Create Balanced Binary Tree using its Leaf Nodes without using extra space

0 0 12 minutes read

Prerequisites: Binary Tree to Doubly Linked List
Given a Binary Tree, the task is to create a Balanced Binary Tree from all the leaf nodes of the given Binary Tree.

Examples:

Input:

Output: 7 8 5 9 10 
Explanation: Required balanced binary tree will be:

Input:

Output: 13 21 29 7 15
Explanation: Required balanced binary tree is:
              29
             /  \
            21   7
           /       \
          13       15

Approach:
Follow the steps below to solve the problem:

Find all the leaf nodes in the given binary tree and create a doubly linked list using them.
To create a Balanced Binary Tree from the above doubly linked list do the following:
- Find the middle node of the doubly linked list formed above and set it as a root node of the resultant tree.
- Recursively iterate for the left and right of the current middle node in the doubly linked list repeat the above steps until all nodes are covered.
Print the newly created balanced binary tree.

Below is the implementation of the above approach:

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Structure for Linked list and tree
class Node {
public:
    int data;
    Node *left, *right;
};
 
// Function that returns the count of
// nodes in the given linked list
int countNodes(Node* head)
{
    // Initialize count
    int count = 0;
 
    Node* temp = head;
 
    // Iterate till the end of LL
    while (temp) {
 
        temp = temp->right;
 
        // Increment the count
        count++;
    }
 
    // Return the final count
    return count;
}
 
// Function to return the root of
// the newly created balanced binary
// tree from the given doubly LL
Node* sortedListToBSTRecur(
    Node** head_ref, int n)
{
    // Base Case
    if (n <= 0)
        return NULL;
 
    // Recursively construct
    // the left subtree
    Node* left = sortedListToBSTRecur(
        head_ref, n / 2);
 
    // head_ref now refers to
    // middle node, make middle node
    // as root of BST
    Node* root = *head_ref;
 
    // Set pointer to left subtree
    root->left = left;
 
    // Change head pointer of
    // Linked List for parent
    // recursive calls
    *head_ref = (*head_ref)->right;
 
    // Recursively construct the
    // right subtree and link it
    // with root
        root->right
        = sortedListToBSTRecur(
            head_ref, n - n / 2 - 1);
 
    // Return the root of Balanced BT
    return root;
}
Node* sortedListToBST(Node* head)
{
    /*Count the number of 
    nodes in Linked List */
    int n = countNodes(head);
 
    /* Construct BST */
    return sortedListToBSTRecur(
        &head, n);
}
 
// Function to find the leaf nodes and
// make the doubly linked list of
// those nodes
Node* extractLeafList(Node* root,
                      Node** head_ref)
{
    // Base cases
    if (root == NULL)
        return NULL;
 
    if (root->left == NULL
        && root->right == NULL) {
 
        // This node is added to doubly
        // linked list of leaves, and
        // set right pointer of this
        // node as previous head of DLL
        root->right = *head_ref;
 
        // Change left pointer
        // of previous head
        if (*head_ref != NULL)
            (*head_ref)->left = root;
 
        // Change head of linked list
        *head_ref = root;
 
        // Return new root
        return NULL;
    }
 
    // Recur for right & left subtrees
    root->right = extractLeafList(root->right,
                                  head_ref);
    root->left = extractLeafList(root->left,
                                 head_ref);
 
    // Return the root
    return root;
}
 
// Function to allocating new Node
// int Binary Tree
Node* newNode(int data)
{
    Node* node = new Node();
    node->data = data;
    node->left = NULL;
    node->right = NULL;
    return node;
}
 
// Function for inorder traversal
void print(Node* root)
{
    // If root is not NULL
    if (root != NULL) {
 
        print(root->left);
 
        // Print the root's data
        cout << root->data
             << " ";
        print(root->right);
    }
}
 
// Function to display nodes of DLL
void printList(Node* head)
{
    while (head) {
 
        // Print the data
        cout << head->data << " ";
        head = head->right;
    }
}
 
// Driver Code
int main()
{
    // Given Binary Tree
    Node* head = NULL;
    Node* root = newNode(1);
 
    root->left = newNode(2);
    root->right = newNode(3);
    root->left->left = newNode(4);
    root->left->right = newNode(5);
    root->right->right = newNode(6);
    root->left->left->left = newNode(7);
    root->left->left->right = newNode(8);
    root->right->right->left = newNode(9);
    root->right->right->right = newNode(10);
 
    // Function Call to extract leaf Node
    root = extractLeafList(
        root, &head);
 
    // Function Call to create Balanced BT
    root = sortedListToBST(head);
 
