Radar Installation
Time Limit: 1000MS   Memory Limit: 10000K
Total Submissions: 96177   Accepted: 21378

Description

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

Source

Beijing 2002

可将点的坐标转为在x轴上对应的位置，然后根据右端对应的值进行排序判断。

#include<cstdio>
#include<algorithm>
#include<cmath>
using namespace std;
struct pos
{
	double left,right;
};
bool flag;
bool compare(pos a, pos b)
{
	return a.right < b.right;
}
int main()
{
	int n;
	double d;
	int m = 1;
	pos a[1005];
	while (~scanf("%d %lf", &n, &d))
	{
		if (!n || !d)
		{
			break;
		}
		int sum = 1;
		flag = true;
		double x, y;
		for (int i = 0; i<n; i++)
		{
			scanf("%lf %lf", &x, &y);
			if (!flag)
			{
				continue;
			}
			if (y > d)
			{
				flag = false;
				continue;
			}
			a[i].left = x - sqrt(d*d - y*y);
			a[i].right = x + sqrt(d*d - y*y);
		}
		
		if (!flag)
		{
			printf("Case %d: -1\n",m);
			m++;
			continue;
		}
		sort(a, a + n,compare);
		double temp = a[0].right;
		for (int i = 1; i < n; i++)
		{
			if (temp<a[i].left)
			{
				sum++;
				temp = a[i].right;
			}
		}
		printf("Case %d: %d\n", m,sum);
		m++;
	}
	return 0;
}