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## BJP5 Exercise 17.21: matches

Language/Type: Java binary trees implementing IntTree
Author: Marty Stepp (on 2019/09/19)

Write a method `matches` that returns a count of the number of nodes in one tree that match nodes in another tree. A match is defined as a pair of nodes that are in the same position in the two trees relative to their overall root and that store the same data. Consider, for example, the following trees:

```          tree1
+---+
| 3 |
+---+
/     \
+---+     +---+
| 4 |     | 7 |
+---+     +---+
/     \         \
+---+     +---+     +---+
| 0 |     | 9 |     | 2 |
+---+     +---+     +---+
\
+---+
| 8 |
+---+
```
```          tree2
+---+
| 3 |
+---+
/     \
+---+     +---+
| 6 |     | 7 |
+---+     +---+
/         /     \
+---+     +---+     +---+
| 0 |     | 9 |     | 2 |
+---+     +---+     +---+
\
+---+
| 8 |
+---+
```

The overall root of the two trees match (both are 3). The nodes at the top of the left subtrees of the overall root do not match (one is 4 and one is 6). The top of the right subtrees of the overall root match (both are 7). The next level of the tree has 2 matches for the nodes storing 0 and 2 (there are two nodes that each store 9 at this level, but they are in different positions relative to the overall root of the tree). The nodes at the lowest level both store 8, but they aren't a match because they are in different positions. Therefore, these two trees have a total of 4 matches. Therefore the calls of `tree1.matches(tree2)` and `tree2.matches(tree1)` would each return `4`.

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