PointsInAPlane | Topcoder Archive

Problem Statement

You are given a collection of points in the plane, with x[i] and y[i] representing the i-th point. Return the number of triangles that can be formed using three of the points as vertices.

Definition

Class:: PointsInAPlane
Method:: howManyTriangles
Parameters:: int[], int[]
Returns:: int
Method signature:: int howManyTriangles(int[] x, int[] y)
(be sure your method is public)

Notes

Three points can only form a triangle if they are not colinear.

Constraints

x will contain between 1 and 50 elements, inclusive.
y will contain the same number of elements as x.
Each element of x will be between -1,000,000,000 and 1,000,000,000, inclusive.
Each element of y will be between -1,000,000,000 and 1,000,000,000, inclusive.
No two points will be at the same position.

Examples

```
{0, 1, 2}
```
```
{0, 1, 0}
```
```
Returns: 1
```
These three points for a triangle.
```
{0, 1, 2}
```
```
{0, 0, 0}
```
```
Returns: 0
```
These three points sit along the x-axis, and are all collinear.
```
{0, 1, 2, 3}
```
```
{0, 2, 1, 3}
```
```
Returns: 4
```
Pick any three points, and they form a triangle.
```
{0, 1, 2, 1}
```
```
{0, 0, 0, 1}
```
```
Returns: 3
```

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