Polyline | Topcoder Archive

Problem Statement

A "Polyline" is a continuous line composed of one or more line segments. In a rectangle defined by four points (0,0), (a, 0), (a, b), and (0, b), we can draw a polyline starting from the point (x0, y0) to the end point (x1, y1) with at least one intersection point with each of the four edges of the rectangle. Write a class Polyline with a method length that returns the shortest length of such a polyline.

Definition

Class:: Polyline
Method:: length
Parameters:: int, int, int, int, int, int
Returns:: double
Method signature:: double length(int a, int b, int x0, int y0, int x1, int y1)
(be sure your method is public)

Notes

The polyline must not exceed the boundaries of the given rectangle.
The starting point and ending point may overlap.
Your return value must have an absolute or relative error less than 1e-9.

Constraints

a and b will be between 2 and 200 inclusive.
x0 and x1 will be between 1 and (a-1) inclusive.
y0 and y1 will be between 1 and (b-1) inclusive.

Examples

```
4
```
```
3
```
```
1
```
```
1
```
```
3
```
```
2
```
```
Returns: 7.810249675906654
```
```
4
```
```
3
```
```
1
```
```
1
```
```
2
```
```
2
```
```
Returns: 8.602325267042627
```
```
4
```
```
3
```
```
1
```
```
1
```
```
1
```
```
2
```
```
Returns: 9.433981132056603
```
```
50
```
```
70
```
```
20
```
```
40
```
```
20
```
```
40
```
```
Returns: 172.04650534085255
```

Returns: 299.9549966244937

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