PackingBallsDiv2.txt

PROBLEM STATEMENT
We have R red, G green, and B blue balls.
We want to divide them into as few packages as possible.
Each package must contain 1, 2, or 3 balls.
Additionally, each package must be either a "normal set" (all balls in the package have the same color), or a "variety set" (no two balls have the same color).
Compute and return the smallest possible number of packages.

DEFINITION
Class:PackingBallsDiv2
Method:minPacks
Parameters:int, int, int
Returns:int
Method signature:int minPacks(int R, int G, int B)


CONSTRAINTS
-R, G, and B will each be between 1 and 100, inclusive.


EXAMPLES

0)
4
2
4

Returns: 4

We have 4 red, 2 green, and 4 blue balls.
Clearly, we need at least four packages to store 10 balls.
One possibility of using exactly four packages looks as follows: RGB, RG, RR, BBB.
(I.e., the first package has 1 ball of each color, the second package has a red and a green ball, and so on.)

1)
1
7
1

Returns: 3

Here the only possible solution is to have one package with RGB and two packages with GGG each.

2)
2
3
5

Returns: 4



3)
78
53
64

Returns: 66



4)
100
100
100

Returns: 100