Circle and Lattice Points - GeeksforGeeks


Circle and Lattice Points - GeeksforGeeks
Given a circle of radius r in 2-D with origin or (0, 0) as center. The task is to find the total lattice points on circumference. Lattice Points are points with coordinates as integers in 2-D space.

To find lattice points, we basically need to find values of (x, y) which satisfy the equation x2 + y2 = r2.
int countLattice(int r)
{
    if (r <= 0)
        return 0;
 
    // Initialize result as 4 for (r, 0), (-r. 0),
    // (0, r) and (0, -r)
    int result = 4;
 
    // Check every value that can be potential x
    for (int x=1; x<r; x++)
    {
        // Find a potential y
        int ySquare = r*r - x*x;
        int y = sqrt(ySquare);
 
        // checking whether square root is an integer
        // or not. Count increments by 4 for four
        // different quadrant values
        if (y*y == ySquare)
            result += 4;
    }
 
    return result;
}
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