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

Datetime:2016-08-23 01:17:22         Topic:         Share        Original >>

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

For example,

```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 C++ implementation of above idea –

```// C++ program to calculate height of a special tree
// whose leaf nodes forms a circular doubly linked list
#include <iostream>
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;
}```

Output:

`Height of tree is 4`