic Tree(N-array Tree) to Binary Tree

Prerequisite: Generic Trees(N-array Trees)

In this article, we will discuss the conversion of the Generic Tree to a Binary Tree. Following are the rules to convert a Generic(N-array Tree) to a Binary Tree:

• The root of the Binary Tree is the Root of the Generic Tree.
• The left child of a node in the Generic Tree is the Left child of that node in the Binary Tree.
• The right sibling of any node in the Generic Tree is the Right child of that node in the Binary Tree.

Examples:
Convert the following Generic Tree to Binary Tree:

Below is the Binary Tree of the above Generic Tree:

Note: If the parent node has only the right child in the general tree then it becomes the rightmost child node of the last node following the parent node in the binary tree. In the above example, if node B has the right child node L then in binary tree representation L would be the right child of node D.

Below are the steps for the conversion of Generic Tree to Binary Tree:

1. As per the rules mentioned above, the root node of general tree A is the root node of the binary tree.
2. Now the leftmost child node of the root node in the general tree is B and it is the leftmost child node of the binary tree.
3. Now as B has E as its leftmost child node, so it is its leftmost child node in the binary tree whereas it has C as its rightmost sibling node so it is its right child node in the binary tree.
4. Now C has F as its leftmost child node and D as its rightmost sibling node, so they are its left and right child node in the binary tree respectively.
5. Now D has I as its leftmost child node which is its left child node in the binary tree but doesn’t have any rightmost sibling node, so doesn’t have any right child in the binary tree.
6. Now for I, J is its rightmost sibling node and so it is its right child node in the binary tree. 
7. Similarly, for J, K is its leftmost child node and thus it is its left child node in the binary tree.
8. Now for C, F is its leftmost child node, which has G as its rightmost sibling node, which has H as its just right sibling node and thus they form their left, right, and right child node respectively.

Example :

C++

#include <iostream>
#include <vector>

class TreeNode {
public:
    int val;
    TreeNode* left;
    TreeNode* right;
    std::vector<TreeNode*> children;
    TreeNode(int val)
    {
        this->val = val;
        this->left = this->right = nullptr;
    }
};

TreeNode* convert(TreeNode* root)
{
    if (!root) {
        return nullptr;
    }

    if (root->children.size() == 0) {
        return root;
    }

    if (root->children.size() == 1) {
        root->left = convert(root->children[0]);
        return root;
    }

    root->left = convert(root->children[0]);
    root->right = convert(root->children[1]);

    for (int i = 2; i < root->children.size(); i++) {
        TreeNode* rightTreeRoot = root->right;
        while (rightTreeRoot->left != nullptr) {
            rightTreeRoot = rightTreeRoot->left;
        }
        rightTreeRoot->left = convert(root->children[i]);
    }

    return root;
}

void printTree(TreeNode* root)
{
    if (!root) {
        return;
    }
    std::cout << root->val << " ";
    printTree(root->left);
    printTree(root->right);
}

int main()
{
    TreeNode* root = new TreeNode(1);
    root->children.push_back(new TreeNode(2));
    root->children.push_back(new TreeNode(3));
    root->children.push_back(new TreeNode(4));
    root->children.push_back(new TreeNode(5));

    root->children[0]->children.push_back(new TreeNode(6));
    root->children[0]->children.push_back(new TreeNode(7));
    root->children[3]->children.push_back(new TreeNode(8));
    root->children[3]->children.push_back(new TreeNode(9));

    TreeNode* binaryTreeRoot = convert(root);

    // Output: 1 2 3 4 5 6 7 8 9
    printTree(binaryTreeRoot);
}

Java

import java.util.ArrayList;
import java.util.List;

public class GenericTreeToBinaryTree {

    public static class TreeNode {
        int val;
      TreeNode left,right;

