ThePresents | Topcoder Archive

Problem Statement

Santa Claus has n small boxes, all of equal size, containing presents for the children. Each box is a A x A x A cube. Santa wants to pack all of the small boxes into a large rectangular box with dimensions length x width x height. Each small box must be placed inside the big box with its sides parallel to the sides of the big box.

Return the maximal possible value of A that will allow Santa Claus to fit all of the small boxes into the big one. Note that A is not necessarily an integer.

Definition

Class:: ThePresents
Method:: find
Parameters:: int, int, int, int
Returns:: double
Method signature:: double find(int n, int length, int width, int height)
(be sure your method is public)

Notes

The returned value must be accurate to within a relative or absolute value of 1E-9.

Constraints

n will be between 1 and 1,000,000,000, inclusive.
length, width and height will be between 1 and 1,000,000,000, inclusive.

Examples

```
2
```
```
2
```
```
2
```
```
2
```
```
Returns: 1.0
```
There's room for eight 1x1x1 presents in the big box. However, if the presents are larger than 1x1x1, there is only room for one at most.
```
1
```
```
12
```
```
47
```
```
5
```
```
Returns: 5.0
```
Just one present.
```
10
```
```
4
```
```
2
```
```
10
```
```
Returns: 2.0
```
There will be no free space left in the big box.
```
77
```
```
146
```
```
523
```
```
229
```
```
Returns: 52.300000000000004
```

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