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 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 <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; } |
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 contibuted 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 |
Output:
Height of tree is 4
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