Flee | Topcoder Archive

Problem Statement

You are a point in the plane. You start at the coordinates (0, 0) and you want to flee far away, to the coordinates (10^100, 0). Your path can be any continuous curve.

You are given int[]s x and y. For each valid i, there is a guard standing on the point with coordinates (x[i], y[i]). The guards do not move. You want to avoid the guards as much as possible.

Formally, for any point P in the plane, we define its safety level S(P) as the distance to the closest guard. The safety level of a path is the minimum safety level of a point on the path. Find a path with the largest possible safety level and return its safety level.

Definition

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

Notes

Your return value must have an absolute or a relative error smaller than 1e-9.

Constraints

x will contain between 1 and 3 elements, inclusive.
x and y will contain the same number of elements.
Each element in x and y will be between -1,000 and 1,000, inclusive.

Examples

```
{1,1,-7}
```
```
{5,-5,0}
```
```
Returns: 5.0
```
You can go from (0, 0) to (10^100, 0) directly. The safety level of this path is 5, because when you are at (1, 0) the distance to the closest guard is 5.
```
{1,1}
```
```
{-5,-5}
```
```
Returns: 5.0990195135927845
```
One optimal path is the following polyline: (0, 0) -- (-100, 0) -- (-100, -10000) -- (10^100, 0).

{1,1,-8}

{5,-5,0}

Returns: 5.0990195135927845

{232,312,-432}

{498,-374,24}

Returns: 432.6661530556787

```
{0}
```
```
{0}
```
```
Returns: 0.0
```
Each valid path starts in the point (0, 0). This point contains a guard and therefore its safety level is 0. Hence, the safety level of any valid path will be 0.

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