Pillars | Topcoder Archive

Problem Statement

On a horizontal line, there are two vertical pillars. The distance between their bottoms is w. The height of the first pillar is an integer, chosen uniformly at random in the range 1 through x, inclusive. The height of the second pillar is an integer, chosen uniformly at random in the range 1 through y, inclusive. The tops of both pillars will be connected by a straight piece of rope.

You are given the ints w, x, and y. Compute and return the expected length of the rope.

Definition

Class:: Pillars
Method:: getExpectedLength
Parameters:: int, int, int
Returns:: double
Method signature:: double getExpectedLength(int w, int x, int y)
(be sure your method is public)

Notes

Your return value must have a relative or an absolute error of less than 1e-9.
In this task, the expected rope length can be computed as the average rope length over all possible cases.

Constraints

w will be between 1 and 1000, inclusive.
x will be between 1 and 100,000, inclusive.
y will be between 1 and 100,000, inclusive.

Examples

```
1
```
```
1
```
```
1
```
```
Returns: 1.0
```
The rope always has a length of 1.
```
1
```
```
5
```
```
1
```
```
Returns: 2.387132965131785
```
There are 5 possible (equiprobable) cases in which the length of the rope is 1, sqrt(2), sqrt(5), sqrt(10) and sqrt(17). The correct answer is the arithmetic average of these 5 numbers.
```
2
```
```
3
```
```
15
```
```
Returns: 6.737191281760445
```
```
10
```
```
15
```
```
23
```
```
Returns: 12.988608956320535
```

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