POJ 1328 - Radar Installation(贪心)
2016-10-09 21:02
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Radar Installation
Time Limit: 1000MS Memory Limit: 10000K
Total Submissions: 78169 Accepted: 17491
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
Source
题意:
给出N个点和雷达的搜索半径,求在x轴上最少分布多少个雷达.
解题思路:
对于每个点,找出能搜索到的雷达在x轴上的分布.那么就是一个区间选点问题.
数轴上有n个闭区间[ai,bi]。取尽量少的点,使得每个区间内都至少有一个点(不同区间内含的点可以是同一个)。
贪心策略:
按照b1<=b2<=b3…(b相同时按a从大到小)的方式排序排序,从前向后遍历,当遇到没有加入集合的区间时,选取这个区间的右端点b。
证明:
为了方便起见,如果区间i内已经有一个点被取到,我们称区间i被满足。
1、首先考虑区间包含的情况,当小区间被满足时大区间一定被满足。所以我们应当优先选取小区间中的点,从而使大区间不用考虑。
按照上面的方式排序后,如果出现区间包含的情况,小区间一定在大区间前面。所以此情况下我们会优先选择小区间。
则此情况下,贪心策略是正确的。
2、排除情况1后,一定有a1<=a2<=a3……。
AC代码:
Time Limit: 1000MS Memory Limit: 10000K
Total Submissions: 78169 Accepted: 17491
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
Source
题意:
给出N个点和雷达的搜索半径,求在x轴上最少分布多少个雷达.
解题思路:
对于每个点,找出能搜索到的雷达在x轴上的分布.那么就是一个区间选点问题.
数轴上有n个闭区间[ai,bi]。取尽量少的点,使得每个区间内都至少有一个点(不同区间内含的点可以是同一个)。
贪心策略:
按照b1<=b2<=b3…(b相同时按a从大到小)的方式排序排序,从前向后遍历,当遇到没有加入集合的区间时,选取这个区间的右端点b。
证明:
为了方便起见,如果区间i内已经有一个点被取到,我们称区间i被满足。
1、首先考虑区间包含的情况,当小区间被满足时大区间一定被满足。所以我们应当优先选取小区间中的点,从而使大区间不用考虑。
按照上面的方式排序后,如果出现区间包含的情况,小区间一定在大区间前面。所以此情况下我们会优先选择小区间。
则此情况下,贪心策略是正确的。
2、排除情况1后,一定有a1<=a2<=a3……。
AC代码:
#include<stdio.h> #include<math.h> #include<limits.h> #include<algorithm> using namespace std; struct node { double left; double right; }qdu[1000]; bool cmp1(node a,node b) { return a.left>b.left; } bool cmp2(node a,node b) { return a.right<b.right; } int main() { int n; double d; int flag = 1; while(~scanf("%d%lf",&n,&d),n||d) { int bf = 0; if(d<0) bf = 1; for(int i = 0;i < n;i++) { double x; double y; scanf("%lf%lf",&x,&y); if(y > d) bf = 1; qdu[i].left = x-sqrt(d*d-y*y); qdu[i].right = x+sqrt(d*d-y*y); } if(bf) { printf("Case %d: -1\n",flag++); continue; } sort(qdu,qdu+n,cmp1); sort(qdu,qdu+n,cmp2); int cnt = 0; double radar = INT_MIN; for(int i = 0;i < n;i++) { if(radar < qdu[i].left) { cnt++; radar = qdu[i].right; } } printf("Case %d: %d\n",flag++,cnt); } return 0; }
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