TemperatureScales | Topcoder Archive

Problem Statement

Due to historical reasons people measure temperature in different scales, such as Fahrenheit and Celsius. Your task is to convert a temperature from one scale to another. It is known that both scales are linear with respect to each other (i.e., there are real numbers a and b such that temperature t presented in the first scale can be converted to the second by the law t'=a*t+b).

You are given 5 ints: f1, the freezing point of water in the first scale; b1, the boiling point of water in the first scale; f2, the freezing point of water in the second scale; b2, the boiling point of water in the second scale; and t, the temperature in the first scale. Return t converted into the second scale.

Definition

Class:: TemperatureScales
Method:: convert
Parameters:: int, int, int, int, int
Returns:: double
Method signature:: double convert(int f1, int b1, int f2, int b2, int t)
(be sure your method is public)

Notes

The return value must be within 1e-9 absolute or relative error of the actual result.
Because the boiling and the freezing points of water depend on the atmospheric pressure, you may assume that both the scales are under the same circumstances.

Constraints

f1,b1,f2,b2 and t will each be between -1000 and 1000, inclusive.
f1 will be less than b1.
f2 will be less than b2.

Examples

```
0
```
```
100
```
```
0
```
```
100
```
```
28
```
```
Returns: 28.0
```
These are two identical scales, so temperatures in both of them coincide.
```
0
```
```
100
```
```
1
```
```
101
```
```
28
```
```
Returns: 29.0
```
The second scale is shifted up 1 degree relative to the first scale.

-1000

-999

-1000

Returns: 3999000.0

```
-10
```
```
0
```
```
1
```
```
2
```
```
17
```
```
Returns: 3.7
```

-123

Returns: -114.66666666666667

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