        List<TreeNode> children;

        public TreeNode(int val)
        {
            this.val = val;
            this.children = new ArrayList<>();
        }
    }

    public static TreeNode convert(TreeNode root)
    {
        if (root == null) {
            return null;
        }

        if (root.children.size() == 0) {
            return root;
        }

        if (root.children.size() == 1) {
            root.left = convert(root.children.get(0));
            return root;
        }

        root.left = convert(root.children.get(0));
        root.right = convert(root.children.get(1));

        List<TreeNode> remainingChildren
            = root.children.subList(2,
                                    root.children.size());
        TreeNode rightTreeRoot = root.right;
        while (remainingChildren.size() > 0) {
            if (rightTreeRoot.children.size() == 0) {
                rightTreeRoot.left
                    = convert(remainingChildren.get(0));
            }
            else {
                rightTreeRoot.right
                    = convert(remainingChildren.get(0));
            }
            remainingChildren = remainingChildren.subList(
                1, remainingChildren.size());
        }

        return root;
    }

    public static void main(String[] args)
    {
        TreeNode root = new TreeNode(1);
        root.children.add(new TreeNode(2));
        root.children.add(new TreeNode(3));
        root.children.add(new TreeNode(4));
        root.children.add(new TreeNode(5));

        root.children.get(0).children.add(new TreeNode(6));
        root.children.get(0).children.add(new TreeNode(7));

        root.children.get(3).children.add(new TreeNode(8));
        root.children.get(3).children.add(new TreeNode(9));

        TreeNode binaryTreeRoot = convert(root);

        // Output: 1 2 3 4 5 6 7 8 9
        printTree(binaryTreeRoot);
    }

    public static void printTree(TreeNode root)
    {
        if (root == null) {
            return;
        }
        System.out.print(root.val + " ");
        printTree(root.left);
        printTree(root.right);
    }
}

Python3

class TreeNode:
    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None
        self.children = []


def convert(root):
    if not root:
        return None

    if len(root.children) == 0:
        return root

    if len(root.children) == 1:
        root.left = convert(root.children[0])
        return root

    root.left = convert(root.children[0])
    root.right = convert(root.children[1])

    for i in range(2, len(root.children)):
        rightTreeRoot = root.right
        while rightTreeRoot.left != None:
            rightTreeRoot = rightTreeRoot.left
        rightTreeRoot.left = convert(root.children[i])

    return root


def printTree(root):
    if not root:
        return
    print(root.val, end=" ")
    printTree(root.left)
    printTree(root.right)


root = TreeNode(1)
root.children.append(TreeNode(2))
root.children.append(TreeNode(3))
root.children.append(TreeNode(4))
root.children.append(TreeNode(5))

root.children[0].children.append(TreeNode(6))
root.children[0].children.append(TreeNode(7))

root.children[3].children.append(TreeNode(8))
root.children[3].children.append(TreeNode(9))

binaryTreeRoot = convert(root)

# Output: 1 2 3 4 5 6 7 8 9
printTree(binaryTreeRoot)

C#

using System;
using System.Collections.Generic;

class TreeNode {

    // Value of the node
    public int val;

    // Pointer to the left child of
    // the node (used to represent the
    // n-ary tree as a binary tree)
    public TreeNode left;

    // Pointer to the right child of the node
    // (used to represent the n-ary tree as a
    // binary tree)
    public TreeNode right;
    // List of children of the node (used to
    // represent the n-ary tree)
    public List<TreeNode> children;

    // Constructor to initialize the node with a given value
    public TreeNode(int val)
    {
        this.val = val;
        this.left = this.right = null;
        this.children = new List<TreeNode>();
    }
}

class Program {

    // Convert the given n-ary tree to binary tree
    static TreeNode Convert(TreeNode root)
    {
        // If root is null, return null
        if (root == null) {
            return null;
        }

        // If root has no children, return root
        if (root.children.Count == 0) {
            return root;
        }

        // If root has only one child, make the
        // child as the left child of root
        if (root.children.Count == 1) {
            root.left = Convert(root.children[0]);
            return root;
        }

