B

Assume the coasting is an infinite straight line. Land is in one side of coasting, sea in the other. Each small island is a point locating in the sea side. And any radar installation, locating on the coasting, can only cover d distance, so an island in the sea can be covered by a radius installation, if the distance between them is at most d.

We use Cartesian coordinate system, defining the coasting is the x-axis. The sea side is above x-axis, and the land side below. Given the position of each island in the sea, and given the distance of the coverage of the radar installation, your task is to write a program to find the minimal number of radar installations to cover all the islands. Note that the position of an island is represented by its x-y coordinates.

Figure A Sample Input of Radar Installations

Input
The input consists of several test cases. The first line of each case contains two integers n (1<=n<=1000) and d, where n is the number of islands in the sea and d is the distance of coverage of the radar installation. This is followed by n lines each containing two integers representing the coordinate of the position of each island. Then a blank line follows to separate the cases.

The input is terminated by a line containing pair of zeros
Output
For each test case output one line consisting of the test case number followed by the minimal number of radar installations needed. “-1” installation means no solution for that case.
Sample Input
3 2
1 2
-3 1
2 1

1 2
0 2

0 0
Sample Output
Case 1: 2
Case 2: 1

import java.util.ArrayList;import java.util.Arrays;import java.util.Comparator;import java.util.Scanner;/** * Created by 95112 on 11/12/2017. */public class RadarInstallation {    public static void main(String[] args)    {        ArrayList<String> answers = new ArrayList<String>();        int times =1;        Scanner scanner = new Scanner(System.in);        int n,d;        do {            n = scanner.nextInt();            d = scanner.nextInt();            if (n==0 && d== 0)                break;            Island[] islands = new Island[n];            int maxHeigh = 0;             for (int i =0; i < n; i++)            {                int x ,y;                x = scanner.nextInt();                y = scanner.nextInt();                if (maxHeigh<y)                    maxHeigh = y;                double dValue = Math.sqrt(d*d - y *y);                islands[i] = new Island(x - dValue,x + dValue);            }            if (maxHeigh > d)            {                answers.add("Case "+times+": -1");                times++;                continue;            }            Arrays.sort(islands, new Comparator<Island>() {                @Override                public int compare(Island o1, Island o2) {                    if (o1.left < o2.left)                        return  -1;                    else                        return 1;                }            });             int count = 0;             double end = -999999999999999999999999.0;             for (int i =0 ; i< n; i++){                 if (islands[i].left <= end){                     if (islands[i].right < end)                         end = islands[i].right;                 }else {                     count++;                     end = islands[i].right;                 }             }            answers.add("Case "+times+": "+count);            times++;        }while (true);        for (String answer : answers){            System.out.println(answer);        }    }}class Island{    double left;    double right;    public Island(double x,double y)    {        left = x;        right = y;    }}