    // Print Inorder traversal New Balanced BT
    print(root);
    return 0;
}

Java

// Java program for 
// the above approach
import java.util.*;
class GFG{
 
// Structure for Linked 
// list and tree
static class Node 
{
  public int data;
  Node left, right;
};
   
static Node head;
   
// Function that returns the 
// count of nodes in the given 
// linked list
static int countNodes(Node head)
{
  // Initialize count
  int count = 0;
 
  Node temp = head;
 
  // Iterate till the 
  // end of LL
  while (temp != null) 
  {
    temp = temp.right;
 
    // Increment the count
    count++;
  }
 
  // Return the final count
  return count;
}
 
// Function to return the root of
// the newly created balanced binary
// tree from the given doubly LL
static Node sortedListToBSTRecur(int n)
{
  // Base Case
  if (n <= 0)
    return null;
 
  // Recursively construct
  // the left subtree
  Node left = sortedListToBSTRecur(n / 2);
 
  // head now refers to
  // middle node, make 
  // middle node as root of BST
  Node root = head;
 
  // Set pointer to left subtree
  root.left = left;
 
  // Change head pointer of
  // Linked List for parent
  // recursive calls
  head = head.right;
 
  // Recursively construct the
  // right subtree and link it
  // with root
  root.right = sortedListToBSTRecur(n - n / 
                                    2 - 1);
 
  // Return the root 
  // of Balanced BT
  return root;
}
   
static Node sortedListToBST()
{
  // Count the number of 
  // nodes in Linked List
  int n = countNodes(head);
 
  // Construct BST
  return sortedListToBSTRecur(n);
}
 
// Function to find the leaf nodes and
// make the doubly linked list of
// those nodes
static Node extractLeafList(Node root)
{
  // Base cases
  if (root == null)
    return null;
 
  if (root.left == null && 
      root.right == null) 
  {
    // This node is added to doubly
    // linked list of leaves, and
    // set right pointer of this
    // node as previous head of DLL
    root.right = head;
 
    // Change left pointer
    // of previous head
    if (head != null)
      head.left = root;
 
    // Change head of linked list
    head = root;
 
    // Return new root
    return head;
  }
 
  // Recur for right & 
  // left subtrees
  root.right = 
       extractLeafList(root.right);
  root.left = 
       extractLeafList(root.left);
 
  // Return the root
  return root;
}
 
// Function to allocating new 
// Node int Binary Tree
static Node newNode(int data)
{
  Node node = new Node();
  node.data = data;
  node.left = null;
  node.right = null;
  return node;
}
 
// Function for inorder traversal
static void print(Node root)
{
  // If root is not null
  if (root != null) 
  {
    print(root.left);
 
    // Print the root's data
    System.out.print(root.data + " ");
    print(root.right);
  }
}
 
// Function to display nodes of DLL
static void printList(Node head)
{
  while (head != null) 
  {
    // Print the data
    System.out.print(head.data + " ");
    head = head.right;
  }
}
 
// Driver Code
public static void main(String[] args)
{
  // Given Binary Tree
  head = null;
  Node root = newNode(1);
 
  root.left = newNode(2);
  root.right = newNode(3);
  root.left.left = newNode(4);
  root.left.right = newNode(5);
  root.right.right = newNode(6);
  root.left.left.left = newNode(7);
  root.left.left.right = newNode(8);
  root.right.right.left = newNode(9);
  root.right.right.right = newNode(10);
 
  // Function Call to 
  // extract leaf Node
  root = extractLeafList(root);
 
  // Function Call to create 
  // Balanced BT
  root = sortedListToBST();
 
  // Print Inorder traversal 
  // New Balanced BT
  print(root);
}
}
 
// This code is contributed by Amit Katiyar 

Python3

# Python3 program for the above approach
 
# Structure for Linked list and tree
class newNode:
     
    def __init__(self, data):
         
        self.data = data
        self.left = None
        self.right = None
 
head  = None
 
# Function that returns the count of
# nodes in the given linked list
def countNodes(head1):
     
    # Initialize count
    count = 0
 
    temp = head1
 
    # Iterate till the end of LL
    while (temp):
        temp = temp.right
 
        # Increment the count
        count += 1
 
    # Return the final count
    return count
 
# Function to return the root of
# the newly created balanced binary
# tree from the given doubly LL
def sortedListToBSTRecur(n):
     
    global head
     
    # Base Case
    if (n <= 0):
        return None
 
    # Recursively construct
    # the left subtree
    left = sortedListToBSTRecur(n // 2)
 
    # head_ref now refers to
    # middle node, make middle node
    # as root of BST
    root = head
 
    # Set pointer to left subtree
    root.left = left
 
    # Change head pointer of
    # Linked List for parent
    # recursive calls
    head =  head.right
 
    # Recursively construct the
    # right subtree and link it
    # with root
    root.right = sortedListToBSTRecur(n - n //
                                      2 - 1)
 
