POJ1328——Radar Installation
2014-06-01 09:36
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Radar InstallationDescriptionAssume 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.InputThe 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
OutputFor 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
Sample Output
OutputFor 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 题目大意:x轴上可以放置雷达(放置位置可为小数),以放置位置为圆心,d为半径做圆来覆盖岛屿,输出最小的雷达数以覆盖所有的岛屿。无法覆盖输出-1。 解题思路:假设某个岛屿的坐标为(x,y),则在(x-sqrt(d*d-y*y),x+sqrt(d*d-y*y))范围内的雷达可以覆盖到此岛屿。 先求出各个岛屿的可覆盖雷达范围,在根据其区间左端点进行排序,再通过贪心确定需要的最少雷达数。 ps:当一个岛屿的纵坐标大于d时,不可能覆盖到,输出-1。 ps2:进行贪心时,设置一个变量tmpr=p[1].r。 当p[i].r<tmpr时,tmpr=p[i].r 否则p[i]点会漏掉。 当p[i].l>tmpr是,tmpr=p[i].r,cnt++ Code:
#include<cstdio> #include<cmath> #include<algorithm> using namespace std; struct point { double x,y; double l,r; } p[100000]; bool cmp(struct point a,struct point b) { return a.l<b.l; } int main() { double m,d,tmpr; int i,n,ok,cnt,times=0; while (scanf("%d %lf",&n,&d)!=EOF) { times++; ok=1; if (n==0&&d==0) break; for (i=1; i<=n; i++) { scanf("%lf %lf",&p[i].x,&p[i].y); if (p[i].y>d) ok=0; p[i].l=p[i].x-sqrt(d*d-p[i].y*p[i].y); p[i].r=p[i].x+sqrt(d*d-p[i].y*p[i].y); } if (ok) { sort(p+1,p+n+1,cmp); tmpr=p[1].r; cnt=1; for (i=2; i<=n; i++) { if (p[i].l>tmpr) tmpr=p[i].r,cnt++; if (p[i].r<tmpr) tmpr=p[i].r; } printf("Case %d: %d\n",times,cnt); } else printf("Case %d: -1\n",times); } return 0; }
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