ThreeTrees | Topcoder Archive

Problem Statement

You are looking to plant a new tree somewhere in your field, which 10 meters wide and 10 meters long. The must be planted at a location that is at least distance away from where any other tree is planted. You are given the location of any other trees in int[]s x and y, where (x[i], y[i]) indicates the location of the i-th tree.

Calculate the total area in which it would be safe to plant the new tree.

Definition

Class:: ThreeTrees
Method:: area
Parameters:: int[], int[], int
Returns:: double
Method signature:: double area(int[] x, int[] y, int distance)
(be sure your method is public)

Notes

Your return value must be within 1e-6 absolute or relative error to be considered correct.

Constraints

x will have between 0 and 3 elements, inclusive.
x and y will have the same number of elements.
Each element of x will be between 0 and 10, inclusive.
Each element of y will be between 0 and 10, inclusive.
distance will be between 0 and 20, inclusive.

Examples

```
{5}
```
```
{5}
```
```
5
```
```
Returns: 21.460183689207042
```
There's a circle of radius 5, centered right in the center of the field, in which we cannot plant the tree. Thus our answer is 100 - pi * 5^2.
```
{2, 8}
```
```
{2, 8}
```
```
2
```
```
Returns: 74.86725878970901
```
Here, there's two circles of radius two that are not available, so we calculate 100 - 2 * pi * 2^2.
```
{0, 1, 5}
```
```
{0, 0, 3}
```
```
6
```
```
Returns: 17.95288785134835
```
Three trees, and whole lot of area that isn't suitable.
```
{0}
```
```
{0}
```
```
20
```
```
Returns: 0.0
```
In a 10x10 field with even a single tree already planted, there's nowhere to put another without being too close to the existing tree.

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