POJ 1328 Radar Installation 贪心
2014-07-15 13:12
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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
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
Sample Output
题意 :有n个小岛 并给出海岸线上雷达覆盖的半径d,雷达只能放置于海岸线上(x轴),给出每个小岛的坐标,问至少要多少个雷达才能把小岛全部覆盖。
代码:
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 <p>Case 2: 1</p>
题意 :有n个小岛 并给出海岸线上雷达覆盖的半径d,雷达只能放置于海岸线上(x轴),给出每个小岛的坐标,问至少要多少个雷达才能把小岛全部覆盖。
代码:
#include<iostream> #include<cstdio> #include<cmath> #include<algorithm> using namespace std; struct node{ double l,r; }q[1002]; bool cmp(node a,node b) { return a.r<b.r; } int main() { int m,n,a,b,i,t,k=0,s; while(cin>>m>>n) { k++; t=0; if(m==0&&n==0) break; s=1; for(i=0;i<m;i++) { cin>>a>>b; if(b>n) //如果某岛y值大于半径 一定不能覆盖 t=1; q[i].l=a-sqrt((double)n*n-b*b); q[i].r=a+sqrt((double)n*n-b*b); //求出每个岛要被覆盖 能放置的雷达区域 } if(t==1) { cout<<"Case "<<k<<": -1"<<endl; continue; } sort(q,q+m,cmp); //关于右端排序 double ld=q[0].r; for(i=1;i<m;i++) { if(q[i].l>ld) { s++; ld=q[i].r; } else if(q[i].r<ld) ld=q[i].r; } cout<<"Case "<<k<<": "<<s<<endl; } return 0; }
将每个小岛的能安置的雷达区间求出来,然后对每个区间的右端点按从小到大排序,将第一个雷达放在第一个区间的右端点,然后对下一个区间进行判断: 1.如果下一个区间的左端点在雷达的右边,那么雷达一定不能覆盖到下一个岛屿,雷达数加1,将新雷达放置在下一个区间的右端点 2.如果下一个区间的右端点在雷达的左边,那么雷达能够覆盖,将雷达放置到下一个区间的右端点 3.如果下一个区间的左端点在雷达的左边,右端点在雷达的右边,即两个区间相交,那么雷达能覆盖下一个岛屿,雷达位置不变 注意用double处理
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