 ## hasPath

Author: Marty Stepp (on 2010/12/28)

Write a method `hasPath` that could be added to the `IntTree` class from lecture and section. The method accepts start and end integers 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 found in the tree, and end must be in one of start's subtrees; otherwise the method returns `false`. The result is trivially `true` if start and end are the same; in such a case, you are simply checking whether a node exists in the tree with that value.

For example, suppose a variable of type `IntTree` called `tree` stores the following elements:

```                  +----+
| 67 |
+----+
/          \
/                \
+----+                +----+
| 80 |                | 52 |
+----+                +----+
/      \              /
/        \            /
+----+     +----+      +----+
| 16 |     | 21 |      | 99 |
+----+     +----+      +----+
/
/
+----+
| 45 |
+----+
```

The table below shows what the state of the tree would be if various calls were made:

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.

You may define private helper methods to solve this problem, but otherwise you may not call any other methods of the class nor create any data structures (arrays, lists, etc.). You should not modify the tree in any way in your code.

Assume that you are adding this method to the `IntTree` class as defined below:

```public class IntTree {
private IntTreeNode overallRoot;
...
}
```