GridPointsOnCircle | Topcoder Archive

Problem Statement

You will be given rSquare, the square of the radius of a circle. You are to return the number of lattice points (points with integer coordinates) that lie on the circumference of a circle with this radius centered at the origin of the (cartesian) coordinate system.

Definition

Class:: GridPointsOnCircle
Method:: countPoints
Parameters:: int
Returns:: int
Method signature:: int countPoints(int rSquare)
(be sure your method is public)

Constraints

rSquare will be between 1 and 2,000,000,000, inclusive.

Examples

```
1
```
```
Returns: 4
```
A circle with radius 1 centered at the origin goes through 4 lattice points: (1,0), (0,1), (-1,0) and (0,-1).
```
25
```
```
Returns: 12
```
A circle with radius 5 goes through the points (+/-3, +/-4), (+/-4, +/-3), (0, +/-5) and (+/-5, 0) (12 points).
```
3
```
```
Returns: 0
```
No lattice point is at distance sqrt(3) from the origin.
```
44
```
```
Returns: 0
```
```
50
```
```
Returns: 12
```

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