Diameter of a Binary Tree in O(n) [A new method]

The diameter of a tree is the number of nodes on the longest path between two leaves in the tree. The diagram below shows two trees each with diameter nine, the leaves that form the ends of the longest path are colored (note that there may be more than one path in the tree of the same diameter).

Examples:

Input :     1
          /   \
        2      3
      /  \
    4     5

Output : 4

Input :     1
          /   \
        2      3
      /  \ .    \
    4     5 .    6

Output : 5

We have discussed a solution in below post. 
Diameter of a Binary Tree

In this post a new simple O(n) method is discussed. Diameter of a tree can be calculated by only using the height function, because the diameter of a tree is nothing but maximum value of (left_height + right_height + 1) for each node. So we need to calculate this value (left_height + right_height + 1) for each node and update the result. Time complexity – O(n)  

Implementation:

Output

Diameter is 4

Time complexity: O(n) ,  where n is number of nodes in binary tree .
Auxiliary Space: O(h) for call stack , where h is height of binary tree .