Perimeter | Topcoder Archive

Problem Statement

We must cover the perimeter of a rectangular area with n sensors. The sensors are identical, and each sensor covers a circular area. The sensors may be placed anywhere.

The rectangle has width w and height h. Given n, w, and h, determine the minimum sensor radius that will allow us to cover the rectangle's perimeter.

Definition

Class:: Perimeter
Method:: minRadius
Parameters:: int, int, int
Returns:: double
Method signature:: double minRadius(int n, int w, int h)
(be sure your method is public)

Notes

A return value with either an absolute or relative error of less than 1.0E-9 is considered correct.

Constraints

n will be between 1 and 5, inclusive.
w and h will each be between 1 and 1000, inclusive.

Examples

```
5
```
```
1
```
```
1000
```
```
Returns: 100.00124999218755
```
The best sensor placement is evenly spaced along the long central axis.
```
1
```
```
100
```
```
100
```
```
Returns: 70.71067811865473
```
Put the sensor at the center of the rectangle, so the answer is 50*sqrt(2).
```
4
```
```
100
```
```
100
```
```
Returns: 35.355339059327335
```
Divide the rectangle in quarters and place each sensor in the middle of one of the quarters. The return value is 25*sqrt(2).
```
5
```
```
622
```
```
531
```
```
Returns: 182.23311960891868
```

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