hasPath

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

Write a member function named `hasPath` that could be added to the `BinaryTree` class. The function accepts integers start and end as parameters and returns `true` if a path can be found in the tree from start down to end. In other words, both start and end must be element data values that are found in the tree, and end must be below start, in one of start's subtrees; otherwise the function returns `false`. If start and end are the same, you are simply checking whether a single node exists in the tree with that data value. If the tree is empty, your function should return `false`.

For example, suppose a `BinaryTree` variable named `tree` stores the following elements. The table below shows the results of several various calls to your function:

```           67
/      \
80            52
/    \         /
16     21      99
/
45
```
Call Result Reason
`tree.hasPath(67, 99)` `true` path exists 67 -> 52 -> 99
`tree.hasPath(80, 45)` `true` path exists 80 -> 21 -> 45
`tree.hasPath(67, 67)` `true` node exists with `data` of 67
`tree.hasPath(16, 16)` `true` node exists with `data` of 16
`tree.hasPath(52, 99)` `true` path exists 52 -> 99
`tree.hasPath(99, 67)` `false` nodes do exist, but in wrong order
`tree.hasPath(80, 99)` `false` nodes do exist, but there is no path from 80 to 99
`tree.hasPath(67, 100)` `false` end of 100 doesn't exist in the tree
`tree.hasPath(-1, 45)` `false` start of -1 doesn't exist in the tree
`tree.hasPath(42, 64)` `false` start/end of -1 and 45 both don't exist in the tree

An empty tree does not contain any paths, so if the tree is empty, your method should return `false`. You should not assume that your tree is a binary search tree (BST); its elements could be stored in any order.

Constraints: Your member function should not modify the tree's state; the state of the tree should remain constant with respect to your function. 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.