## BJP3 Exercise 17.17: combineWith

Author: Robert Baxter (on 2013/04/01)

Write a method `combineWith` that could be added to the `IntTree` class. The method accepts another binary tree of integers as a parameter and combines the two trees into a new third tree which is returned. The new tree's structure should be a union of the structures of the two original trees. It should have a node in any location where there was a node in either of the original trees (or both). The nodes of the new tree should store an integer indicating which of the original trees had a node at that position (`1` if just the first tree had the node, `2` if just the second tree had the node, `3` if both trees had the node).

For example, suppose `IntTree` variables `t1` and `t2` have been initialized and store the following trees:

`t1` `t2`
```            +----+
|  9 |
+----+
/      \
/        \
+----+      +----+
|  6 |      | 14 |
+----+      +----+
/      \           \
/        \           \
+----+      +----+      +----+
|  9 |      |  2 |      | 11 |
+----+      +----+      +----+
/
/
+----+
|  4 |
+----+
```
```            +----+
|  0 |
+----+
/      \
/        \
+----+      +----+
| -3 |      |  8 |
+----+      +----+
/           /      \
/           /        \
+----+      +----+      +----+
|  8 |      |  5 |      |  6 |
+----+      +----+      +----+
\
\
+----+
|  1 |
+----+
```

Then the following call:

`IntTree t3 = t1.combineWith(t2);`

Will return a reference to the following tree:

`t3`
```               +---+
| 3 |
___ +---+ ___
/               \
+---+               +---+
| 3 |               | 3 |
+---+               +---+
/     \             /     \
+---+     +---+     +---+     +---+
| 3 |     | 1 |     | 2 |     | 3 |
+---+     +---+     +---+     +---+
/               \
+---+               +---+
| 1 |               | 2 |
+---+               +---+
```

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 such as arrays, lists, etc. Your method should not change the structure or contents of either of the two trees being compared.

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

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

This is a partial class problem. Submit code that will become part of an existing Java class as described. You do not need to write the complete class, just the portion described in the problem.