## limitPathSum

Language/Type: C++ binary trees pointers recursion
Author: Marty Stepp (on 2016/06/16)

Write a member function named `limitPathSum` that could be added to the `BinaryTree` class. Your function should accept an integer value representing a maximum, and remove nodes to guarantee that the sum of values on any path from the root to a node does not exceed that maximum. For example, if variable `tree` refers to the tree below at left, the call of `tree.limitPathSum(50);` will require removing node `12` because the sum from the root down to that node is more than 50 (29 + 17 + -7 + 12 = 51). Similarly, we have to remove node `37` because its sum is (29 + 17 + 37 = 83). When you remove a node, you remove anything under it, so removing `37` also removes `16`. We also remove the node with `14` because its sum is (29 + 15 + 14 = 58). If the data stored at the root is greater than the given maximum, remove all nodes, leaving an empty (`NULL`) tree. Free the memory associated with each node you remove, but only remove the nodes that are necessary to remove.

`tree` after `tree.limitPathSum(50);`
```           29
/    \
17        15
/  \      /  \
-7    37   4    14
/  \     \      /  \
11   12    16   -9    19
```
```           29
/    \
17        15
/         /
-7         4
/
11
```

Constraints: 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).

Write the member function as it would appear in `BinaryTree.cpp`. You do not need to declare the function header that would appear in `BinaryTree.h`. Assume that you are adding this method to the `BinaryTree` class as defined below:

```class BinaryTree {
private:
BinaryTreeNode* root;   // NULL for an empty tree
...

public:
};

struct BinaryTreeNode {
int data;
BinaryTreeNode* left;
BinaryTreeNode* right;
...
}
```
Type your C++ solution code here:

This is a member function problem. Submit a member function that will become part of an existing C++ class. You do not need to write the complete class, just the member function described in the problem.