Parallelograms | Topcoder Archive

Problem Statement

A parallelogram is a quadrilateral with two sets of parallel sides.

You are given three distinct points A(xA,yA), B(xB,yB) and C(xC,yC) in the plane.

Consider all non-degenerate parallelograms such that A, B, and C are three of its vertices. Your method should return the difference between the largest and the smallest possible perimeter of such a parallelogram. If there is no such parallelogram, return -1 instead.

Definition

Class:: Parallelograms
Method:: getDifference
Parameters:: int, int, int, int, int, int
Returns:: double
Method signature:: double getDifference(int xA, int yA, int xB, int yB, int xC, int yC)
(be sure your method is public)

Constraints

xA, yA, xB, yB, xC and yC will be between -5,000 and 5,000, inclusive.
A, B, and C will be three different points.

Examples

```
0
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```
0
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```
0
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1
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```
1
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```
0
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Returns: 0.8284271247461898
```
For this input there are three possible parallelograms, with the fourth vertex at (1,1), (1,-1), or (-1,1). In the first case, we get a 1 by 1 square with a perimeter of 4. In both the second and third cases, we get a parallelogram with side lengths 1 and sqrt(2), with a perimeter of approximately 4.828427.
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0
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```
0
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4
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```
0
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```
0
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```
3
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```
Returns: 4.0
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In this case the largest possible perimeter is 18 and the smallest possible perimeter is 14.
```
0
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```
0
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1
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```
0
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47
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```
0
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Returns: -1.0
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No parallelogram can have three vertices on the same line. Therefore, the answer for this test case is -1.
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1
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```
2
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```
3
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```
4
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```
8
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```
7
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```
Returns: 11.547796284592874
```
```
2
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-1
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```
-7
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```
2
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```
-1
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```
0
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```
Returns: -1.0
```
One more example of three points on the same line.

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