        // If root has more than one child, make the first
        // child as the left child of root and the second
        // child as the right child of root
        root.left = Convert(root.children[0]);
        root.right = Convert(root.children[1]);

        // For each of the remaining children, create a new
        // binary tree and add it as the left child of the
        // rightmost node in the binary tree of the previous
        // child
        for (int i = 2; i < root.children.Count; i++) {
            TreeNode rightTreeRoot = root.right;
            while (rightTreeRoot.left != null) {
                rightTreeRoot = rightTreeRoot.left;
            }
            rightTreeRoot.left = Convert(root.children[i]);
        }

        // Return the root of the binary tree
        return root;
    }

    // Print the binary tree in pre-order traversal
    static void PrintTree(TreeNode root)
    {
        // If root is null, return
        if (root == null) {
            return;
        }

        // Print the value of the node
        Console.Write(root.val + " ");

        // Recursively print the left
        // subtree
        PrintTree(root.left);

        // Recursively print the
        // right subtree
        PrintTree(root.right);
    }

    static void Main(string[] args)
    {
        // Create an n-ary tree
        TreeNode root = new TreeNode(1);
        root.children.Add(new TreeNode(2));
        root.children.Add(new TreeNode(3));
        root.children.Add(new TreeNode(4));
        root.children.Add(new TreeNode(5));
        root.children[0].children.Add(new TreeNode(6));
        root.children[0].children.Add(new TreeNode(7));
        root.children[3].children.Add(new TreeNode(8));
        root.children[3].children.Add(new TreeNode(9));

        // Convert the n-ary tree to binary tree
        TreeNode binaryTreeRoot = Convert(root);

        // Print the binary tree in pre-order traversal
        // Expected output: 1 2 3 4 5 6 7 8 9
        PrintTree(binaryTreeRoot);
    }
}
// This code is contributed by Shivam Tiwari

Javascript

class TreeNode {
constructor(val) {
this.val = val;
this.left = null;
this.right = null;
this.children = [];
}
}

// Converts a tree with multiple children to a binary tree
function convert(root) {
// If the root is null, return null
if (!root) {
return null;
}
// If the node has no children, return the node
if (root.children.length === 0) {
    return root;
}

// If the node has one child, set it as the left child and return the node
if (root.children.length === 1) {
    root.left = convert(root.children[0]);
    return root;
}

// If the node has two or more children, set the first two as left and right child and
// attach the rest of the children to the right subtree
root.left = convert(root.children[0]);
root.right = convert(root.children[1]);

for (let i = 2; i < root.children.length; i++) {
    let rightTreeRoot = root.right;
    // Find the leftmost node in the right subtree to attach the rest of the children
    while (rightTreeRoot.left !== null) {
        rightTreeRoot = rightTreeRoot.left;
    }
    rightTreeRoot.left = convert(root.children[i]);
}

return root;
}

// Prints the tree in pre-order
function printTree(root) {
// If the root is null, return
if (!root) {
return;
}
console.log(root.val);
printTree(root.left);
printTree(root.right);
}

// Example usage
let root = new TreeNode(1);
root.children.push(new TreeNode(2));
root.children.push(new TreeNode(3));
root.children.push(new TreeNode(4));
root.children.push(new TreeNode(5));

root.children[0].children.push(new TreeNode(6));
root.children[0].children.push(new TreeNode(7));

root.children[3].children.push(new TreeNode(8));
root.children[3].children.push(new TreeNode(9));

let binaryTreeRoot = convert(root);

printTree(binaryTreeRoot);

Output

1 2 6 7 3 4 5 8 9 

Time Complexity: O(n)

Auxiliary Space: O(h)

Approach-2:-Converting a generic tree to a binary tree using a pre-order traversal

The first approach involves converting a generic tree to a binary tree using a pre-order traversal. The steps involved in this approach are as follows:

   Create a binary tree node with the data of the current node in the generic tree.
   Set the left child of the binary tree node to be the result of recursively converting the first child of the current node in the generic tree.
   Set the right child of the binary tree node to be the result of recursively converting the next sibling of the current node in the generic tree.
   Return the binary tree node.

