a) Write a RECURSIVE function to count the number of non-leaf nodes in a general Binary Tree. A leaf node is a node with no children.

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a) Write a RECURSIVE function to count the number of non-leaf nodes in a general Binary Tree. A leaf node is a node with no children. 

b) Now, assume you have a full binary tree with n nodes. A full binary tree is a binary tree in which all leave nodes have the same depth and all internal (non-leaf) nodes have exactly two children. Write a recurrence relation for the time complexity of your algorithm in part a once the input to your function is a full binary tree. Explain why you came up with such a recurrence relation. Then bound the relation in Big-O(). (You might use Master Theorem if applicable). Please show all work in depth for each step. 

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