Write the definition of a (recursive) member function of the `BinarySearchTree` class named `countGreaterThan` that takes a parameter `n` of type `elemType` and returns the number of nodes whose `data` field is greater than parameter `n`. ```cpp// BinaryTree.h#include using namespace std;// Definition of the Nodetemplate struct TreeNode { elemType data; TreeNode *left; TreeNode *right;};// Definition of class Binary Treetemplate class BinaryTree {protected: TreeNode *root;public: BinaryTree(); BinaryTree(const BinaryTree& otherTree); ~BinaryTree(); bool isEmpty() const; virtual bool search(const elemType& searchItem) const = 0; virtual void insert(const elemType& insertItem) = 0; virtual void deleteNode(const elemType& deleteItem) = 0;private: int height(TreeNode *p) const; int nodeCount(TreeNode *p) const; int leafCount(TreeNode *p) const;};// BinarySearchTree.h#include "BinaryTree.h"using namespace std;template class BinarySearchTree: public BinaryTree {public: bool search(const elemType& searchItem) const; void insert(const elemType& insertItem); void deleteNode(const elemType& deleteItem);private: void displayAscending(TreeNode *p) const; TreeNode * getTreeMax(TreeNode *p) const; TreeNode * getTreeMin(TreeNode *p) const;};```### ExplanationThis code represents the class specifications for a `BinaryTree` class and a `BinarySearchTree` class in C++. These classes are for managing binary trees and binary search trees, respectively.- **TreeNode Structure**: This template structure holds the data for each node and pointers to left and right child nodes.- **BinaryTree Class**: - Inherits the `TreeNode` structure. - Protected member `root` points to the root of the tree. - Public member functions include constructors, destructors, and methods to check if the tree is empty, search, insert, and delete nodes. - Private member functions calculate the height, the number of nodes, and the number of leaf nodes.- **BinarySearchTree Class**:

Answer :-First Declare this function in the public section of class BinaryTree. The root is declared in the protective section and this will be accessed by the function. That's why we don't need root in the parameter section of function. The Recursive Function countGreaterThan - int countGreaterThan(elemType key){ if(root==NULL) return 0; root=root->left; int left=countGreaterThan(key); root=root->right; int right=countGreaterThan(key); return left+right+(root->data>key?1:0); }

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Write the definition of a (recursive) member function of the BinarySearch Tree class named countGreaterThan that takes a parameter n of type elemType and returns the number of nodes whose data field is greater than parameter n. Edit Format Table 12pt v Paragraph v |BIUA

Write the definition of a (recursive) member function of the BinarySearch Tree class named countGreaterThan that takes a parameter n of type elemType and returns the number of nodes whose data field is greater than parameter n. Edit Format Table 12pt v Paragraph v |BIUA

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Question

Write the definition of a (recursive) member function of the `BinarySearchTree` class named `countGreaterThan` that takes a parameter `n` of type `elemType` and returns the number of nodes whose `data` field is greater than parameter `n`.

```cpp
// BinaryTree.h
#include <iostream>
using namespace std;

// Definition of the Node
template <class elemType>
struct TreeNode {
elemType data;
TreeNode<elemType> *left;
TreeNode<elemType> *right;
};

// Definition of class Binary Tree
template <class elemType>
class BinaryTree {
protected:
TreeNode<elemType> *root;
public:
BinaryTree();
BinaryTree(const BinaryTree<elemType>& otherTree);
~BinaryTree();
bool isEmpty() const;
virtual bool search(const elemType& searchItem) const = 0;
virtual void insert(const elemType& insertItem) = 0;
virtual void deleteNode(const elemType& deleteItem) = 0;
private:
int height(TreeNode<elemType> *p) const;
int nodeCount(TreeNode<elemType> *p) const;
int leafCount(TreeNode<elemType> *p) const;
};

// BinarySearchTree.h
#include "BinaryTree.h"
using namespace std;

template <class elemType>
class BinarySearchTree: public BinaryTree<elemType> {
public:
bool search(const elemType& searchItem) const;
void insert(const elemType& insertItem);
void deleteNode(const elemType& deleteItem);
private:
void displayAscending(TreeNode<elemType> *p) const;
TreeNode<elemType> * getTreeMax(TreeNode<elemType> *p) const;
TreeNode<elemType> * getTreeMin(TreeNode<elemType> *p) const;
};
```

### Explanation

This code represents the class specifications for a `BinaryTree` class and a `BinarySearchTree` class in C++. These classes are for managing binary trees and binary search trees, respectively.

- **TreeNode Structure**: This template structure holds the data for each node and pointers to left and right child nodes.

- **BinaryTree Class**:
- Inherits the `TreeNode` structure.
- Protected member `root` points to the root of the tree.
- Public member functions include constructors, destructors, and methods to check if the tree is empty, search, insert, and delete nodes.
- Private member functions calculate the height, the number of nodes, and the number of leaf nodes.

- **BinarySearchTree Class**:

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