    # Return the root of Balanced BT
    return root
 
def sortedListToBST():
     
    global head
     
    # Count the number of nodes
    # in Linked List 
    n = countNodes(head)
 
    # Construct BST 
    return sortedListToBSTRecur(n)
 
# Function to find the leaf nodes and
# make the doubly linked list of
# those nodes
def extractLeafList(root):
     
    global head
     
    # Base cases
    if (root == None):
        return None
 
    if (root.left == None and
       root.right == None):
         
        # This node is added to doubly
        # linked list of leaves, and
        # set right pointer of this
        # node as previous head of DLL
        root.right = head
 
        # Change left pointer
        # of previous head
        if (head != None):
            head.left = root
 
        # Change head of linked list
        head = root
 
        # Return new root
        return head
 
    # Recur for right & left subtrees
    root.right = extractLeafList(root.right)
    root.left = extractLeafList(root.left)
 
    # Return the root
    return root
 
# Function for inorder traversal
def print1(root):
     
    # If root is not NULL
    if (root != None):
        print1(root.left)
 
        # Print the root's data
        print(root.data, end = " ")
        print1(root.right)
 
# Function to display nodes of DLL
def printList(head):
     
    while(head):
         
        # Print the data
        print(head.data, end = " ")
        head = head.right
 
# Driver Code
if __name__ == '__main__':
     
    # Given Binary Tree
    root = newNode(1)
    root.left = newNode(2)
    root.right = newNode(3)
    root.left.left = newNode(4)
    root.left.right = newNode(5)
    root.right.right = newNode(6)
    root.left.left.left = newNode(7)
    root.left.left.right = newNode(8)
    root.right.right.left = newNode(9)
    root.right.right.right = newNode(10)
 
    # Function Call to extract leaf Node
    root = extractLeafList(root)
 
    # Function Call to create Balanced BT
    root = sortedListToBST()
 
    # Print Inorder traversal New Balanced BT
    print1(root)
 
# This code is contributed by ipg2016107

C#

// C# program for the above approach
using System;
 
class GFG{
 
// Structure for Linked 
// list and tree
public class Node 
{
    public int data;
    public Node left, right;
};
   
static Node head;
   
// Function that returns the 
// count of nodes in the given 
// linked list
static int countNodes(Node head)
{
     
    // Initialize count
    int count = 0;
     
    Node temp = head;
     
    // Iterate till the 
    // end of LL
    while (temp != null) 
    {
        temp = temp.right;
         
        // Increment the count
        count++;
    }
     
    // Return the readonly count
    return count;
}
 
// Function to return the root of
// the newly created balanced binary
// tree from the given doubly LL
static Node sortedListToBSTRecur(int n)
{
     
    // Base Case
    if (n <= 0)
        return null;
     
    // Recursively construct
    // the left subtree
    Node left = sortedListToBSTRecur(n / 2);
     
    // head now refers to
    // middle node, make 
    // middle node as root of BST
    Node root = head;
     
    // Set pointer to left subtree
    root.left = left;
     
    // Change head pointer of
    // Linked List for parent
    // recursive calls
    head = head.right;
     
    // Recursively construct the
    // right subtree and link it
    // with root
    root.right = sortedListToBSTRecur(n - n / 
                                      2 - 1);
     
    // Return the root 
    // of Balanced BT
    return root;
}
   
static Node sortedListToBST()
{
     
    // Count the number of 
    // nodes in Linked List
    int n = countNodes(head);
     
    // Construct BST
    return sortedListToBSTRecur(n);
}
 
// Function to find the leaf nodes and
// make the doubly linked list of
// those nodes
static Node extractLeafList(Node root)
{
     
    // Base cases
    if (root == null)
        return null;
     
    if (root.left == null && 
        root.right == null) 
    {
         
        // This node is added to doubly
        // linked list of leaves, and
        // set right pointer of this
        // node as previous head of DLL
        root.right = head;
         
        // Change left pointer
        // of previous head
        if (head != null)
            head.left = root;
         
        // Change head of linked list
        head = root;
         
        // Return new root
        return head;
    }
     
    // Recur for right & 
    // left subtrees
    root.right = extractLeafList(
                 root.right);
    root.left = extractLeafList(
                root.left);
     
    // Return the root
    return root;
}
 
// Function to allocating new 
// Node int Binary Tree
static Node newNode(int data)
{
    Node node = new Node();
    node.data = data;
    node.left = null;
    node.right = null;
    return node;
}
 
// Function for inorder traversal
static void print(Node root)
{
     
    // If root is not null
    if (root != null) 
    {
        print(root.left);
         
