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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