MixingLiquids | Topcoder Archive

Problem Statement

In Chemistry, there's a different meaning to the word 'solution' than in programming. When we mix x liters of some substance with (100-x) liters of water, we get 100 liters of x-% solution of that substance.

You are given several bottles containing solutions of the same substance. The i-th bottle contains amount[i] liters of percent[i]-% solution. Return the maximal number of liters of need-% solution we can get by pouring together some of these bottles (possibly partially, see example 0).

Definition

Class:: MixingLiquids
Method:: howMuch
Parameters:: int[], int[], int
Returns:: double
Method signature:: double howMuch(int[] percent, int[] amount, int need)
(be sure your method is public)

Notes

The returned value must have an absolute or relative error less than 1e-9.

Constraints

percent will contain between 1 and 50 elements, inclusive.
Each element of percent will be between 0 and 100, inclusive.
amount will contain the same number of elements as percent.
Each element of amount will be between 1 and 1000, inclusive.
need will be between 0 and 100, inclusive.

Examples

```
{0, 100}
```
```
{20, 30}
```
```
50
```
```
Returns: 40.0
```
We have 20 liters of water and 30 liters of pure substance. We need a 50% solution, so we combine all the water with 20 liters of substance.
```
{0, 100}
```
```
{20, 30}
```
```
60
```
```
Returns: 50.0
```
We can use everything we have.
```
{90, 70, 80}
```
```
{10, 10, 10}
```
```
50
```
```
Returns: 0.0
```
All our bottles contain too much substance.

{30, 80, 60}

{40, 10, 15}

Returns: 35.18518518518519

{50,50,50}

{395,971,964}

Returns: 2330.0

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