Count of Fibonacci paths in a Binary tree

Given a Binary Tree, the task is to count the number of Fibonacci paths in the given Binary Tree. 

Fibonacci Path is a path which contains all nodes in root to leaf path are terms of Fibonacci series.

Example: 

Input:
 0
 / \
 1 1
 / \ / \
 1 10 70 1
 / \
 81 2
Output: 2 
Explanation:
There are 2 Fibonacci path for
the above Binary Tree, for x = 3,
Path 1: 0 1 1
Path 2: 0 1 1 2

Input:
 8
 / \
 4 81
 / \ / \
 3 2 70 243
 / \
 81 909
Output: 0

Approach: The idea is to use Preorder Tree Traversal. During preorder traversal of the given binary tree do the following:  

1. First calculate the Height of binary tree .
2. Now create a vector of length equals height of tree, such that it contains Fibonacci Numbers.
3. If current value of the node at i^th level is not equal to i^th term of fibonacci series or pointer becomes NULL then return the count.
4. If the current node is a leaf node then increment the count by 1.
5. Recursively call for the left and right subtree with the updated count.
6. After all-recursive call, the value of count is number of Fibonacci paths for a given binary tree.

Below is the implementation of the above approach: 

2

Time Complexity: O(n), where n is the number of nodes in the given tree.
Auxiliary Space: O(h), where h is the height of the tree.