countingSquares.java

import java.io.*;
import java.util.StringTokenizer;

public class TaskA {
    private static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }
    }

    public static void main(String args[]) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        TaskA.InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        solve(in, out);
        out.close();
    }

    private static void solve(InputReader in, PrintWriter out) {
        double xc = in.nextDouble();
        double yc = in.nextDouble();
        double rc = in.nextDouble();
        int numSquares = countSquaresInCircle(xc, yc, rc);
        out.println(numSquares);
    }

    /**
    runtime complexity is : O(r*r)
    **/
    private static int countSquaresInCircle(double xc, double yc, double rc) {
        int answer = 0;

        long leftX = (long) (xc - rc);
        long topY = (long) (yc + rc);

        long bottomY = (long) (yc - rc);
        long rightX = (long) (xc + rc);

        for (long y = topY; y >= bottomY; y--) {
            for (long x = leftX; x <= rightX; x++) {
                if (isValidSquare(x, y, xc, yc, rc)) {
                    answer++;
                }
            }
        }
        return answer;
    }

    private static boolean isValidSquare(long bottomLeftX, long bottomLeftY, double centreX, double centreY, double radius) {

        double sqrtTwo = Math.sqrt(2);

        long sqX1 = bottomLeftX;
        long sqY1 = bottomLeftY;

        long sqX2 = bottomLeftX;
        long sqY2 = bottomLeftY + 1;

        long sqX3 = bottomLeftX + 1;
        long sqY3 = bottomLeftY;

        long sqX4 = (long) (bottomLeftX + sqrtTwo);
        long sqY4 = (long) (bottomLeftY + sqrtTwo);


        return Math.sqrt(Math.pow(centreX - sqX1, 2) + Math.pow(centreY - sqY1, 2)) <= radius
                && Math.sqrt(Math.pow(centreX - sqX2, 2) + Math.pow(centreY - sqY2, 2)) <= radius
                && Math.sqrt(Math.pow(centreX - sqX3, 2) + Math.pow(centreY - sqY3, 2)) <= radius
                && Math.sqrt(Math.pow(centreX - sqX4, 2) + Math.pow(centreY - sqY4, 2)) <= radius;
    }
}