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countMultiples

Language/Type: Java binary trees implementing IntTree
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Author: Robert Baxter

Write a method countMultiples that could be added to the IntTree class from lecture and section. The method returns a count of the number of multiples of a particular value in the binary tree. Given a number n, a value m is considered a multiple of n if it can be expressed as (k * n) for some integer k. For example, suppose that an IntTree variable tree stores a reference to the following tree: 

               +---+
               | 6 |
           ___ +---+ ___
         /               \
     +---+               +---+
     | 2 |               | 9 |
     +---+               +---+
    /     \                   \
+---+     +---+               +---+
| 5 |     | 3 |               | 4 |
+---+     +---+               +---+
         /     \             /     \
     +---+     +---+     +---+     +---+
     | 8 |     | 6 |     | 7 |     | 0 |
     +---+     +---+     +---+     +---+

The table below shows various calls and the values they should return:

Call Value Returned Reason
tree.countMultiples(2); 6 six multiples of 2 : 6, 2, 8, 6, 4, 0
tree.countMultiples(4); 3 three multiples of 4 : 8, 4, 0
tree.countMultiples(3); 5 five multiples of 3 : 6, 3, 6, 9, 0
tree.countMultiples(1); 10 all ten values are multiples of 1

Your method should throw an IllegalArgumentException if passed the value 0.

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 the tree.

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

public class IntTree {
    private IntTreeNode overallRoot;
    ...
}
Type your solution here:


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.

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