The time complexity of this approach is O(n), where n is the number of nodes in the generic tree.

Here’s the main function for this approach:

C++

#include <iostream>
#include <vector>

using namespace std;

struct TreeNode {
    int val;
    TreeNode *left, *right;

    TreeNode(int x) : val(x), left(NULL), right(NULL) {}
};

struct Node {
    int val;
    vector<Node *> children;

    Node(int x) : val(x) {}
};

TreeNode *generic_to_binary(Node *root) {
    if (root == NULL) {
        return NULL;
    }

    TreeNode *binaryRoot = new TreeNode(root->val);

    if (root->children.size() > 0) {
        binaryRoot->left = generic_to_binary(root->children[0]);
    }

    TreeNode *current = binaryRoot->left;

    for (int i = 1; i < root->children.size(); i++) {
        Node *child = root->children[i];
        current->right = generic_to_binary(child);
        current = current->right;
    }

    return binaryRoot;
}

void printTree(TreeNode *root) {
    if (root == NULL) {
        return;
    }

    cout << root->val << " ";
   printTree(root->left);
  printTree(root->right);
}

int main() {
    Node *root = new Node(1);
    root->children.push_back(new Node(2));
    root->children.push_back(new Node(3));
    root->children.push_back(new Node(4));
    root->children.push_back(new Node(5));

    root->children[0]->children.push_back(new Node(6));
    root->children[0]->children.push_back(new Node(7));

    root->children[3]->children.push_back(new Node(8));
    root->children[3]->children.push_back(new Node(9));

    TreeNode *binaryTreeRoot = generic_to_binary(root);


   printTree(binaryTreeRoot);

    return 0;
}

Java

// Java program for the above approach
import java.util.*;

class TreeNode {
    int val;
    TreeNode left, right;

    TreeNode(int x)
    {
        val = x;
        left = null;
        right = null;
    }
}

class Node {
    int val;
    List<Node> children;

    Node(int x)
    {
        val = x;
        children = new ArrayList<Node>();
    }
}

class Main {
    public static TreeNode generic_to_binary(Node root)
    {
        if (root == null) {
            return null;
        }

        TreeNode binaryRoot = new TreeNode(root.val);

        if (root.children.size() > 0) {
            binaryRoot.left
                = generic_to_binary(root.children.get(0));
        }

        TreeNode current = binaryRoot.left;

        for (int i = 1; i < root.children.size(); i++) {
            Node child = root.children.get(i);
            current.right = generic_to_binary(child);
            current = current.right;
        }

        return binaryRoot;
    }

    public static void printTree(TreeNode root)
    {
        if (root == null) {
            return;
        }

        System.out.print(root.val + " ");
        printTree(root.left);
        printTree(root.right);
    }

    public static void main(String[] args)
    {
        Node root = new Node(1);
        root.children.add(new Node(2));
        root.children.add(new Node(3));
        root.children.add(new Node(4));
        root.children.add(new Node(5));

        root.children.get(0).children.add(new Node(6));
        root.children.get(0).children.add(new Node(7));

        root.children.get(3).children.add(new Node(8));
        root.children.get(3).children.add(new Node(9));

        TreeNode binaryTreeRoot = generic_to_binary(root);

        printTree(binaryTreeRoot);
    }
}

// This code is contributed by Prince Kumar

Python3

class TreeNode:
    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None
        self.children = []


def generic_to_binary(root: 'Node') -> TreeNode:
    if not root:
        return None

    # create a binary tree node with the data of the current node
    binary_node = TreeNode(root.val)

    # convert the first child to a binary tree and set as left child of binary_node
    if root.children:
        binary_node.left = generic_to_binary(root.children[0])