        // Print the root's data
        Console.Write(root.data + " ");
        print(root.right);
    }
}
 
// Function to display nodes of DLL
static void printList(Node head)
{
    while (head != null) 
    {
         
        // Print the data
        Console.Write(head.data + " ");
        head = head.right;
    }
}
 
// Driver Code
public static void Main(String[] args)
{
     
    // Given Binary Tree
    head = null;
    Node root = newNode(1);
     
    root.left = newNode(2);
    root.right = newNode(3);
    root.left.left = newNode(4);
    root.left.right = newNode(5);
    root.right.right = newNode(6);
    root.left.left.left = newNode(7);
    root.left.left.right = newNode(8);
    root.right.right.left = newNode(9);
    root.right.right.right = newNode(10);
     
    // Function call to 
    // extract leaf Node
    root = extractLeafList(root);
     
    // Function call to create 
    // Balanced BT
    root = sortedListToBST();
     
    // Print Inorder traversal 
    // New Balanced BT
    print(root);
}
}
 
// This code is contributed by Amit Katiyar

Javascript

<script>
    // Javascript program for the above approach
     
    // Structure for Linked
    // list and tree
    class Node
    {
        constructor(data) {
           this.left = null;
           this.right = null;
           this.data = data;
        }
    }
 
    let head;
 
    // Function that returns the
    // count of nodes in the given
    // linked list
    function countNodes(head)
    {
      // Initialize count
      let count = 0;
 
      let temp = head;
 
      // Iterate till the
      // end of LL
      while (temp != null)
      {
        temp = temp.right;
 
        // Increment the count
        count++;
      }
 
      // Return the final count
      return count;
    }
 
    // Function to return the root of
    // the newly created balanced binary
    // tree from the given doubly LL
    function sortedListToBSTRecur(n)
    {
      // Base Case
      if (n <= 0)
        return null;
 
      // Recursively construct
      // the left subtree
      let left = sortedListToBSTRecur(parseInt(n / 2, 10));
 
      // head now refers to
      // middle node, make
      // middle node as root of BST
      let root = head;
 
      // Set pointer to left subtree
      root.left = left;
 
      // Change head pointer of
      // Linked List for parent
      // recursive calls
      head = head.right;
 
      // Recursively construct the
      // right subtree and link it
      // with root
      root.right = sortedListToBSTRecur(n - parseInt(n / 2, 10) - 1);
 
      // Return the root
      // of Balanced BT
      return root;
    }
 
    function sortedListToBST()
    {
      // Count the number of
      // nodes in Linked List
      let n = countNodes(head);
 
      // Construct BST
      return sortedListToBSTRecur(n);
    }
 
    // Function to find the leaf nodes and
    // make the doubly linked list of
    // those nodes
    function extractLeafList(root)
    {
      // Base cases
      if (root == null)
        return null;
 
      if (root.left == null &&
          root.right == null)
      {
        // This node is added to doubly
        // linked list of leaves, and
        // set right pointer of this
        // node as previous head of DLL
        root.right = head;
 
        // Change left pointer
        // of previous head
        if (head != null)
          head.left = root;
 
        // Change head of linked list
        head = root;
 
        // Return new root
        return head;
      }
 
      // Recur for right &
      // left subtrees
      root.right =
           extractLeafList(root.right);
      root.left =
           extractLeafList(root.left);
 
      // Return the root
      return root;
    }
 
    // Function to allocating new
    // Node int Binary Tree
    function newNode(data)
    {
      let node = new Node(data);
      return node;
    }
 
    // Function for inorder traversal
    function print(root)
    {
      // If root is not null
      if (root != null)
      {
        print(root.left);
 
        // Print the root's data
        document.write(root.data + " ");
        print(root.right);
      }
    }
 
    // Function to display nodes of DLL
    function printList(head)
    {
      while (head != null)
      {
        // Print the data
        document.write(head.data + " ");
        head = head.right;
      }
    }
     
    // Given Binary Tree
    head = null;
    let root = newNode(1);
 
    root.left = newNode(2);
    root.right = newNode(3);
    root.left.left = newNode(4);
    root.left.right = newNode(5);
    root.right.right = newNode(6);
    root.left.left.left = newNode(7);
    root.left.left.right = newNode(8);
    root.right.right.left = newNode(9);
    root.right.right.right = newNode(10);
 
    // Function Call to
    // extract leaf Node
    root = extractLeafList(root);
 
    // Function Call to create
    // Balanced BT
    root = sortedListToBST();
 
    // Print Inorder traversal
    // New Balanced BT
    print(root);
  
 // This code is contributed by mukesh07.
</script>

Output:

7 8 5 9 10

Time Complexity: O(N), where N is the number of nodes in the given tree.
Auxiliary Space Complexity: O(1)

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