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Find height of a special binary tree whose leaf nodes are connected

  • Difficulty Level : Medium
  • Last Updated : 08 Oct, 2021

Given a special binary tree whose leaf nodes are connected to form a circular doubly linked list, find its height.

For example, 

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         1 
       /   \ 
      2      3 
    /  \ 
   4    5
  /   
 6 

In the above binary tree, 6, 5 and 3 are leaf nodes and they form a circular doubly linked list. Here, the left pointer of leaf node will act as a previous pointer of circular doubly linked list and its right pointer will act as next pointer of circular doubly linked list. 

The idea is to follow similar approach as we do for finding height of a normal binary tree. We recursively calculate height of left and right subtrees of a node and assign height to the node as max of the heights of two children plus 1. But left and right child of a leaf node are null for normal binary trees. But, here leaf node is a circular doubly linked list node. So for a node to be a leaf node, we check if node’s left’s right is pointing to the node and its right’s left is also pointing to the node itself.



Below is the implementation of above idea –  

C++




// C++ program to calculate height of a special tree
// whose leaf nodes forms a circular doubly linked list
#include <bits/stdc++.h>
using namespace std;
  
// A binary tree Node
struct Node {
    int data;
    Node *left, *right;
};
  
// function to check if given node is a leaf node or node
bool isLeaf(Node* node)
{
    // If given node's left's right is pointing to given
    // node and its right's left is pointing to the node
    // itself then it's a leaf
    return node->left && node->left->right == node
           && node->right && node->right->left == node;
}
  
/* Compute the height of a tree -- the number of
Nodes along the longest path from the root node
down to the farthest leaf node.*/
int maxDepth(Node* node)
{
    // if node is NULL, return 0
    if (node == NULL)
        return 0;
  
    // if node is a leaf node, return 1
    if (isLeaf(node))
        return 1;
  
    // compute the depth of each subtree and take maximum
    return 1
           + max(maxDepth(node->left),
                 maxDepth(node->right));
}
  
// Helper function that allocates a new tree node
Node* newNode(int data)
{
    Node* node = new Node;
    node->data = data;
    node->left = NULL;
    node->right = NULL;
  
    return node;
}
  
// Driver code
int main()
{
    Node* root = newNode(1);
  
    root->left = newNode(2);
    root->right = newNode(3);
    root->left->left = newNode(4);
    root->left->right = newNode(5);
    root->left->left->left = newNode(6);
  
    // Given tree contains 3 leaf nodes
    Node* L1 = root->left->left->left;
    Node* L2 = root->left->right;
    Node* L3 = root->right;
  
    // create circular doubly linked list out of
    // leaf nodes of the tree
  
    // set next pointer of linked list
    L1->right = L2, L2->right = L3, L3->right = L1;
  
    // set prev pointer of linked list
    L3->left = L2, L2->left = L1, L1->left = L3;
  
    // calculate height of the tree
    cout << "Height of tree is " << maxDepth(root);
  
    return 0;
}

Java




// Java implementation to calculate height of a special tree
// whose leaf nodes forms a circular doubly linked list
import java.io.*;
import java.util.*;
  
// User defined node class
class Node {
    int data;
    Node left, right;
    // Constructor to create a new tree node
    Node(int key)
    {
        data = key;
        left = right = null;
    }
}
  
class GFG {
  
    // function to check if given node is a leaf node or
    // node
    static boolean isLeaf(Node node)
    {
        // If given node's left's right is pointing to given
        // node and its right's left is pointing to the node
        // itself then it's a leaf
        return (node.left != null && node.left.right == node
                && node.right != null
                && node.right.left == node);
    }
    /* Compute the height of a tree -- the number of
    Nodes along the longest path from the root node
    down to the farthest leaf node.*/
    static int maxDepth(Node node)
    {
        // if node is NULL, return 0
        if (node == null)
            return 0;
  
        // if node is a leaf node, return 1
        if (isLeaf(node))
            return 1;
  
        // compute the depth of each subtree and take
        // maximum
        return 1
            + Math.max(maxDepth(node.left),
                       maxDepth(node.right));
    }
  
    // Driver code
    public static void main(String args[])
    {
        Node root = new Node(1);
  
        root.left = new Node(2);
        root.right = new Node(3);
        root.left.left = new Node(4);
        root.left.right = new Node(5);
        root.left.left.left = new Node(6);
  
        // Given tree contains 3 leaf nodes
        Node L1 = root.left.left.left;
        Node L2 = root.left.right;
        Node L3 = root.right;
  
        // create circular doubly linked list out of
        // leaf nodes of the tree
  
        // set next pointer of linked list
        L1.right = L2;
        L2.right = L3;
        L3.right = L1;
  
        // set prev pointer of linked list
        L3.left = L2;
        L2.left = L1;
        L1.left = L3;
  
        // calculate height of the tree
        System.out.println("Height of tree is "
                           + maxDepth(root));
    }
}
// This code is contributed by rachana soma

Python3




""" program to Delete a Tree """
  
# Helper function that allocates a new
# node with the given data and None
# left and right poers.
  
  
class newNode:
  
    # Construct to create a new node
    def __init__(self, key):
        self.data = key
        self.left = None
        self.right = None
  
# function to check if given node is a leaf node or node
  
  
def isLeaf(node):
  
