Construct a Perfect Binary Tree with given Height

Given an integer N, the task is to generate a perfect binary tree with height N such that each node has a value that is the same as its depth. Return the inorder traversal of the generated binary tree.

A Perfect binary tree is a type of binary tree where every internal node has exactly two child nodes and all leaf nodes are at same level. 

Examples:

Input: N = 2
Output: 2 1 2 0 2 1 2
Explanation: The structure of the tree is as following

Perfect Binary Tree with height 2

Input: N = 1
Output: 1 0 1

Approach: The problem can be solved using level order traversal based on the following observation:

As there is a requirement to fill each node with the value that is the same as its depth so use the level order traversal. In each step fill a total level and mark all the nodes with the value same as the depth.

Follow the steps mentioned below to implement the approach:

• Initiate a variable to store the depth of the current level.
• Initiate a queue to store the node of each level and perform the level order traversal.
• In each iteration get all the nodes in that level and continue the following until the depth is N:
  • Increase the depth by 1.
  • Pop the nodes at the current level.
  • Generate the child nodes for each node.
  • Add the new child nodes for further processing.
• After the traversal is complete, the tree is prepared.
• Print the inorder traversal of the tree.

Below is the implementation of the above approach.

Java

// Java code to implement the approach

import java.util.*;

// Class to hold tree node data
// and left, right children
class TreeNode {
    public long val;
    public TreeNode left;
    public TreeNode right;

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

// Class to create the perfect binary tree
class BinaryTree {

    // Method to construct a binary tree
    public static TreeNode perfectBinaryTree(int depth)
    {
        // Return root with 0 as val if height is 0
        if (depth == 0)
            return new TreeNode(0);

        // Initiate queue to store
        // the nodes on each level
        Queue<TreeNode> queue
            = new LinkedList<>();

        // Create a root node with value 0
        long i = 0;
        TreeNode root = new TreeNode(i);

        // Add the root node to the queue
        // for further processing
        queue.add(root);

        // Iterate through the queue till its empty
        while (!queue.isEmpty()) {

            // Check the size of the queue to iterate
            // through each node on the same level
            int size = queue.size();

            // Increment the value of node
            // upon each level
            i++;

            // Break the loop if the value of the node
            // reaches given depth
            // else process the node in the queue
            if (i > depth) {
                break;
            }
            else {
                // Add the left and right child
                // for the node in the queue and
                // add those newly created child nodes
                // to the queue.
                for (int j = 0; j < size; j++) {
                    TreeNode node = queue.remove();
                    node.left = new TreeNode(i);
                    node.right = new TreeNode(i);

                    queue.add(node.left);
                    queue.add(node.right);
                }
            }
        }

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

    // Inorder traversal of the tree (Left Root Right)
    public static void inOrderTraversal(TreeNode node)
    {
        if (node == null)
            return;
        inOrderTraversal(node.left);
        System.out.print(node.val + " ");
        inOrderTraversal(node.right);
    }

    // Driver code
    public static void main(String[] args)
    {
        int N = 2;

        // Function call to build the tree
        TreeNode binaryTreeRoot
            = perfectBinaryTree(N);

        // Function call to print the tree
        inOrderTraversal(binaryTreeRoot);
    }
}

C#

// C# code to implement the approach
using System;
using System.Collections.Generic;

// Class to hold tree node data
// and left, right children
public class TreeNode {
  public long val;
  public TreeNode left;
  public TreeNode right;

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

// Class to create the perfect binary tree
public class BinaryTree {

  // Method to construct a binary tree
  public static TreeNode perfectBinaryTree(int depth) {
    // Return root with 0 as val if height is 0
    if (depth == 0)
      return new TreeNode(0);

    // Initiate queue to store
    // the nodes on each level
    Queue<TreeNode> queue = new Queue<TreeNode>();

    // Create a root node with value 0
    long i = 0;
    TreeNode root = new TreeNode(i);

    // Add the root node to the queue
    // for further processing
    queue.Enqueue(root);

    // Iterate through the queue till its empty
    while (queue.Count!=0) {

      // Check the size of the queue to iterate
      // through each node on the same level
      int size = queue.Count;

      // Increment the value of node
      // upon each level
      i++;

      // Break the loop if the value of the node
      // reaches given depth
      // else process the node in the queue
      if (i > depth) {
        break;
      } else {
        // Add the left and right child
        // for the node in the queue and
        // add those newly created child nodes
        // to the queue.
        for (int j = 0; j < size; j++) {
          TreeNode node = queue.Dequeue();
          node.left = new TreeNode(i);
          node.right = new TreeNode(i);

          queue.Enqueue(node.left);
          queue.Enqueue(node.right);
        }
      }
    }

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

  // Inorder traversal of the tree (Left Root Right)
  public static void inOrderTraversal(TreeNode node) {
    if (node == null)
      return;
    inOrderTraversal(node.left);
    Console.Write(node.val + " ");
    inOrderTraversal(node.right);
  }

  // Driver code
  public static void Main(String[] args) {
    int N = 2;

    // Function call to build the tree
    TreeNode binaryTreeRoot = perfectBinaryTree(N);

    // Function call to print the tree
    inOrderTraversal(binaryTreeRoot);
  }
}

// This code is contributed by shikhasingrajput

Javascript

        // JavaScript code for the above approach
        class TreeNode {
    constructor(val) {
        this.val = val;
        this.left = null;
        this.right = null;
    }
}

class BinaryTree {
    static perfectBinaryTree(depth) {
        if (depth === 0) {
            return new TreeNode(0);
        }

        const queue = [];
        let i = 0;
        const root = new TreeNode(i);
        queue.push(root);

        while (queue.length > 0) {
            const size = queue.length;
            i++;
            if (i > depth) {
                break;
            }
            else {
                for (let j = 0; j < size; j++) {
                    const node = queue.shift();
                    node.left = new TreeNode(i);
                    node.right = new TreeNode(i);
                    queue.push(node.left);
                    queue.push(node.right);
                }
            }
        }

        return root;
    }

    static inOrderTraversal(node) {
        if (node === null) return;
        this.inOrderTraversal(node.left);
        console.log(node.val + " ");
        this.inOrderTraversal(node.right);
    }
}

const N = 2;
const binaryTreeRoot = BinaryTree.perfectBinaryTree(N);
BinaryTree.inOrderTraversal(binaryTreeRoot);

 // This code is contributed by Potta Lokesh.

Output

2 1 2 0 2 1 2 

Time Complexity: O(2^N)
Auxiliary Space: O(2^N)