Here's the implementation of the `nodeDifference` member function in the `BST` class that calculates the difference between the number of nodes in the right subtree and the left subtree:
```cpp
class BST {
private:
struct Node {
int data_;
Node* left_;
Node* right_;
Node(int data) : data_(data), left_(nullptr), right_(nullptr) {}
};
Node* root_;
public:
// Other member functions...
int nodeDifference() const {
return nodeDifferenceHelper(root_);
}
private:
int nodeDifferenceHelper(Node* node) const {
if (node == nullptr) {
return 0;
}
int leftCount = countNodes(node->left_);
int rightCount = countNodes(node->right_);
return rightCount - leftCount;
}
int countNodes(Node* node) const {
if (node == nullptr) {
return 0;
}
return 1 + countNodes(node->left_) + countNodes(node->right_);
}
};
```
In this code, the `nodeDifference` member function calls the `nodeDifferenceHelper` function to calculate the difference between the number of nodes in the right subtree and the left subtree. If the tree is empty (root is `nullptr`), the function returns 0.
The `nodeDifferenceHelper` function recursively traverses the tree and counts the number of nodes in the left and right subtrees using the `countNodes` helper function. It then returns the difference between the counts.
The `countNodes` function is a recursive function that counts the number of nodes in a subtree. It starts by checking if the current node is `nullptr`. If so, it returns 0. Otherwise, it counts the current node and recursively calls `countNodes` on the left and right subtrees, adding their counts.
The runtime requirement of this implementation is O(n) since it needs to traverse all the nodes in the tree once to count them.