CarrotField | Topcoder Archive

Problem Statement

We have a rectangular field with corners in points (0,0), (0,H), (W, H), and (W, 0). There is a carrot in every point with integer coordinates that lies inside or on the boundary of the field. Thus, there are exactly (H+1)*(W+1) carrots.

Someone is going to drop a bomb onto this field. The point where the bomb lands will be chosen uniformly at random from all points that lie inside or on the boundary of the field (including points with non-integer coordinates). When the bomb lands, it explodes and destroys all carrots that are within Euclidean distance R from the point of explosion.

You are given the ints H, W, and R. Return the expected number of destroyed carrots.

Definition

Class:: CarrotField
Method:: expectedValue
Parameters:: int, int, int
Returns:: double
Method signature:: double expectedValue(int H, int W, int R)
(be sure your method is public)

Notes

Your return value must have absolute or relative error smaller than 1e-7.

Constraints

H, W, and R will be between 1 and 100,000, inclusive.

Examples

```
1
```
```
1
```
```
1
```
```
Returns: 3.141592653589793
```
The field is a 1x1 square with a carrot in each corner. Sometimes the bomb will destroy three of the four carrots. Other times (when it drops somewhere around the center of the square) it will destroy all four of them. Thus, the expected number of destroyed carrots must be somewhere between 3 and 4. The exact value happens to be pi = 3.14159...
```
20
```
```
22
```
```
25
```
```
Returns: 481.5403826061094
```
```
5
```
```
50
```
```
8
```
```
Returns: 85.87765067992017
```
```
100
```
```
100
```
```
999
```
```
Returns: 10201.0
```
Regardless of where the bomb drops, the radius of its explosion is so large that it will destroy all the carrots.
```
1
```
```
1
```
```
100000
```
```
Returns: 4.0
```

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