    # If given node's left's right is pointing to given node
    # and its right's left is pointing to the node itself
    # then it's a leaf
    return node.left and node.left.right == node and \
        node.right and node.right.left == node
  
  
""" Compute the height of a tree -- the number of 
Nodes along the longest path from the root node 
down to the farthest leaf node."""
  
  
def maxDepth(node):
  
    # if node is None, return 0
    if (node == None):
        return 0
  
    # if node is a leaf node, return 1
    if (isLeaf(node)):
        return 1
  
    # compute the depth of each subtree and take maximum
    return 1 + max(maxDepth(node.left), maxDepth(node.right))
  
  
# Driver Code
if __name__ == '__main__':
    root = newNode(1)
  
    root.left = newNode(2)
    root.right = newNode(3)
    root.left.left = newNode(4)
    root.left.right = newNode(5)
    root.left.left.left = newNode(6)
  
    # Given tree contains 3 leaf nodes
    L1 = root.left.left.left
    L2 = root.left.right
    L3 = root.right
  
    # create circular doubly linked list out of
    # leaf nodes of the tree
  
    # set next pointer of linked list
    L1.right = L2
    L2.right = L3
    L3.right = L1
  
    # set prev pointer of linked list
    L3.left = L2
    L2.left = L1
    L1.left = L3
  
    # calculate height of the tree
    print("Height of tree is ", maxDepth(root))
  
# This code is contributed by
# Shubham Singh(SHUBHAMSINGH10)

C#




// C# implementation to calculate height of a special tree
// whose leaf nodes forms a circular doubly linked list
using System;
  
// User defined node class
public class Node {
    public int data;
    public Node left, right;
    // Constructor to create a new tree node
    public Node(int key)
    {
        data = key;
        left = right = null;
    }
}
  
public class GFG {
  
    // function to check if given node is a leaf node or
    // node
    static bool isLeaf(Node node)
    {
        // If given node's left's right is pointing to given
        // node and its right's left is pointing to the node
        // itself then it's a leaf
        return (node.left != null && node.left.right == node
                && node.right != null
                && node.right.left == node);
    }
    /* Compute the height of a tree -- the number of
    Nodes along the longest path from the root node
    down to the farthest leaf node.*/
    static int maxDepth(Node node)
    {
        // if node is NULL, return 0
        if (node == null)
            return 0;
  
        // if node is a leaf node, return 1
        if (isLeaf(node))
            return 1;
  
        // compute the depth of each subtree and take
        // maximum
        return 1
            + Math.Max(maxDepth(node.left),
                       maxDepth(node.right));
    }
  
    // Driver code
    public static void Main(String[] args)
    {
        Node root = new Node(1);
  
        root.left = new Node(2);
        root.right = new Node(3);
        root.left.left = new Node(4);
        root.left.right = new Node(5);
        root.left.left.left = new Node(6);
  
        // Given tree contains 3 leaf nodes
        Node L1 = root.left.left.left;
        Node L2 = root.left.right;
        Node L3 = root.right;
  
        // create circular doubly linked list out of
        // leaf nodes of the tree
  
        // set next pointer of linked list
        L1.right = L2;
        L2.right = L3;
        L3.right = L1;
  
        // set prev pointer of linked list
        L3.left = L2;
        L2.left = L1;
        L1.left = L3;
  
        // calculate height of the tree
        Console.WriteLine("Height of tree is "
                          + maxDepth(root));
    }
}
  
// This code is contributed by 29AjayKumar

Javascript




<script>
// Javascript implementation to calculate height of a special tree
// whose leaf nodes forms a circular doubly linked list
class Node
{
    constructor(key)
    {
        this.data = key;
        this.left = this.right = null;
    }
}
  
// function to check if given node is a leaf node or
    // node
function isLeaf(node)
{
  
    // If given node's left's right is pointing to given
        // node and its right's left is pointing to the node
        // itself then it's a leaf
        return (node.left != null && node.left.right == node
                && node.right != null
                && node.right.left == node);
}
  
/* Compute the height of a tree -- the number of
    Nodes along the longest path from the root node
    down to the farthest leaf node.*/
function maxDepth(node)
{
  
     // if node is NULL, return 0
        if (node == null)
            return 0;
    
        // if node is a leaf node, return 1
        if (isLeaf(node))
            return 1;
    
        // compute the depth of each subtree and take
        // maximum
        return 1
            + Math.max(maxDepth(node.left),
                       maxDepth(node.right));
}
  
// Driver code
let root = new Node(1);
    
root.left = new Node(2);
root.right = new Node(3);
root.left.left = new Node(4);
root.left.right = new Node(5);
root.left.left.left = new Node(6);
  
// Given tree contains 3 leaf nodes
let L1 = root.left.left.left;
let L2 = root.left.right;
let L3 = root.right;
  
// create circular doubly linked list out of
// leaf nodes of the tree
  
// set next pointer of linked list
L1.right = L2;
L2.right = L3;
L3.right = L1;
  
// set prev pointer of linked list
L3.left = L2;
L2.left = L1;
L1.left = L3;
  
// calculate height of the tree
document.write("Height of tree is "
                   + maxDepth(root));
  
// This code is contributed by rag2127
</script>

Output: 

Height of tree is 4

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