FountainOfLife | Topcoder Archive

Problem Statement

A Fountain of Life is a special fountain that produces the elixir of life at a constant speed of elixir liters per second. A dark mage managed to cast a Curse of Death on the Fountain so in addition to the elixir it now produces a deadly poison at a constant speed of poison liters per second. Both the poison and elixir are collected in an infinitely large pool around the Fountain and form a mixture. The mixture will become deadly once the percentage of poison in the mixture is at least 50%. Your task is to calculate the time at which the mixture will become deadly. At the beginning (0-th second) the pool contains pool liters of 100% elixir.

Your program must return a double, the time in seconds at which the mixture becomes deadly. If the mixture never becomes deadly, return -1.0.

Definition

Class:: FountainOfLife
Method:: elixirOfDeath
Parameters:: int, int, int
Returns:: double
Method signature:: double elixirOfDeath(int elixir, int poison, int pool)
(be sure your method is public)

Notes

The returned value must be accurate to within a relative or absolute value of 1E-9.

Constraints

elixir will be between 1 and 10000, inclusive.
poison will be between 1 and 10000, inclusive.
pool will be between 1 and 10000, inclusive.

Examples

```
1
```
```
2
```
```
2
```
```
Returns: 2.0
```
At t = 0s there are 2 liters of 100% elixir. At t = 1s there are 3 liters of elixir and 2 liters of poison for a total volume of 5 liters. 2 liters of poison is 40% of 5 liters so the mixture is still not deadly. At t = 2s there are 4 liters of elixir and 4 liters of poison for a total volume of 8 liters. 4 liters of poison is exactly 50% of the mixture so it is now deadly.
```
200
```
```
100
```
```
1
```
```
Returns: -1.0
```
With 200 liters of elixir per second and only 100 liters of poison per second, the mixture never becomes deadly.
```
9999
```
```
10000
```
```
10000
```
```
Returns: 10000.0
```
It might take a long time for the mixture to become deadly.
```
1
```
```
10000
```
```
1
```
```
Returns: 1.0001000100010001E-4
```
On the other hand, it might take a short time for the mixture to become deadly.
```
40
```
```
43
```
```
41
```
```
Returns: 13.666666666666666
```

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