PackingBallsDiv2 | Topcoder Archive

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)
(be sure your method is public)

Constraints

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

Examples

```
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
```
```
7
```
```
1
```
```
Returns: 3
```
Here the only possible solution is to have one package with RGB and two packages with GGG each.
```
2
```
```
3
```
```
5
```
```
Returns: 4
```
```
78
```
```
53
```
```
64
```
```
Returns: 66
```
```
100
```
```
100
```
```
100
```
```
Returns: 100
```

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