CheckPolygon | Topcoder Archive

Problem Statement

A simple polygon is a polygon with the following properties:

the length of each side is positive
no two consecutive sides are parallel
no two non-consecutive sides share a common point

You are given two int[]s X and Y, each with N elements. Find out whether there is a simple polygon whose vertices (in the order in which they lie on its boundary) are the points (X[0], Y[0]), (X[1], Y[1]), ... (X[N-1], Y[N-1]).

If the given points are the vertices of a simple polygon, calculate its area A and return a String that contains the decimal representation of A with one digit after the decimal point. If the given points are not the vertices of a simple polygon, return the String "Not simple" (quotes for clarity).

Definition

Class:: CheckPolygon
Method:: check
Parameters:: int[], int[]
Returns:: String
Method signature:: String check(int[] X, int[] Y)
(be sure your method is public)

Notes

The correct return value is always uniquely defined by problem statement. In particular, if the points represent a valid polygon, its area is always a rational number with at most one decimal digit.

Constraints

X will contain between 3 and 50 elements, inclusive.
Each element of X will be between -1,000,000,000 and 1,000,000,000, inclusive.
X and Y will contain same number of elements.
Each element of Y will be between -1,000,000,000 and 1,000,000,000, inclusive.

Examples

```
{0,0,1}
```
```
{0,1,0}
```
```
Returns: "0.5"
```
These three points are the vertices of a small triangle.
```
{0,1,2,0,2}
```
```
{0,2,0,1,1}
```
```
Returns: "Not simple"
```
These points, in the given order, are not the vertices of a simple polygon. The closed polyline that passes through these five points intersets itself five times.
```
{0,1,2,1,0,1}
```
```
{0,0,1,2,2,1}
```
```
Returns: "2.0"
```
Note that you must return the string "2.0". The printed number must have exactly one decimal place, even if that digit is zero. The string "2" is not a correct answer.

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