Problem:
Problem D: Circle and Points

You are given N points in the xy-plane. You have a
circle of radius one and move it on the xy-plane, so as to
enclose as many of the points as possible. Find how many points can be
simultaneously enclosed at the maximum. A point is considered
enclosed by a circle when it is inside or on the circle.

Fig 1. Circle and Points

Input

The input consists of a series of data sets, followed by a single line
only containing a single character '0', which indicates the end of the
input. Each data set begins with a line containing an integer N,
which indicates the number of points in the data set. It is
followed by N lines describing the coordinates of the
points. Each of the N lines has two decimal fractions X
and Y, describing the x- and y-coordinates of a
point, respectively. They are given with five digits after the decimal
point.

You may assume 1 <= N <= 300, 0.0 <= X <= 10.0, and 0.0
<= Y <= 10.0. No two points are closer than 0.0001. No two
points in a data set are approximately at a distance of 2.0. More
precisely, for any two points in a data set, the distance d
between the two never satisfies 1.9999 <= d <= 2.0001. Finally,
no three points in a data set are simultaneously very close to a
single circle of radius one. More precisely,
let P1, P2, and P3 be any three points in a
data set, and d1, d2, and d3
the distances from an arbitrarily selected point in the xy-plane to each of them
respectively. Then it never simultaneously holds that 0.9999 <=
di <= 1.0001 (i = 1, 2, 3).

Output

For each data set, print a single line containing the maximum number
of points in the data set that can be simultaneously enclosed by a
circle of radius one. No other characters including leading and
trailing spaces should be printed.

Sample Input

3
6.47634 7.69628
5.16828 4.79915
6.69533 6.20378
6
7.15296 4.08328
6.50827 2.69466
5.91219 3.86661
5.29853 4.16097
6.10838 3.46039
6.34060 2.41599
8
7.90650 4.01746
4.10998 4.18354
4.67289 4.01887
6.33885 4.28388
4.98106 3.82728
5.12379 5.16473
7.84664 4.67693
4.02776 3.87990
20
6.65128 5.47490
6.42743 6.26189
6.35864 4.61611
6.59020 4.54228
4.43967 5.70059
4.38226 5.70536
5.50755 6.18163
7.41971 6.13668
6.71936 3.04496
5.61832 4.23857
5.99424 4.29328
5.60961 4.32998
6.82242 5.79683
5.44693 3.82724
6.70906 3.65736
7.89087 5.68000
6.23300 4.59530
5.92401 4.92329
6.24168 3.81389
6.22671 3.62210
0

Output for the Sample Input

2
5
5
11

Solution in JAVA (judge verdict: Accepted)


import java.io.IOException;
import java.util.HashMap;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.Scanner;

public class Main {
	
	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		
		
		while(true){
			final int n = sc.nextInt();
			
			if(n == 0){
				break;
			}
			
			Point2D[] points = new Point2D[n];
			
			for(int i = 0; i < n; i++){
				points[i] = new Point2D(sc.nextDouble(), sc.nextDouble());
			}
			
			int max = 1;
			
			for(int fst = 0; fst < n; fst++){
				for(int snd = 0; snd < n; snd++){
					Point2D[] cross = Point2D.cross_ss(points[fst], 1, points[snd], 1);
					
					for(Point2D cross_c : cross){
						int count = 0;
						
						for(int i = 0; i < n; i++){
							if(cross_c.dist(points[i]) < 1.0 + Point2D.EPS){
								count++;
							}
						}
						
						max = Math.max(max, count);
					}
				}
			}
			
			System.out.println(max);
		}
		
	}
}

class Point2D {
    public double x;
    public double y;
 
    public static final double EPS = 1e-6;
 
    public Point2D(double x, double y) {
        this.x = x;
        this.y = y;
    }
 
    public Point2D(Point2D point) {
        this.x = point.x;
        this.y = point.y;
    }
 
    public String toString() {
        return x + "," + y;
    }
 
    @Override
    public boolean equals(Object o) {
        if (o instanceof Point2D) {
            Point2D another = (Point2D) o;
            if (this.x - EPS < another.x && this.x + EPS > another.x
                    && this.y - EPS < another.y && this.y + EPS > another.y) {
                return true;
            }
             
            return false;
 
            // return this.x == another.x && this.y == another.y;
        }
        return false;
    }
 
    public Point2D add(double x, double y) {
        return new Point2D(this.x + x, this.y + y);
    }
 
    public Point2D sub(double x, double y) {
        return add(-x, -y);
    }
 
    public Point2D add(Point2D another) {
        return add(another.x, another.y);
    }
 
    public Point2D sub(Point2D another) {
        return sub(another.x, another.y);
    }
 
    public Point2D mul(double d) {
        return new Point2D(this.x * d, this.y * d);
    }
 
    public Point2D div(double d) {
        return new Point2D(this.x / d, this.y / d);
    }
 
    public double dot(double x, double y) {
        return this.x * x + this.y * y;
    }
 
    public double dot(Point2D another) {
        return dot(another.x, another.y);
    }
 
    public double cross(double x, double y) {
        return this.x * y - this.y * x;
    }
 
    public double cross(Point2D another) {
        return cross(another.x, another.y);
    }
 
    public double dist(double x, double y) {
        return Math.sqrt((this.x - x) * (this.x - x) + (this.y - y)
                * (this.y - y));
    }
 
