Radar installation (Greedy)

Radar installation

Time limit:1000 ms		Memory limit:10000 K
Total submissions:54295		Accepted:12208

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 abve 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 21 2-3 12 11 20 20 0
Sample Output
Case 1: 2Case 2: 1
题意：有一个坐标轴，在x轴的上方时海，下方是陆地，x轴为海岸线，海上有n个小岛，因为种种原因要在海岸线上装雷达，每个雷达的覆盖范围是以r为半径的圆，请用最少的雷达数覆盖所有的小岛，当无法完全覆盖时输出-1；
思路：典型的贪心思想。以小岛为圆心以r为半径做园，计算出圆与x轴的左交点和右交点。左交点为x-sqrt（r*r-y*y），右交点为x+sqrt（r*r+y*y）；然后对左交点从小到大排序，令初始雷达为最小岛屿的右交点，如果i点的左交点在雷达的右面，则需要重新装一个雷达，然后令当前点为新雷达的右交点，否则如果i点的右交点在当前雷达的左边，则把当前雷达的位置更新为该点的右交点。
#include <stdio.h>#include <math.h>#include <string.h>#include <stdlib.h>#include <algorithm>using namespace std;struct node{    double l,r;}point[1010];int cmp(struct node a,struct node b)//对左交点进行排序；{    return a.l<b.l;}int main(){    int n,r,i;    double x,y,t;//用t来储存当前雷达的位置    int cnt=1;    while(~scanf("%d %d",&n,&r))    {        if(n==0&&r==0)            break;        int ans=1;//记录安装雷达的个数        for(i=0;i<n;i++)        {            scanf("%lf %lf",&x,&y);            point[i].l=x-sqrt(r*r-y*y);//当前点与x轴的左交点            point[i].r=x+sqrt(r*r-y*y);//当前点与x轴的右交点            if(y>r||y<0||r<=0)//列举出三种无法覆盖的情况                ans=-1;        }        sort(point,point+n,cmp);//排序        t=point[0].r;//令初始值为位置最小岛屿的右交点        for(i=1;i<n&&ans!=-1;i++)        {            if(point[i].l>t)            {                ans++;                t=point[i].r;            }           if(point[i].r<t)                {                    t=point[i].r;                }        }        printf("Case %d: %d\n",cnt++,ans);    }    return 0;}

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Radar installation (Greedy)