RedAndBluePoints | Topcoder Archive

Problem Statement

Fox Ciel likes blue points and hates red points.
There are some blue points and some red points in a two-dimensional plane. Ciel wants to draw a convex polygon. The polygon must not contain any red points. On the other hand, it should contain as many blue points as possible. A point on the boundary of a polygon counts as being contained in the polygon. The polygon is allowed to be degenerated: a point and a single line segment do also count as polygons.
You are given four int[]s: blueX, blueY, redX and redY. For each valid i, there is a blue point with coordinates blueX[i] and blueY[i]. The red points are described in the same way by redX and redY.
Return the largest number of blue points a valid polygon may contain.

Definition

Class:: RedAndBluePoints
Method:: find
Parameters:: int[], int[], int[], int[]
Returns:: int
Method signature:: int find(int[] blueX, int[] blueY, int[] redX, int[] redY)
(be sure your method is public)

Constraints

Both blueX and blueY will contain B elements.
Both redX and redY will contain R elements.
Both B and R will be between 1 and 50.
Each element of blueX, blueY, redX and redY will be between 0 and 1000.
No two points will be in the same exact position.
No three points will lie on the same line.

Examples

```
{0,0,10,10}
```
```
{0,10,0,10}
```
```
{100}
```
```
{120}
```
```
Returns: 4
```
There's a square of blue points, and the only red point is outside the square, so the answer is 4.
```
{0,0,10,10}
```
```
{0,10,0,10}
```
```
{3}
```
```
{4}
```
```
Returns: 3
```
In this case, we have one red point inside the square so we can't use the four blue points, we're only allowed to use 3 of them, that may be for example (0,10), (10,0) and (10,10) to form a triangle.

{0,0,10,10}

{0,10,0,10}

{3,6}

{2,7}

Returns: 2

```
{0}
```
```
{0}
```
```
{1}
```
```
{1}
```
```
Returns: 1
```
```
{5, 6, 6}
```
```
{9, 0, 5}
```
```
{7}
```
```
{6}
```
```
Returns: 3
```

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