FallingPoints | Topcoder Archive

Problem Statement

You are given a int[] X containing the x-coordinates of several points. Each point starts at an infinitely high y-coordinate. Starting with the first point, each point falls down until it is either a distance of R away from a previously fallen point or it reaches y = 0. Each point (after the first point) will start falling only when the previous one stops. Return a double[], where the i-th element is the final y-coordinate of the i-th point.

Definition

Class:: FallingPoints
Method:: getHeights
Parameters:: int[], int
Returns:: double[]
Method signature:: double[] getHeights(int[] X, int R)
(be sure your method is public)

Notes

Each element of your return value must have an absolute or relative error less than 1e-9.

Constraints

X will contain between 1 and 50 elements, inclusive.
All elements of X will be between 0 and 1,000, inclusive.
R will be between 1 and 1,000, inclusive.

Examples

```
{0}
```
```
10
```
```
Returns: {0.0 }
```
There is only one point and it will just fall down.
```
{1,100}
```
```
10
```
```
Returns: {0.0, 0.0 }
```
Both points will fall down.
```
{0,9}
```
```
10
```
```
Returns: {0.0, 4.358898943540674 }
```
The first point falls down. The second point stops at a distance of 10 away from the first point.

{0,9,19}

Returns: {0.0, 4.358898943540674, 4.358898943540674 }

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