Symmetry | Topcoder Archive

Problem Statement

A line of symmetry is a line through the cartesian plane such that if you reflect everything from one side of the line to the other, you still have the same image. For example, if the x-axis is a line of symmetry, it means that for every point (x,y) there is also a point (x,-y).

Your task is, given a list of points, determine how many such lines exist.

Definition

Class:: Symmetry
Method:: countLines
Parameters:: String[]
Returns:: int
Method signature:: int countLines(String[] points)
(be sure your method is public)

Constraints

Each element of points will be formatted as a list of x,y pairs "<x1> <y1> <x2> <y2> <x3> <y3> ...", where there is exactly one space between every two terms, and both <xi> and <yi> are integers.
<xi> and <yi> will both be between -10,000 and 10,000, inclusive.
Each point will be unique.
There will be between 2 and 200 points, inclusive.

Examples

```
{"1 1 1 -1 -1 1 -1 -1"}
```
```
Returns: 4
```
This looks something like this (where '-' and '|' represent the axes, and '*' represents a point): | | * | * | --------+-------- | * | * | | There are 4 lines of symmetry. Both axes are lines of symmetry, as are the line y = x and y = -x.
```
{"0 0 2 1 0 5 -2 4"}
```
```
Returns: 2
```

{"0 100 100 0","0 0 100 100","51 52"}

Returns: 0

```
{"0 0","100 0","50 87"}
```
```
Returns: 1
```

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