TCHS-3-1000

Problem Statement
	A decomposition of a non-negative integer n is a list of non-negative integers that sum to exactly n. The product of a decomposition is the product of all its members. For example, if n = 4, the following decompositions are possible: 4 = 1+1+1+1, product is 1*1*1*1 = 1. 4 = 1+1+2, product is 1*1*2 = 2. 4 = 1+3, product is 1*3 = 3. 4 = 2+2, product is 2*2 = 4. 4 = 4, product is 4. Given an int n, determine the decomposition of n with the maximal product, and return that product modulo 10007. In the example above, the maximal product is 4 (the product of the decomposition 2 + 2).
Definition
	Class: BestDecomposition Method: maxProduct Parameters: int Returns: int Method signature: int maxProduct(int n) (be sure your method is public)
Constraints
-	n will be between 0 and 10000, inclusive.
Examples
0)
	0 Returns: 0
1)
	1 Returns: 1
2)
	5 Returns: 6 5 = 2 + 3, 2 * 3 = 6
3)
	7 Returns: 12 7 = 3 + 4, 3 * 4 = 12
4)
	9931 Returns: 4664

public class BestDecomposition {

	public int maxProduct(int n) {
		int p = n < 3 ? n : new int[]{3, 4, 6}[n%3];
		for (int i = 1; i < n / 3; i++)
			p = p * 3 % 10007;
		return p;
	}
	
}