POJ1328解题报告 (贪心)

Radar Installation
Time Limit: 1000MS Memory Limit: 10000K
Total Submissions: 87836 Accepted: 19690
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

解题思路：
找到以该岛屿为圆心的圆与x轴交点所在的区间。
我们就可以计算出所有岛屿的雷达所在的区间，得到一个区间数组。

我们将这个数组按照区间左部分进行排序，那么重叠部分就表明这些岛屿的雷达可以共用一个。从而计算出最终解。
AC代码

import java.util.Arrays;import java.util.Comparator;import java.util.Scanner;public class Main {    /**     * @param args     */    static Main poj=new Main();    static Node[] node;    static Region region[];    static int n,d;    class Node{        int begin;        int end;    }    class Region{        double x,y;    }    class cmp implements Comparator<Region>{        @Override        public int compare(Region o1, Region o2) {            // TODO Auto-generated method stub            if(o1.x>o2.x){                return 1;            }else if(o1.x<o2.x){                return -1;            }else{                return 0;            }        }    }    public static void main(String[] args) {        // TODO Auto-generated method stub        Scanner scan=new Scanner(System.in);        int t=1;        while(scan.hasNext()){            n=scan.nextInt();            d=scan.nextInt();            if(n==0&&d==0){                break;            }            node=new Node[n];            region=new Region[n];            for(int i=0;i<n;i++){                node[i]=poj.new Node();                node[i].begin=scan.nextInt();                node[i].end=scan.nextInt();            }                        int min = calMin();            System.out.println("Case "+t+": "+min);            t++;            scan.nextLine();        }    }    private static int calMin() {        // TODO Auto-generated method stub        int t=0;        for(int i=0;i<n;i++){//计算每个岛屿在横坐标的区域            Node ss=node[i];            if(ss.end<0||ss.end>d||d<0){                return -1;            }            double x=Math.sqrt(Math.pow(d, 2)-Math.pow(ss.end, 2));            region[t]=poj.new Region();            region[t].x=ss.begin-x;            region[t].y=ss.begin+x;            t++;        }        //排序        Arrays.sort(region,0,t,poj.new cmp());        int num = 0;          double right = -1;        for(int i=0;i<t;i++){            Region s=region[i];            if(i==0){                num++;                right=s.y;            }            else{                if(s.x<=right){                    if(s.y<right){                        right=s.y;                    }                }else{                    num++;                    right=s.y;                }            }        }        return num;    }}