    public double dist(Point2D another) {
        return dist(another.x, another.y);
    }
 
    public double dist_o() {
        return dist(0, 0);
    }
 
    public Point2D unit() {
        return div(dist_o());
    }
 
    public boolean pol(Point2D start, Point2D end) {
        return end.sub(start).cross(this.sub(start)) < EPS;
    }
 
    public boolean pos(Point2D start, Point2D end) {
        return (start.dist(this) + this.dist(end) < start.dist(end) + EPS);
    }
 
    public double pld(Point2D start, Point2D end) {
        return Math.abs((end.sub(start).cross(this.sub(start)))
                / end.sub(start).dist_o());
    }
 
    public double psd(Point2D start, Point2D end) {
        if (end.sub(start).dot(this.sub(start)) < EPS) {
            return this.dist(start);
        } else if (start.sub(end).dot(this.sub(end)) < EPS) {
            return this.dist(end);
        } else {
            return end.sub(start).cross(this.sub(start)) / end.dist(start);
        }
    }
 
    public static boolean intersect_s(Point2D a1, Point2D a2, Point2D b1,
            Point2D b2) {
        return (a2.sub(a1).cross(b1.sub(a1)) * a2.sub(a1).cross(b2.sub(a1)) < EPS)
                && (b2.sub(b1).cross(a1.sub(b1)) * b2.sub(b1).cross(a2.sub(b1)) < EPS);
    }
 
    public static boolean insersect_l(Point2D a1, Point2D a2, Point2D b1,
            Point2D b2) {
        return a1.sub(a2).cross(b1.sub(b2)) < EPS;
    }
 
    public static Point2D interpoint_s(Point2D a1, Point2D a2, Point2D b1,
            Point2D b2) {
        Point2D b = b2.sub(b1);
        double d1 = Math.abs(b.cross(a1.sub(b1)));
        double d2 = Math.abs(b.cross(a2.sub(b1)));
        double t = d1 / (d1 + d2);
        Point2D a = a2.sub(a1), v = a.mul(t);
        return a1.add(v);
    }
 
    public static Point2D interpoint_l(Point2D a1, Point2D a2, Point2D b1,
            Point2D b2) {
        Point2D a = a2.sub(a1);
        Point2D b = b2.sub(b1);
        double t = b.cross(b1.sub(a1)) / b.cross(a);
        Point2D v = a.mul(t);
        return a1.add(v);
    }
 
    public static Point2D[] cross_ss(Point2D p1, double r1, Point2D p2,
            double r2) {
        double dis = p1.dist(p2);
 
        if (r1 + EPS > r2 && r1 - EPS < r2 && dis < EPS) {
            return new Point2D[0]; // same
        }
 
        if (dis - EPS < r1 + r2 && dis + EPS > r1 + r2) {
            Point2D tmp = p2.sub(p1);
            tmp = tmp.mul(r1 / tmp.dist_o());
            Point2D ret[] = new Point2D[1];
            ret[0] = p1.add(tmp);
            return ret;
        } else if (dis + EPS > r1 + r2) {
            return new Point2D[0]; // out
        }
 
        double dis_m = Math.abs(r1 - r2);
 
        if (dis_m + EPS > dis && dis_m - EPS < dis) {
            Point2D tmp = null;
            if (r1 > r2) {
                tmp = p2.sub(p1);
            } else {
                tmp = p1.sub(p2);
            }
 
            double min = Math.min(r1, r2);
 
            tmp = tmp.mul((min + tmp.dist_o()) / tmp.dist_o());
 
            Point2D ret[] = new Point2D[1];
            ret[0] = p1.add(tmp);
            return ret;
        } else if (dis_m + EPS > dis) {
            return new Point2D[0]; // inner
        } else {
            Point2D ret[] = new Point2D[2];
 
            double theta = Math.acos((dis * dis + r1 * r1 - r2 * r2)
                    / (2 * dis * r1));
            double a = Math.atan2(p2.y - p1.y, p2.x - p1.x);
 
            ret[0] = new Point2D(r1 * Math.cos(a + theta) + p1.x, r1
                    * Math.sin(a + theta) + p1.y);
            ret[1] = new Point2D(r1 * Math.cos(a - theta) + p1.x, r1
                    * Math.sin(a - theta) + p1.y);
            return ret;
        }
    }
 
    public void interpoint_lc(Point2D start, Point2D end, Point2D c, double r,
            Point2D ans[]) {
        if (c.pld(start, end) > r + EPS)
            return;
        Point2D v = end.sub(start).unit();
        double delta = v.dot(start.sub(c)) * v.dot(start.sub(c))
                - start.dist(c) * start.dist(c) + r * r;
        double t = -v.dot(start.sub(c));
        double s = Math.sqrt(delta);
        ans[0] = start.add(v.mul(t + s));
        ans[1] = start.add(v.mul(t + s));
    }
 
    public Point2D normal_vector(Point2D p, Point2D a, Point2D b) {
        Point2D v = b.sub(a).unit();
        v = v.cross(p.sub(a)) > 0 ? new Point2D(v.y, (-1) * v.x) : new Point2D(
                (-1) * v.y, v.x);
        return v.mul(p.pld(a, b));
    }
 
    public double area(Point2D a, Point2D b, Point2D c) {
        return Math.abs((c.sub(a).cross(b.sub(a))) * 0.5);
    }
 
}