    # convert the next sibling to a binary tree and set as right child of binary_node
    current = binary_node.left
    for child in root.children[1:]:
        current.right = generic_to_binary(child)
        current = current.right

    return binary_node


def printTree(root):
    if not root:
        return
    print(root.val, end=" ")
    printTree(root.left)
    printTree(root.right)


root = TreeNode(1)
root.children.append(TreeNode(2))
root.children.append(TreeNode(3))
root.children.append(TreeNode(4))
root.children.append(TreeNode(5))

root.children[0].children.append(TreeNode(6))
root.children[0].children.append(TreeNode(7))

root.children[3].children.append(TreeNode(8))
root.children[3].children.append(TreeNode(9))

binaryTreeRoot = generic_to_binary(root)

# Output: 1 2 6 7 3 4 5 8 9
printTree(binaryTreeRoot)

C#

// C# program for the above approach

using System;
using System.Collections.Generic;

public class TreeNode
{
    public int val;
    public TreeNode left, right;

    public TreeNode(int x)
    {
        val = x;
        left = null;
        right = null;
    }
}

public class Node
{
    public int val;
    public List<Node> children;

    public Node(int x)
    {
        val = x;
        children = new List<Node>();
    }
}

public class MainClass
{
    public static TreeNode generic_to_binary(Node root)
    {
        if (root == null)
        {
            return null;
        }

        TreeNode binaryRoot = new TreeNode(root.val);

        if (root.children.Count > 0)
        {
            binaryRoot.left = generic_to_binary(root.children[0]);
        }

        TreeNode current = binaryRoot.left;

        for (int i = 1; i < root.children.Count; i++)
        {
            Node child = root.children[i];
            current.right = generic_to_binary(child);
            current = current.right;
        }

        return binaryRoot;
    }

    public static void printTree(TreeNode root)
    {
        if (root == null)
        {
            return;
        }

        Console.Write(root.val + " ");
        printTree(root.left);
        printTree(root.right);
    }

    public static void Main()
    {
        Node root = new Node(1);
        root.children.Add(new Node(2));
        root.children.Add(new Node(3));
        root.children.Add(new Node(4));
        root.children.Add(new Node(5));

        root.children[0].children.Add(new Node(6));
        root.children[0].children.Add(new Node(7));

        root.children[3].children.Add(new Node(8));
        root.children[3].children.Add(new Node(9));

        TreeNode binaryTreeRoot = generic_to_binary(root);

        printTree(binaryTreeRoot);
    }
}

// This code is contributed rishabmalhdijo

Javascript

class TreeNode {
  constructor(val) {
    this.val = val;
    this.left = null;
    this.right = null;
    this.children = [];
  }
}

function generic_to_binary(root) {
  if (!root) {
    return null;
  }

  // create a binary tree node with the data of the current node
  const binary_node = new TreeNode(root.val);

  // convert the first child to a binary tree and set as left child of binary_node
  if (root.children.length > 0) {
    binary_node.left = generic_to_binary(root.children[0]);
  }

  // convert the next sibling to a binary tree and set as right child of binary_node
  let current = binary_node.left;
  for (let i = 1; i < root.children.length; i++) {
    current.right = generic_to_binary(root.children[i]);
    current = current.right;
  }

  return binary_node;
}

function printTree(root) {
  if (!root) {
    return;
  }
  console.log(root.val);
  printTree(root.left);
  printTree(root.right);
}

const root = new TreeNode(1);
root.children.push(new TreeNode(2));
root.children.push(new TreeNode(3));
root.children.push(new TreeNode(4));
root.children.push(new TreeNode(5));

root.children[0].children.push(new TreeNode(6));
root.children[0].children.push(new TreeNode(7));

root.children[3].children.push(new TreeNode(8));
root.children[3].children.push(new TreeNode(9));

const binaryTreeRoot = generic_to_binary(root);

// Output: 1 2 6 7 3 4 5 8 9
printTree(binaryTreeRoot);

Output

1 2 6 7 3 4 5 8 9 

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