AYITACM2016省赛第二周(dp+其他) A-雷达装置(区间选点问题)
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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
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
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
分析:
计算至少需要多少个雷达,可以覆盖这条小路,因为累的的覆盖区域是圆形,所以要想完全覆盖,就要找到内接四边形的长,半径大于长,选取合适的点!
#include<stdio.h>#include<math.h>#include<algorithm>using namespace std;struct S{ double a,b;} s[1010];double cmp( S x,S y){ return x.b<y.b;}int main(){ int i,n,k=1,f,v; double j,x,y,m; while(scanf("%d %lf",&n,&m)&&m+n) { f=0; for(i=0; i<n; i++) { scanf("%lf%lf",&x,&y); if(y>m||y<-m) //如果y坐标大于雷达半径,说明覆盖不到 f=1; s[i].a=x-sqrt(m*m-y*y);//通过三角形公式转化为区间 s[i].b=x+sqrt(m*m-y*y); } sort(s,s+n,cmp); v=1,j=s[0].b; for(i=1; i<n; i++) if(s[i].a>j) //如果左端点大于前一个的右端点,说明需要增加雷达 { v++; j=s[i].b; } if(f==1) { v=-1; f=0; } printf("Case %d: %d\n",k++,v); } return 0;}
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