 ## BJP3 Exercise 12.10: digitMatch

Language/Type: Java recursion recursive programming
Author: Robert Baxter (on 2013/04/01)

Write a recursive method `digitMatch` that accepts two non-negative integers as parameters and that returns the number of digits that match between them. Two digits match if they are equal and have the same position relative to the end of the number (i.e. starting with the ones digit). In other words, the method should compare the last digits of each number, the second-to-last digits of each number, the third-to-last digits of each number, and so forth, counting how many pairs match. For example, for the call of `digitMatch(1072503891, 62530841)`, the method would compare as follows:

```1 0 7 2 5 0 3 8 9 1
| | | | | | | |
6 2 5 3 0 8 4 1
```

The method should return `4` in this case because 4 of these pairs match (2-2, 5-5, 8-8, and 1-1). Below are more examples:

Call Value Returned
`digitMatch(38, 34)` `1`
`digitMatch(5, 5552)` `0`
`digitMatch(892, 892)` `3`
`digitMatch(298892, 7892)` `3`
`digitMatch(380, 0)` `1`
`digitMatch(123456, 654321)` `0`
`digitMatch(1234567, 67)` `2`

Your method should throw an `IllegalArgumentException` if either of the two parameters is negative. You are not allowed to construct any structured objects other than `String`s (no array, `List`, `Scanner`, etc.) and you may not use any loops to solve this problem; you must use recursion.