Write a function named height that accepts a pointer to the root of a binary tree of integers.
Your function should return the height of a tree.
The height is defined to be the number of levels (i.e., the number of nodes along the longest path from the root to a leaf).
For example, an empty tree has height 0.
A tree of one node has height 1.
A tree whose root has one or two leaves as children has height 2, and so on.
If a pointer named root points to the root of the following tree, the call of height(root) should return 4:
(7 (4 (2 (1) (3)) (5 / (6))) (8))
Constraints:
You must implement your function recursively and without using loops.
Do not construct any new BinaryTreeNode objects in solving this problem (though you may create as many BinaryTreeNode* pointer variables as you like).
Do not use any auxiliary data structures to solve this problem (no array, vector, stack, queue, string, etc).
Your function should not modify the tree's state; the state of the tree should remain constant with respect to your function.
Assume that you are using the BinaryTreeNode structure as defined below:
struct BinaryTreeNode {
int data;
BinaryTreeNode* left;
BinaryTreeNode* right;
};
